Q JEE MAIN 2021 S2

Which of the following is the negation of the statement "for all $M>0$, there exists $x \in S$ such that...

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Statement I: Two forces $(\vec{P}+\vec{Q})$ and $(\vec{P}-\vec{Q})$ where $(\vec{P} \perp \vec{Q})$, when act at an angle $\theta_1$ to each other,...

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A ray of light AO in vacuum is incident on a glass slab at angle $60^{\circ}$ and refracted at angle...

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Two coaxial discs, having moments of inertia $I_1$ and $\frac{1}{2}$, are rotating with respective angular velocities $\omega_1$ and $\frac{\omega_1}{2}$ about...

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If $\lim _{x \rightarrow \infty}\left(\sqrt{x^2-x+1}-a x\right)=b$, then the ordered pair $(a b)$ is :

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The value of the inkegral $\int_0^1 \frac{\sqrt{x} d x}{(1+x)(1+3 x)(3+x)}$ is :

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If $0

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Two poles, $A B$ of length a metres and $C D$ of length $a+b(b \neq a)$ metres are erected at...

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If $y(x)=\cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right), x \in\left(\frac{\pi}{2}, \pi\right)$, then $\frac{d y}{d x}$ at $x=\frac{5 \pi}{6}$ is :

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Q JEE MAIN_2021_

The area of the region bounded by the parabola $(y-2)^2=(x-1)$, the tangent to it at the point whose ordinate is...

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Q JEE MAIN_2021_

Let $\mathbb{N}$ be the set of all integers, $$ \begin{aligned} & A=\left\{(x, y) \in \mathbb{Z} \times \mathbb{Z}:(x-2)^2+y^2 \leq 4\right\} \\...

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The Boolean expression $(p \wedge q) \Rightarrow((r \wedge q) \wedge p)$ is equivalent to $i$

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A box open from top is made from a rectangular sheet of dimension a × b by cutting squares each...

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The set of all values of $k>-1$, for which the equation $...

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Let [ $\lambda$ ] be the greatest integer less than or equal to $\lambda$. The set of all values of...

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Let $A(a, 0), B(b, 2 b+1)$ and $C(0, b), b \neq 0,|b| \neq 1$, be points such that the area...

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Q JEE MAIN_2021_

If the solution curve of the differential equation $\left(2 x-10 y^3\right) d y+y d x=0$, passes through the points $(0,1)$...

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Q JEE MAIN_2021_

The equation of the plane passing through the line of intersection of the planes $\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=1$ and $...

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If two tangents drawn from a point $P$ to the parabola $y^2=16(x-3)$ are at right angles, then the locus of...

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A differential equation representing the family of parabolas with axis parallel to y-axis and whose length of latus rectum is...

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Each of the persons A and B independently tosses three fair coins. The probability that both of them get the...

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Q JEE MAIN 2020

If the system of equations $$ \begin{aligned} & x+y+z=2 \\ & 2 x+4 y-z=6 \\ & 3 x+2 y+\lambda z=\mu...

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Q JEE Main 2021

Let $f(x)$ be a cubic polynomial with $f(1)=-10, f(-1)=6$, and has a local_minima at $x=1$, and $f^{\prime}(x)$ has a local...

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Let $B$ be the centre of the circle $x^2+y^2-2 x+4 y+1=0$. Let the tangents at two point $P$ and $Q$...

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If the line $y=m x$ bisects the area enclosed by the lines $x=0, y=0, x=3 / 2$ and the curve...

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The number of elements in the set $\left\{A=\left(\begin{array}{ll}a & b \\ 0 & d\end{array}\right): a, b, d \in\{-1,0,1\}\right.$ and $\left.(I-A)^3=I-A^3\right\}$...

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If $S=\frac{7}{5}+\frac{9}{5^2}+\frac{13}{5^3}+\frac{19}{5^4}+\ldots$, then 160 S is equal to $\_\_\_\_$ .

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A tangent line L is drawn at the point $(2,-4)$ on the parabola $\mathrm{y}^2=8 \mathrm{x}$. If the line L is...

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Q JEE Main 2021

If $...

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Q JEE MAIN 2021

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that...

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If $\left(\frac{3^6}{4^4}\right) k$ is the term, independent of x , in the binomial expansion of $\left(\frac{x}{4}-\frac{12}{x^2}\right)^{12}$, then k is equal...

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Q JEE MAIN 2019

Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm,...

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Q JEE Main 2021

The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is ______.

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If $x \phi(\mathrm{x})=\int_5^x\left(3 t^2-2 \phi^{\prime}(\mathrm{t})\right) d t, x>-2$, and $\phi(0)=4$, then $\phi(2)$ is

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Q JEE MAIN 2021

The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so...

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If the variable line $3 x+4 y=\alpha$ lies between the two circles $(x-1)^2+(y-1)^2=1$ and $(x-9)^2+(y-1)^2=4$, without intercepting a chord on...

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If the coefficient of $a^7 b^8$ in the expansion of $(a+2 b+4 a b)^{10}$ is $K .2^{16}$, then $K$ is...

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The mean of 10 numbers $$ 7 \times 8,10 \times 10,13 \times 12,16 \times 14, \ldots . \text { is...

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The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then...

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If ' $R$ ' is the least value of ' $a$ ' such that the function $f(x)=x^2+a x+1$ is increasing...

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Q JEE MAIN 2019

The pressure wave, P = 0.01sin $[1000 t-3 \times] \mathrm{Nm}^{-2}$ , corresponds to the sound produced by a vibrating blade...

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The square of the distance of the point of intersection of the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+1}{6}$ and the plane $2 x-y+z=6$ from...

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A point $Z$ moves in the complex plane such that arg $\left(\frac{z-2}{z+2}\right)-\frac{\pi}{4}$, then the minimum value of $|Z-9 \sqrt{2}-2 \mathrm{i}|^2$...

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Q JEE MAIN 2021

Let $[\mathrm{t}]$ denote the greatest integer $\leq 1$. Then the value of 8 . $\int_{-\frac{1}{2}}^1([2 x]|\mathrm{x}|) d x$ is

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Q JEE MAIN 2019

A moving coil galvanometer has resistance $50 \Omega$ and it indicates full deflection at 4 mA current. A voltmeter is...

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Q JEE Main 2021

If $[x]$ is the greatest integer $\leq x$, then $\pi^2 \int_0^2\left(\sin \frac{\pi x}{2}\right)(x-[x]) \quad d x$ is equal to :

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Let $f$ be any continuous function on $[0,2]$ and twice differentiable on $(0,2)$. If $f(0)=0, f(1)=1$ and $f(2)=2$, then

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Q JEE MAIN 2021

The line $12 x \cos \theta+5 y \sin \theta=60$ is tangent to which of the following curves?

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Q JEE MAIN 2019

A solid sphere of mass ‘M’ and radius ‘a’ is surrounded by a uniform concentric spherical shell of thickness 2a...

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If $a_r=\cos \frac{2 r \pi}{9}+i \sin \frac{2 r \pi}{9}, r=1,2,3, \ldots, \mathrm{i}=\sqrt{-1}$ then the determinant $...

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Q JEE MAIN 2021

A vertical pole fixed to the horizontal ground is divided in the ratio 3 : 7 by a mark on...

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Q JEE MAIN 2019

A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror...

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Following figure shows two processes A and B for a gas. If $\Delta Q_A$ and $\Delta Q_B$ are the amount...

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A circular coil has moment of inertia $0.8 \mathrm{~kg} \mathrm{~m}^2$ around any diameter and is carrying current to produce a...

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A capacitor with capacitance 5$\mu \mathrm{F}$ is charged to 5$\mu \mathrm{C}$. If the plates are pulled apart to reduce the...

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Q JEE MAIN 2021

$\lim _{x \rightarrow 0} \frac{\sin ^2\left(\pi \cos ^4 x\right)}{x^4}$ is equal to:

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For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127°C. At 2...

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If $\frac{d y}{d x}=\frac{2^{x+y}-2^x}{2 y}, \mathrm{y}(0)=1$, then $\mathrm{y}(1)$ is equal to :

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Q JEE MAIN 2019

The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by...

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A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous...

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If the function $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}\frac{1}{x} \log _e\left(\frac{1+\frac{a}{x}}{1-\frac{x}{b}}\right) & , x0\end{array}\right.$ Is continuous at $\mathrm{x}=0$, then $\frac{1}{a}+\frac{1}{b}+\frac{4}{k}$ is equal to :

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A rectangular coil (Dimension 5 cm × 2.5 cm) with 100 turns, carrying a current of 3 A in the...

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A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance...

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The length of the latus rectum of a parabola, whose vertex and focus are on the positive $x$-axis at a...

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Data given for the following reaction is as follows:

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The number of solutions of the equation $32^{\tan ^2 x}+32^{x c^2 x}=81,0 \leq x \leq \frac{\pi}{4}$ is :

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If the following system of linear equations $...

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The number of species having non–pyramidal shape among the following is

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Let A be the set of all points $(\alpha, \beta)$ such that the area of triangle formed by the points...

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cosec18º is a root of the equation :

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If $p$ and $q$ are the lengths of the perpendiculars from the origin on the lines, $...

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Let $a_1, a_2, a 3, \ldots$ be an A.P. If $\frac{a_1+a_2+\ldots+a_{10}}{a_1+a_2+\ldots+a_p}=\frac{100}{p^2}, p \neq 10$, then $\frac{a_{11}}{a_{10}}$ is equal to :

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When 5.1 g of solid $\mathrm{NH}_4 \mathrm{HS}$ is introduced into a two litre evacuated flask at $27^{\circ} \mathrm{C}, 20 \%$...

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The integral $\int \frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}} d x$ is equal to :

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If $z$ is a complex number such that $\frac{z-1}{z-1}$ is purely imaginary, then the minimum value of $|z-(3+3 i)|$ is...

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The number of photons emitted by a monochromatic (single frequency) infrared range finder of power 1 mW and wavelength of...

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A uniform cable of mass ‘M’ and length ‘L’ is placed on a horizontal surface such that its $\left(\frac{1}{n}\right)^{t h}$...

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The resistance of a conductivity cell with cell constant $1.14 \mathrm{~cm}^{-1}$, containing 0.001 M KCl at 298 K is $...

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\text { The sum of the roots of the equation } x+1-2 \log _2\left(3+2^x\right)+2 \log _4\left(10-2^{-x}\right)=0 \text {, is: }

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40 g of glucose (Molar mass $=180$ ) is mixed with 200 mL of water. The freezing point of solution...

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Which of the following is not correct for relation R on the set of real numbers ?

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If $y \frac{d y}{d x}=x\left|\frac{y^2}{x^2}+\frac{\phi\left(\frac{y^2}{x^2}\right)}{\phi^{\prime}\left(\frac{y^2}{x^2}\right)}\right|, x>0, \phi>0$, and $y(1)=-1$, then $\phi\left(\frac{y^2}{4}\right)$ is equal to :

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100 g of propane is completely reacted with 1000 g of oxygen. The mole fraction of carbon dioxide in the...

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The stream of a river is flowing with a speed of 2 km/h. A swimmer can swim at a speed...

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In which one of the following sets all species show disproportionation reaction ?

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Two flasks I and II shown below are connected by a valve of negligible volume. When the valve is opened,...

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A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic...

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A chloro compound "A". (i) forms aldehydes on ozonolysis followed by the hydrolysis. (ii) when vaporized completely 1.53 g of...

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The reaction rate for the reaction| $$ \left[\mathrm{PtCl}_4\right]^{2-}+\mathrm{H}_2 \mathrm{O} \rightleftharpoons\left[\mathrm{Pt}\left(\mathrm{H}_2 \mathrm{O}\right) \mathrm{Cl}_3\right]^{-}+\mathrm{Cl}^{-} $$ was measured as a function of concentrations...

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The number of optical isomers possible for $\left[\mathrm{Cr}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$ is

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The magnetic field of a plane electromagnetic wave is given by : $\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{B}}_0 \hat{\mathrm{i}}\left[\cos (\mathrm{kz}-\omega \mathrm{t})+\mathrm{B}_1 \hat{\mathrm{j}} \cos (\mathrm{kz}+\omega \mathrm{t})\right.$...

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SECTION-B The first order rate constant for the decomposition of $\mathrm{CaCO}_3$ at 700 K is $6.36 \times 10^{-3} \mathrm{~s}^{-1}$ and...

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83 g of ethylene glycol dissolved in 625 g of water. The freezing point of the solution is _______K. (Nearest...

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The transformation occurring in Duma's method is given below :

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Q JEE MAIN 2019

Determine the charge on the capacitor in the following circuit :

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The overall stability constant of the complex ion $\left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\right]^{2+}$ is $2.1 \times 10^{13}$. The overall dissociations constant is $...

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The correct structures of A and B formed in the following reactions are

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100 mL of $\mathrm{Na}_3 \mathrm{PO}_4$ solution contains 3.45 g of sodium. The molarity of the solution is $\_\_\_\_$ $...

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For the galvanic cell $$ \mathrm{Zn}(\mathrm{~s})+\mathrm{Cu}^{2+}(0.02 \mathrm{M}) \rightarrow \mathrm{Zn}^{2+}(0.04 \mathrm{M})+\mathrm{Cu}(\mathrm{~s}) $$ $\mathrm{E}_{\text {cell }}=$ $\_\_\_\_$ $\times 10^{-2} \mathrm{~V}$. (Nearest integer)...

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Which one of the following is formed (mainly) when red phosphorus is heated in a sealed tube at 803 K...

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$$ \text { According to molecular orbital theory, the number of unpaired electron(s) in } \mathrm{O}_2^{2-} \text { is :...

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Sodium oxide reacts with water to produce sodium hydroxide. 20.0 g of sodium oxide is dissolved in 500 mL of...

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A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for photoelectric current is $...

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Hydrolysis of sucrose gives

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For water $\Delta_{\text {vap }} \mathrm{H}=41 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at 373 K and 1 bar pressure. Assuming that water vapour is...

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For the reaction $\mathrm{A} \rightarrow \mathrm{B}$, the rate constant $\mathrm{k}\left(\right.$ in $\left.\mathrm{s}^{-1}\right)$ is given by $$ \log _{10} k=20.35-\frac{\left(2.47 \times...

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If the concentration of glucose $\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6\right)$ in blood is 0.72 g $L^{-1}$, the molarity of glucose in blood...

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The equilibrium constant Kc at 298 K for the reaction $\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}$ is 100 . Starting with an equimolar...

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In the above first order reaction the initial concentration of $\mathrm{N}_2 \mathrm{O}_5$ is $2.40 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1}$ at 318...

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The pH of a solution obtained by mixing 50 mL of 1 M HCl and 30 mL of 1 M...

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Which one of the following tests used for the identification of functional groups in organic compounds does not use copper...

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Number of electrons that Vanadium (Z = 23) has in p-orbitals is equal to ______

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In the sulphur estimation, 0.471 g of an organic compound gave 1.44 g of barium sulphate. The percentage of sulphur...

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A copper complex crystallising in a CCP lattice with a cell edge of 0.4518 nm has been revealed by employing...

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Consider the given reaction, the product A is :

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Consider the given reaction, Identify 'X' and 'Y'

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An aqueous KCl solution of density $1.20 \mathrm{~g} \mathrm{~mL}^{-1}$ has a molality of $3.30 \mathrm{~mol} \mathrm{~kg}^{-1}$. The molarity of the...

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The total number of negative charge in the tetrapeptide, Gly-Glu-Asp-Tyr, at pH 12.5 will be ________. (Integer answer)

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The number of stereoisomers possible for 1,2- dimethyl cyclopropane is :

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The Born-Haber cycle for KCl is evaluated with the following data: $...

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If the standard molar enthalpy change for combustion of graphite powder is $-2.48 \times 10^2 \mathrm{~kJ} \mathrm{~mol}^{-1}$ , the amount...

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The following data was obtained for chemical reaction given below at 975 K . $...

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The ratio of number of water molecules in Mohr's salt and potash alum is $\_\_\_\_$ $\times 10^{-1}$. (Integer answer)

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The number of 4f electrons in the ground state electronic configuration of Gd2+ is ________. [Atomic number of Gd =...

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The $\mathrm{OH}^{-}$concentration in a mixture of 5.0 mL of $0.0504 \mathrm{M} \mathrm{NH}_4 \mathrm{Cl}$ and 2 mL of $0.0210 \mathrm{MNH}_3$ solution...

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Of the following four aqueous solutions, total number of those solutions whose freezing point is lower than that of $...

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These are physical properties of an element (A) Sublimation enthalpy (B) Ionisation enthalpy (C) Hydration enthalpy (D) Electron gain enthalpy...

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$\mathrm{AB}_3$ is an interhalogen T-shaped molecule. The number of lone pairs of electrons on A is $\_\_\_\_$ (Integer answer)

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If $\frac{d y}{d x}=\frac{2^x y+2^y \cdot 2^x}{2^x+2^{x+y} \log _e 2}, y(0)$, then for $y=1$, the value of $x$ lies in...

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The locus of mid-points of the line segments joining $(-3,-5)$ and the points on the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ is :

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Three numbers are in an increasing geometric progression with common ratio $r$. If the middle number is doubled, then the...

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If $\alpha=\lim _{x \rightarrow \pi / 4} \frac{\tan ^3 x-\tan x}{\cos \left(x+\frac{\pi}{4}\right)}$ and $\beta=\lim _{x \rightarrow 0}(\cos x)^{\cot x}$ are...

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The function $f(x)=\left|x^2-2 x-3\right| . e^{\left|9 x^2-12 x+4\right|}$ is not differentiable at exactly:

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Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|2 \vec{a}+3 \vec{b}|=|3 \vec{a}+\vec{b}|$ and the angle between $\vec{a}$ and $\vec{b}$...

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Negation of the statement $(p \vee r) \Rightarrow(q \vee r)$ is :

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Let f be a non - negative function in $[0,1]$ and twice differentiable in $(0,1)$. If $...

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The distance of the point $(-1,2,-2)$ from the line of intersection of the planes $2 x+3 y+2 z=0$ and $...

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Let the equation of the plane, that passes through the point $(1,4,-3)$ and contains the line of intersection of the...

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The sum of 10 terms of the series $\frac{3}{1^2 \times 2^2}+\frac{5}{2^2 \times 3^2}+\frac{7}{3^2 \times 4^2}+\ldots$ is :

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Let $f: N \rightarrow N$ be a function such that $f(m+n)=f(m)+f(n)$ for every $m, n \in N$. If $f(6)=18$, then...

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The number of real roots of the equation $\mathrm{e}^{4 \mathrm{x}}+2 \mathrm{e}^{3 \mathrm{x}}-\mathrm{e}^{\mathrm{x}}-6=0$ is :

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Let $S=\{1,2,3,4,5,6\}$. Then the probability that a randomly chosen onto function $g$ from $S$ to $S$ satisfies $g(3) =2 g(1)$...

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Let *, □ $\in\{\wedge, \vee\}$ be such that the Boolean expression $\left(\mathrm{p}^* \sim q\right) \Rightarrow(\mathrm{p}$ □ q) is a tautology....

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The domain of the function $f(x)=\sin ^{-1}\left(\frac{3 x^2+x-1}{(x-1)^2}\right)+\cos ^{-1}\left(\frac{x-1}{x+1}\right)$ is :

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A wire of length 20 m is to be cut into two pieces. One of the pieces is to be...

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If $\int_6^{16} \frac{\log _e x^2}{\log _e x^2+\log _e\left(x^2-44 x+484\right)} d x$ is equal to :

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Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors mutually perpendicular to each other and have same magnitude. If a vector $\vec{r}$...

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If $\alpha+\beta+\gamma=2 \pi$, then the system of equations $$ \begin{aligned} & x+(\cos \gamma) y+(\cos \beta) z=0 \\ & (\cos \gamma)...

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If $x^2+9 y^2-4 x+3=0, x, y \in \mathbb{R}$, then $x$ and $y$ respectively lie in the intervals:

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When a certain biased die is rolled, a particular face occurs with probability $\frac{1}{6}-x$ and its opposite face occurs with...

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If $\alpha, \beta$ are the distinct roots of $x^2+b x+c=0$, then $\lim _{x \rightarrow \beta} \frac{e^{2\left(x^2+b x+c\right)}-1-2\left(x^2+b x+c\right)}{(x-\beta)^2}$ is equal...

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Let $\frac{\sin A}{\sin B}=\frac{\sin (A-C)}{\sin (C-B)}$, where $A, B, C$ are angles of a triangle $A B C$. If the...

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A tangent and a normal are drawn at the point $\mathrm{P}(2,-4)$ on the parabola $\mathrm{y}^2=8 \mathrm{x}$, which meet the directrix...

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Q JEE MAIN 2021

$\sum_{\mathrm{k}=0}^{20}{ }^{20} \mathrm{C}_{\mathrm{k}} \cdot{ }^{20} \mathrm{C}_{20-\mathrm{k}}$ is equal to :

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Q JEE MAIN 2021

Let us consider a curve, $y=f(x)$ passing through the point $(-2,2)$ and the slope of the tangent to the curve...

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The statement $(p \wedge(p \rightarrow q) \wedge(q \rightarrow r)) \rightarrow r$ is :

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If $U_n=\left(1+\frac{1}{n^2}\right)\left(1+\frac{2^2}{n^2}\right)^2 \cdots\left(1+\frac{n^2}{n^2}\right)^n$, then $\lim _{n \rightarrow \infty}\left(U_n\right)^{n^{\frac{-4}{2}}}$ is equal to :

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Equation of a plane at a distance $\sqrt{\frac{2}{21}}$ from the origin, which contains the line of intersection of the planes...

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Q JEE Main 2021

Let $a, b \in R, b \neq 0$, Define a function $...

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Q JEE Main 2021

The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of...

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If $y=y(x)$ is an implicit function of $x$ such that $\log _e(x+y)=4 x y$, then $\frac{d^2 y}{d x^2}$ at $x=0$...

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Q JEE MAIN 2021

Let y=y(x) be the solution of the differential equation $\frac{d y}{d x}=2(y+2 \sin x-5) x-2 \cos x$ such that $y(0)=7$....

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Q JEE MAIN 2021

In the electrolytic refining of blister copper, the total number of main impurities, from the following, removed as anode mud...

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Q JEE Main 2021

The locus of a point, which moves such that the sum of squares of its distances from the points $(0,0),(1,0)$,...

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If $S=\left\{z \in \mathbb{C}: \frac{z-i}{z+2 i} \in \mathbb{R}\right\}$, then:

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The area of the region $S=\left\{(x, y): 3 x^2 \leq 4 y \leq 6 x+24\right\}$ is $\_\_\_\_$ .

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The empirical formula for a compound with a cubic close packed arrangement of anions and with cations occupying all the...

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The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel...

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Q JEE Main 2021

A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a...

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If the matrix $A=\left[\begin{array}{cc}0 & 2 \\ k & -1\end{array}\right]$ satisfies $A\left(A^3+3 I\right)=2 I$, then the value of $K$ is...

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Q JEE MAIN 2021

Potassium permanganate on heating at 513 K gives a product which is

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If ${ }^1 \mathrm{P}_1+2 \cdot{ }^2 \mathrm{P}_2+3 \cdot{ }^3 \mathrm{P}_3+\ldots+15 \cdot{ }^{15} \mathrm{P}_{15}={ }^9 \mathrm{P}_{\mathrm{r}}-\mathrm{s}, 0 \leq \mathrm{s} \leq 1$,...

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Q JEE MAIN 2021

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Q JEE Main 2021

Let the line $L$ be the projection of the line $\frac{x-1}{2}=\frac{y-3}{1}=\frac{z-4}{2}$ in the plane $x-2 y-z=3$. If $d$ is the...

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Q JEE MAIN 2021

The major product of the following reaction, if it occurs by $\mathrm{SN}_2$ mechanism is

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1.22 g of an organic acid is separately dissolved in 100 g of benzene $\left(\mathrm{K}_{\mathrm{b}}=2.6 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$ and 100...

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Q JEE Main 2021

The sum of all integral values of $k(k \neq 0)$ for which the equation $\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}$ in $x$ has no real...

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Q JEE MAIN 2021

Let A be a fixed point (0, 6) and B be a moving point (2t, 0), Let M be the...

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Lyophilic sols are more stable than lyophobic sols because

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$\mathrm{CH}_4$ is adsorbed on 1 g charcoal at $0^{\circ} \mathrm{C}$ following the Freundlich adsorption isotherm. 10.0 mL of $\mathrm{CH}_4$ is...

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Q JEE MAIN 2021

If for $x, y \in R, x>0$, $y=\log _{10} x+\log _{10} x^{1 / 3}+\log _{10} x^{1 / 9}+\ldots \ldots$ upto...

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Q JEE Main 2021

Let $z=\frac{1-i \sqrt{3}}{2}, i=\sqrt{-1}$. Then the value of $21+\left(z+\frac{1}{z}\right)^3+\left(z^2+\frac{1}{z^2}\right)^3+\left(z^3+\frac{1}{z^3}\right)^3+\ldots+\left(z^{21}+\frac{1}{z^{21}}\right)^3$ is $\_\_\_\_$ .

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Q JEE Main 2021

If the truth value of the Boolean expression $((p \vee q) \wedge(q \rightarrow r) \wedge(\sim r)) \rightarrow(p \wedge q)$ is...

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Q JEE MAIN 2021

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Q JEE MAIN 2021

Which one of the following is used to remove most of plutonium from spent nuclear fuel

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The number of S=O bonds present in sulphurous acid, peroxodisulphuric acid and pyrosulphuric acid, respectively are :

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Let $A B C$ be a triangle with $A(-3,1)$ and $\angle A C B=\theta, 0

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The value of $\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=0}^{2 n-1} \frac{n^2}{n^2 4 r^2}$ is:

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Q JEE MAIN 2021

Identify correct A, B and C in the reaction sequence given below :

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If $y^{1 / 4}+y^{-1 / 4}=2 x$, and $\left(x^2-1\right) \frac{d^2 y}{d x^2}+\alpha x \frac{d y}{d t}+\beta y=0$, then $|\alpha-\beta|$ is...

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If the sum of an infinite GP a, ar, $a r^2, a r^3, \ldots$ is 15 and the sum of...

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Q JEE MAIN 2021

A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is...

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Q JEE MAIN 2021

For the following :

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The major product (A) formed in the reaction given below is

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If $A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{ll}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}$, and $Q=A^{\top} B A$,...

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If the minimum area of the triangle formed by a tangent to the ellipse $\frac{x^2}{b^2}+\frac{y^2}{4 a^2}=1$ and the co-ordinate axis...

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Excess of isobutane on reaction with $\mathrm{Br}_2$ in presence of light at $125^{\circ} \mathrm{C}$ gives which one of the following,...

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The major product of the following reaction is :

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The value of $\int_{\frac{-1}{\sqrt{2}}}^{\frac{1}{\sqrt{2}}}\left(\left(\frac{x+1}{x-1}\right)^2+\left(\frac{x-1}{x+1}\right)^2-2\right)^{\frac{1}{2}} d x$ is

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Q JEE MAIN 2021

Let n be an odd natural number such that the variance of 1, 2, 3, 4, ...., n is 14....

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If the system of linear equations $$ \begin{aligned} & 2 x+y-z=3 \\ & x-y-z=\alpha \\ & 3 x+3 y+\beta z=3...

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Q JEE MAIN 2021

Match List-I with List-II :

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If a line along a chord of the circle $4 x^2+4 y^2+120 x+675=0$, passes through the point $(-30,0)$ and is...

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If $\int \frac{d x}{\left(x^2+x+1\right)^2}=a \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+b\left(\frac{2 x+1}{x^2+x+1}\right)+C, x>0$ where $C$ is the constant of integration, then the value of...

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Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{j}-\hat{k}$. If $\vec{c}$ is a vector-such that $\vec{a} \times \vec{c}=\vec{b}$ and $\vec{a} \cdot \vec{c}=3$, then $...

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Q JEE MAIN 2021

Which among the following is not a polyester ?

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Which one of the following is the major product of the given reaction?

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Let $M$ and $m$ respectively be the maximum and minimum values of the function $f(x)=\tan ^{-1}(\sin x+\cos x)$ in $...

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Which one of the following statements is incorrect ?

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Let $A=\left(\begin{array}{ccc}{[x+1]} & {[x+2]} & {[x+3]} \\ {[x]} & {[x+3]} & {[x+3]} \\ {[x]} & {[x+2]} & {[x+4]}\end{array}\right)$, where $[t]$...

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Q JEE MAIN 2021

The incorrect statement is:

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Given below are two statements. Statement I: Frenkel defects are vacancy as well as interstitial defects. Statement II: Frenkel defect...

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If $A=\{x \in \mathbf{R}:|x-2|>1\}, B=\left\{x \in \mathbf{R}: \sqrt{x^2-3}>1\right\}, C=\{x \in \mathbf{R}:|x-4| \geq 2\}$ and $\mathbf{Z}$ is the set of all...

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The angle between the straight lines, whose direction cosines are given by the equations $2 \ell+2 \mathrm{~m}-\mathrm{n}=0$ and $...

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The equation arg $\left(\frac{z-1}{z+1}\right)=\frac{\pi}{4}$ represents a circle with:

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Let the equation $x^2+y^2+p x+(1-p) y+5=0$ represent circles of varying radius $r \in(0,5]$. Then the number of elements in the...

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The correct order of ionic radii for the ions, $\mathrm{P}^{3-}, \mathrm{S}^{2-}, \mathrm{Ca}^{2+}, \mathrm{K}^{+}, \mathrm{Cl}^{-}$is

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Let $S$ be the sum of all solutions (in radians) of the equation $...

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The correct sequential addition of reagents in the preparation of 3-nitrobenzoic acid from benzene is:

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The number of distinct real roots of the equation $3 x^4+4 x^3-12 x^2+4=0$ is $\_\_\_\_$ .

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Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are...

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Let $S$ be the mirror image of the point $Q(1,3,4)$ with respect to the plane $2 x-y+z+3=0$ and let $...

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Q JEE MAIN 2021

The incorrect expression among the following is:

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Let $\vec{a}=\hat{i}+5 \hat{j}+\alpha \hat{k}, \vec{b}=\hat{i}+3 \hat{j}+\beta \hat{k}$ and $\vec{c}=-\hat{i}+2 \hat{j}+3 \hat{k}$ be three vectors such that, $|\vec{b} \times \vec{c}|=5 \sqrt{3}$...

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Given below are two statements. Statement I: According to Bohr's model of an atom, qualitatively the magnitude of velocity of...

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If ${ }^{20} \mathrm{C}_{\mathrm{r}}$ is the co-efficient of $\mathrm{x}^{\mathrm{r}}$ in the expansion of $(1+\mathrm{x})^{20}$, then the value of $...

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Which one of the following reactions will not yield propionic acid?

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The probability distribution of random variable X is given by: Let $p=P(1

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The sum of the series $\frac{1}{x+1}+\frac{2}{x^2+1}+\frac{2^2}{x^4+1}+\ldots .+\frac{2^{100}}{x^{2^{100}}+1}$ when $x=2$ is

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The least positive integer n such that $\frac{(2 \mathrm{i})^{\mathrm{n}}}{(1-\mathrm{i})^{\mathrm{n}-2}}, \mathrm{i}=\sqrt{-1}$ is a positive integer, is

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Let A be a $3 \times 3$ real matrix. If $\operatorname{det}(2 \operatorname{Adj}(2 \operatorname{Adj}(\operatorname{Adj}(2 A))))=2^{41}$, then the value of $\operatorname{det}\left(A^2\right)$ equal...

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)....

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Let $z_1$ and $z_2$ be two complex numbers such that arg $\left(z_1-z_2\right)=\frac{\pi}{4}$ and $z_1, z_2$ satisfy the equation $|z-3|=$ $\operatorname{Re}(z)$....

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Let $f(x)=\cos \left(2 \tan ^{-1} \sin \left(\cos ^{-1} \sqrt{\frac{1-x}{x}}\right)\right) .0

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Let the mean and variance of four numbers $3,7, x$ and $y(x>y)$ be 5 and 10 respectively. Then the mean...

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Let $S=\{1,2,3,4,5,6,9\}$. Then the number of elements in the set $T=\{A \subseteq S ; A \neq f$ and the sum...

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Let $\lambda \neq 0$ be in R . If $\alpha$ and $\beta$ are the roots of the equation $\mathrm{x}^2-\mathrm{x}+2 \lambda=0$,...

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Let $\theta \in\left(0, \frac{\pi}{2}\right)$. If the system of linear equations $$ \begin{aligned} & \left(1+\cos ^2 \theta\right) x+\sin ^2 \theta y+4...

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Let $\binom{n}{k}$ denotes ${ }^n C_k$ and $...

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Let $\mathrm{A}(\sec \theta, 2 \tan \theta)$ and $\mathrm{B}(\sec \phi, 2 \tan \phi)$, where $\theta+\phi=\pi / 2$, be two points on...

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$$ \text { Spin only magnetic moment in } \mathrm{BM} \text { of }\left[\mathrm{Fe}(\mathrm{CO})_4\left(\mathrm{C}_2 \mathrm{O}_4\right)\right]^{+} \text {is : } $$

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Two circles each of radius 5 units touch each other at the point $(1,2)$. If the equation of their common...

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What are the products formed in sequence when excess of $\mathrm{CO}_2$ is passed in slaked lime?

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For the reaction given below :

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$3 \times 7^{22}+2 \times 10^{22}-44$ when divided by 18 leaves the remainder $\_\_\_\_$

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Given below are two statements. Statement I: The choice of reducing agents for metals extraction can be made by using...

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An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys...

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Which one of the following methods is most suitable for preparing deionized water?

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Among the following compounds I-IV, which one forms a yellow precipitate on reacting sequentially with (i) NaOH (ii) dil. $\mathrm{HNO}_3$...

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Which of the following is NOT an example of fibrous protein ?

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Given below are two statements. Statement I: In the titration between strong acid and weak base methyl orange is suitable...

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If $\int \frac{2 e^x+3 e^{-x}}{4 e^x+7 e^{-x}} d x=\frac{1}{14}\left(u x+v \log _e\left(4 e^x+7 e^{-x}\right)\right)+C$, where $C$ is a constant of...

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Match List-I with List-II

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The oxide that gives $\mathrm{H}_2 \mathrm{O}_2$ most readily on treatment with $\mathrm{H}_2 \mathrm{O}$ is

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The conversion of hydroxyapatite occurs due to presence of F– ions in water. The correct formula of hydroxyapatite is:

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Let $A$ and $B$ be independent events such that $P(A)=p, P(B)=2 p$. The largest value of $p$, for which $P$...

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Which one of the following chemicals is responsible for the production of HCl in the stomach leading to irritation and...

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Let $y=y(x)$ be a solution curve of the differential equation $...

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The compound/s which will show significant intermolecular H–bonding is/are

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On the ellipse $\frac{x^2}{8}+\frac{y^2}{4}=1$ let $P$ be a point in the second quadrant such that the tangent at $P$ to...

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The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by...

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The sum of solutions of the equation $\frac{\cos x}{1+\sin x}=|\tan 2 x|, x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)-\left\{\frac{\pi}{4}-\frac{\pi}{4}\right\}$ is :

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The correct options for the products A and B of the following reactions are :

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In stratosphere most of the ozone formation is assisted by :

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The $\mathrm{Eu}^{2+}$ ion is a strong reducing agent in spite of its ground state electronic configuration (outermost) : [Atomic number...

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Given below are two statements: Statement 1: The limiting molar conductivity of KCl (strong electrolyte) is higher compared to that...

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Arrange the following conformational isomers of n-butane in order of their increasing potential energy :

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Let $Q$ be the foot of the perpendicular from the point $P(7,-2,13)$ on the plane containing the lines $\frac{x+1}{6}=\frac{y-1}{7}=\frac{z-3}{8}$ and...

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The polymer formed on heating Novolac with formaldehyde is :

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Statement I : Ethyl pent- $4-$ yn-oate on reaction with $\mathrm{CH}_3 \mathrm{MgBr}$ gives a $3^{\circ}-$ alcohol. Statement II : In...

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The major product formed in the following reaction is :

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A resistor dissipates 192 J of energy in 1 s when a current of 4A is passed through it. Now,...

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Let $a_1, a_2 \ldots \ldots a_{10}$ be an AP with common difference -3 and $b_1, b_2 \ldots \ldots, b_{10}$ be...

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The major product formed in the following reaction is :

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If the projection of the vector $\hat{i}+2 \hat{j}+\hat{k}$ on the sum of the two vectors $2 \hat{i}+4 \hat{j}-5 \hat{k}$ and...

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Cross-section view of a prism is the equilateral triangle $A B C$ in the figure. The minimum deviation is observed...

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The addition of dilute NaOH to $\mathrm{Cr}^{3+}$ salt solution will give :

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For the cell $$ \mathrm{Cu}(\mathrm{~s})\left|\mathrm{Cu}^{2+}(\mathrm{aq})(0.1 \mathrm{M}) \| \mathrm{Ag}^{+}(\mathrm{aq})(0.01 \mathrm{M})\right| \mathrm{Ag}(\mathrm{~s}) $$ the cell potential $\mathrm{E}_1=0.3095 \mathrm{~V}$ For the cell $$...

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Let $a$ and $b$ respectively be the points of local maximum and local minimum of the function $...

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For the first order reaction $A \rightarrow 2 B, 1$ mole of reactlant $A$ gives 0.2 moles of $B$ after...

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The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1"...

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The major products formed in the following reaction sequence A and B are :

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When 10 mL of an aqueous solution of $\mathrm{KMnO}_4$ was titrated in acidic medium, equal volume of 0.1 M of...

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At very high frequencies, the effective impendance of the given circuit will be $\_\_\_\_$ $\Omega$.

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Choose the correct statement from the following

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The dihedral angle in staggered form of Newman projection of 1,1,1-Trichloro ethane is $\_\_\_\_$ degree. (Round off to the nearest...

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The number of moles of $\mathrm{NH}_3$, that must be added to 2 L of $0.80 \mathrm{M} \mathrm{AgNO}_3$ in order to...

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Which one of the following when dissolved in water gives coloured solution in nitrogen atmosphere?

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200 mL of 0.2 M HCl is mixed with 300 mL of 0.1 M NaOH . The molar heat of...

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Which one of the following compounds is not aromatic ?

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In a solvent 50\% of an acid HA dimerizes and the rest dissociates. The van't Hoff factor of the acid...

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A sample of gas with $\gamma=1.5$ is taken through an adiabatic process in which the volume is compressed from $...

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A peptide synthesized by the reactions of one molecule each of Glycine, Leucine, Aspartic acid and Histidine will have ________...

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Chalcogen group elements are :

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Which one of the following is correct for the adsorption of a gas at a given temperature on a solid...

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The number of f electrons in the ground state electronic configuration of Np (Z = 93) is ________. (Nearest integer)

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3 moles of metal complex with formula $\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_3$ gives 3 moles of silver chloride on treatment with excess of...

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The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the...

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The class of drug to which chlordiazepoxide with above structure belongs is :

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Which one of the following complexes is violet in colour?

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A car is moving on a plane inclined at $30^{\circ}$ to the horizontal with an acceleration of $10 \mathrm{~ms}^{-2}$ parallel...

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The total number of electrons in all bonding molecular orbitals of $\mathrm{O}_2^{2-}$ is $\_\_\_\_$ (Round off to the nearest integer)

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The number of moles of CuO , that will be utilized in Dumas method for estimation nitrogen in a sample...

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)....

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1 mol of an octahedral metal complex with formula $\mathrm{MCl}_3 \cdot 2 \mathrm{~L}$ on reaction with excess of $\mathrm{AgNO}_3$ gives...

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10.0 mL of $0.05 \mathrm{M} \mathrm{KMnO}_4$ solution was consumed in a titration with 10.0 mL of given oxalic acid dihydrate...

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1 kg of 0.75 molal aqueous solution of sucrose can be cooled up to $-4^{\circ} \mathrm{C}$ before freezing. The amount...

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In a Young's double slit experiment, the slits are separated by 0.3 mm and the screen is 1.5 m away...

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A capacitor of $50 \mu \mathrm{~F}$ is connected in a circuit as shown in figure. The charge on the upper...

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Given below are two statements : Statement I : Sphalerite is a sulphide ore of zinc and copper glance is...

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$$ 2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{SO}_3(\mathrm{~g}) $$ The above reaction is carried out in a vessel starting with partial pressure...

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The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to $...

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If the conductivity of mercury at $0^{\circ} \mathrm{C}$ is $1.07 \times 10^6 \mathrm{~S} \mathrm{~m}^{-1}$ and the resistance of a cell...

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The sol given below with negatively charged colloidal particles is :

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A particle is moving with constant acceleration ' $a$ '. Following graph shows $v^2$ versus $x$ (displacement) plot. The acceleration...

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When 400 mL of $0.2 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4$ solution is mixed with 600 mL of 0.1 M NaOH solution, the...

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The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood...

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The electric field in an electromagnetic wave is given by $\mathrm{E}=\left(50 \mathrm{NC}^{-1}\right) \sin \omega(\mathrm{t}-\mathrm{x} / \mathrm{c})$ The energy contained in...

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$\lim _{x \rightarrow 2}\left(\sum_{n=1}^9 \frac{x}{n(n+1) x^2+2(2 n+1) x+4}\right)$ is equal to :

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Indicate the complex/complex ion which did not show any geometrical isomerism :

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In Carius method for estimation of halogens, 0.2 g of an organic compound gave 0.188 g of AgBr . The...

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The equilibrium constant for the reaction $$ \mathrm{A}(\mathrm{~S}) \rightleftharpoons \mathrm{M}(\mathrm{~s})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) $$ is $\mathrm{K}_p=4$. At equilibrium, the partial pressure of...

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A long solenoid with $1000 \mathrm{turns} / \mathrm{m}$ has a core material with relative permeability 500 and volume $10^3 \mathrm{~cm}^3$....

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A circle $C$ touches the line $x=2 y$ at the point $(2,1)$ and intersects the circle $...

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Tyndall effect is more effectively shown by :

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The major product in the above reaction is :

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A block moving horizontally on a smooth surface with a speed of $40 \mathrm{~ms}^{-1}$ splits into two equal parts. If...

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The addition of silica during the extraction of copper from its sulphide ore:-

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In polythionic acid, $\mathrm{H}_2 \mathrm{~S}_{\mathrm{x}} \mathrm{O}_6(\mathrm{x}=3$ to 5$)$ the oxidation state(s) of sulphur is/are :

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)....

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A parallel plate capacitor of capacitance $200 \mu \mathrm{~F}$ is connected to a battery of 200 V . A dielectric...

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The correct sequence of correct reagents for the following transformation is:-

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The value of $\int_{-\frac{\pi}{2}}\left(\frac{\sin \pi^{\sin x}}{1+\pi^2}\right) \mathrm{dx}$

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The spin-only magnetic moment value of $\mathrm{B}_2^{\prime}$ species is $\_\_\_\_$ $\times 10^{-2} \mathrm{BM}$. (Nearest integer) $[$ Given: $\sqrt{3}=1.73]$

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The voltage drop across $15 \Omega$ resistance in the given figure will be $\_\_\_\_$ V.

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The unit of the van der Waals gas equation parameter ' $a$ ' in $\left(P+\frac{a n^2}{V^2}\right)(V-n b)=n R T$ is...

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Match List-I with List-II :

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What is A in the following reaction?

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A 50 watt bulb emits monochromatic red light of wavelength of 795 nm . The number of photons emitted per...

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A 10 inches long pencil $A B$ with mid point $C$ and a small eraser $P$ are placed on the...

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In the following sequence of reactions the P is :

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Given below are two statements : one is labelled as Assertion (A) and other is labelled as Reason (R). Assertion...

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)....

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Select the correct statements. (A) Crystalline solids have long range order. (B) Crystalline solids are isotropic. (C) Amorphous solid are...

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The bond order and magnetic behaviour of $\mathrm{O}_2^{-}$ion are, respectively :

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Let $P$ be the plane passing through the point $(1,2,3)$ and the line of intersection of the planes $...

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If $R_E$ be the radius of Earth, then the ratio between the acceleration due to gravity at a depth '...

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Out of following isomeric forms of uracil, which one is present in RNA ?

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The number of non-ionisable hydrogen atoms present in the final product obtained from the hydrolysis of PCl5 is :

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Number of Cl = O bonds in chlorous acid, chloric acid and perchloric acid respectively are:

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A hall has a square floor of dimension $10 \mathrm{~m} \times 10 \mathrm{~m}$ (see the figure) and vertical walls. If...

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The interaction energy of London forces between two particles is proportional to $\mathrm{r}^{\mathrm{x}}$, where r is the distance between the...

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The nature of oxides $\mathrm{V}_2 \mathrm{O}_3$ and CrO is indexed as ' X ' and ' Y ' type respectively....

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If 80 g of copper sulphate $\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$ is dissolved in delonised water to make 5 L...

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If the Thompson model of the atom was correct, then the result of Rutherford's gold foil experiment would have been

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)....

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If $(\sqrt{3}+i)^{100}=9^{99}(p+i q)$, then $p$ and $q$ are roots of the equation :

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A wire having a linear mass density $9.0 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ is stretched between two rigid supports with...

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The number of water molecules in gypsum, dead burnt plaster and plaster of paris, respectively are:

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The number of atoms in 8 g of sodium is $\mathrm{x} \times 10^{23}$. The value of x is $\_\_\_\_$ (Nearest...

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Match List - I with List - II:

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Statement-I: To get a steady dc output from the pulsating voltage received from a full wave rectifier we can connect...

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The gas 'A' is having very low reactivity reaches to stratosphere. It is non–toxic and non–flammable but dissociated by UV—radiations...

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A square shaped wire with resistance of each side $3 \omega$ is bent to form a complete circle. The resistance...

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The value of $...

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consider the above reaction, and choose the correct statement :

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Which one of the following phenols does not give colour when condensed with phthalic anhydride in presence of conc.$\mathrm{H}_2 \mathrm{SO}_4$

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A resistor dissipates 192 J of energy in 1 s when a current of 4A is passed through it. Now,...

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Acidic ferric chloride solution on treatment with excess of potassium ferrocyanide gives a Prussian blue coloured colloidal species. It is...

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For a body executing S.H.M. : (a) Potential energy is always equal to its K.E. (b) Average potential and kinetic...

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The locus of the mid points of the chords of the hyperbola $x^2-y^2=4$, which touch the parabola $y^2=8 x$, is...

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If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed...

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$$ \mathrm{R}-\mathrm{CN} \xrightarrow[\text { (ii) } \mathrm{H}_2 \mathrm{O}]{\text { (i) } \mathrm{OIBAL}-\mathrm{H}} \mathrm{R}-\mathrm{Y} $$ Consider the above reaction and identify...

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Cross-section view of a prism is the equilateral triangle $A B C$ in the figure. The minimum deviation is observed...

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Which of the following is not a correct statement for primary aliphatic amines?

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For the reaction $2 \mathrm{NO}_2(\mathrm{~g}) \mathrm{N}_2 \mathrm{O}_4(\mathrm{~g})$, when $\Delta \mathrm{S}=-176.0 \mathrm{JK}^{-1}$ and $\Delta \mathrm{H}=-57.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$, the magnitude of $...

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Two fair dice are thrown. The numbers on them are taken as l and m, and a system of linear...

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A particle of mass 1 kg is hanging from a spring of force constant $100 \mathrm{Nm}^{-1}$. The mass is pulled...

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At very high frequencies, the effective impendance of the given circuit will be $\_\_\_\_$ $\Omega$

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A coil is placed in a magnetic field B as shown below :

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The major product of the following reaction is :

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A peptide synthesized by the reactions of one molecule each of Glycine, Leucine, Aspartic acid and Histidine will have ________...

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Compound A gives D-Galactose and D-Glucose on hydrolysis. The compound A is:

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If the conductivity of mercury at $0^{\circ} \mathrm{C}$ is $1.07 \times 10^6 \mathrm{~S} \mathrm{~m}^{-1}$ and the resistance of a cell...

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A sample of gas with $\gamma=1.5$ is taken through an adiabatic process in which the volume is compressed from $...

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If $\sum_{r=1}^{50} \tan ^{-1} \frac{1}{2 r^2}=P$, then the value of $\tan p$ is :

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The correct statement about (A), (B), (C) and (D) is :

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The spin-only magnetic moment value of $\mathrm{B}_2^{+}$species is $\_\_\_\_$ $\times 10^{-2}$ BM. (Nearest integer) $[$ Given: $\sqrt{3}=1.73]$

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Q JEE MAIN 2021

The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the...

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When a rubber ball is taken to a depth of $\_\_\_\_$ m in deep sea, its volume decreases by $...

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A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses...

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Given below are two statements : Statement I : Penicillin is a bacteriostatic type antibiotic. Statement II : The general...

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A 50 watt bulb emits monochromatic red light of wavelength of 795 nm. The number of photons emitted per second...

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In a Young's double slit experiment, the slits are separated by 0.3 mm and the screen is 1.5 m away...

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A particle is moving with constant acceleration ' $a$ '. Following graph shows $v^2$ versus $x$ (displacement) plot. The acceleration...

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Consider a galvanometer shunted with $5 \Omega$ resistance and $2 \%$ of current passes through it. What is the resistance...

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Which refining process is generally used in the purification of low melting metals ?

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If 80 g of copper sulphate $\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$ is dissolved in deionised water to make 5 L...

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To an aqueous solution containing ions such as $\mathrm{Al}^{3+}, \mathrm{Zn}^{2+}, \mathrm{Ca}^{2+}, \mathrm{Fe}^{3+}, \mathrm{Ni}^{2+}, \mathrm{Ba}^{2+}$ and $\mathrm{Cu}^{2+}$ was added conc. HCl...

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The molar solubility of $\mathrm{Zn}(\mathrm{OH})_2$ in 0.1 M NaOH solution is $x \times 10^{-18} \mathrm{M}$. The value of $x$ is...

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A mixture of hydrogen and oxygen has volume $500 \mathrm{~cm}^3$, temperature 300 K , pressure 400 kPa and mass 0.76...

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Deuterium resembles hydrogen in properties but :

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A long solenoid with 1000 turns $/ \mathrm{m}$ has a core material with relative permeability 500 and volume $10^3 \mathrm{~cm}^3$....

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The number of atoms in 8 g of sodium is $x \times 10^{23}$. The value of x is________.(Nearest integer) [Given:...

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A moving proton and electron have the same de- Broglie wavelength. If K and P denote the K.E. and momentum...

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In which one of the following molecules strongest back donation of an electron pair from halide to boron is expected?

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A parallel plate capacitor of capacitance $200 \mu \mathrm{~F}$ is connected to a battery of 200 V . A dielectric...

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The sum of oxidation states of two silver ions in $\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]\left[\mathrm{Ag}(\mathrm{CN})_2\right]$ complex is _______.

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An empty LPG cylinder weighs 14.8 kg. When full, it weighs 29.0 kg and shows a pressure of 3.47 atm....

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Choose the incorrect statement : (a) The electric lines of force entering into a Gaussian surface provide negative flux. (b)...

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A bandwidth of 6 MHz is available for A.M. transmission. If the maximum audio signal frequency used for modulating the...

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Match List–I with List–II : Choose the most appropriate answer from the options given below :

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For thel reaction $2 \mathrm{NO}_2(\mathrm{~g}) \rightleftharpoons \mathrm{N}_2 \mathrm{O}_4(\mathrm{~g})$, when $\Delta \mathrm{S}=-176.0 \mathrm{JK}^{-1}$ and $\Delta \mathrm{H}=-57.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$, the magnitude of...

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If Re be the radius of Earth, then the ratio between the acceleration due to gravity at a depth '...

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The molar solubility of $\mathrm{Zn}(\mathrm{OH})_2$ in 0.1 M NaOH solution is $x \times 10^{-18} \mathrm{M}$. The value of $x$ is...

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An empty LPG cylinder weighs 14.8 kg. When full, it weighs 29.0 kg and shows a pressure of 3.47 atm....

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Statement–I : To get a steady dc output from the pulsating voltage received from a full wave rectifier we can...

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The structure of the starting compound P used in the reaction given below is :

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The number of halogen/(s) forming halic (V) acid is __________.

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Identify the element for which electronic configuration in +3 oxidation state is $[\mathrm{Ar}] 3 \mathrm{~d}^5$ :

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Identify the element for which electronic configuration in +3 oxidation state is $[\mathrm{Ar}] 3 \mathrm{~d}^5:$

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Number of paramagnetic oxides among the following given oxides is __________. $\mathrm{Li}_2 \mathrm{O}, \mathrm{CaO}, \mathrm{Na}_2 \mathrm{O}_2, \mathrm{KO}_2, \mathrm{MgO}$ and $...

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Number of paramagnetic oxides among the following given oxides is $\_\_\_\_$ $\mathrm{Li}_2 \mathrm{O}, \quad \mathrm{CaO}, \quad \mathrm{Na}_2 \mathrm{O}_2, \quad \mathrm{KO}_2$,...

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In the following sequence of reactions, the final product D is :

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The oxide without nitrogen-nitrogen bond is :

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The potassium ferrocyanide solution gives a Prussian blue colour, when added to :

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Which one of the following gives the most stable Diazonium salt

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The potassium ferrocyanide solution gives a Prussian blue colour, when added to

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Given below are two statements : Statement I : The nucleophilic addition of sodium hydrogen sulphite to an aldehyde or...

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The compounds B and C respectively are :

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Hydrogen peroxide reacts with iodine in basic medium to give :

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The stereoisomers that are formed by electrophilic addition of bromine to trans-but-2-ene is/are :

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In the given chemical reaction, colors of the $\mathrm{Fe}^{2+}$ and $\mathrm{Fe}^{3+}$ ions, , are respectively : $...

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Which one of the following compounds is aromatic in nature ?

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A fair die is tossed until six is obtained on it. Let $X$ be the number of required tosses, then...

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Monomer units of Dacron polymer are :

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For a body executing S.H.M. : (a) Potential energy is always equal to its K.E. (b) Average potential and kinetic...

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In an ac circuit, an inductor, a capacitor and a resistor are connected in series with $\mathrm{XL}=\mathrm{R}=\mathrm{Xc}$. Impedance of this...

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A coil is placed in a magnetic field B as shown below :

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The domain of the function $\operatorname{cosec}^{-1}\left(\frac{1+x}{x}\right)$ is :

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Which one of the following gives the most stable Diazonium salt ?

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The equivalent resistance of the given circuit between the terminals A and B is :

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$\mathrm{A}_3 \mathrm{~B}_2$ is a sparingly soluble salt of molar mass $\mathrm{M}\left(\mathrm{g} \mathrm{mol}^{-1}\right)$ and solubility $\times \mathrm{g} \mathrm{L}^{-1}$. The solubility product...

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Angular momentum of a single particle moving with constant speed along circular path

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$\mathrm{Ge}(\mathrm{Z}=32)$ in its ground state electronic configuration has x completely filled orbitals with $\mathrm{m}_{\mathrm{I}}=0$. The value of $x$ is $\_\_\_\_$...

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According to the following figure, the magnitude of the enthalpy change of the reaction $\mathrm{A}+\mathrm{B} \rightarrow \mathrm{M}+\mathrm{N}$ in $\mathrm{kJ} \mathrm{mol}^{-1}$...

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Consider the two statements : $(\mathrm{S} 1):(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$ is a tautology. $...

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Which of the following equations is dimensionally incorrect? Where $\mathrm{t}=$ time, $\mathrm{h}=$ height, $\mathrm{s}=$ surface tension, $\theta=$ angle, $\rho=$ density,...

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https://competishun.com/emw_jee-main-31-08-2021_s1/

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The number of hydrogen bonded water molecule(s) associated with stoichiometry $\mathrm{CuSO}_4 .5 \mathrm{H}_2 \mathrm{O}$ is $\_\_\_\_$ .

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Let $y(x)$ be the solution of the differential equation $2 x^2 d y+\left(e^y-2 x\right) d x=0, x>0$. If $y(e)=1$, then...

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For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for...

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For an ideal gas the instantaneous change in pressure ' $p$ ' with volume ' $v$ ' is given by...

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The point $\mathrm{P}(-2 \sqrt{6}, \sqrt{3})$ lies on the hyperbola $\frac{\mathrm{x}^2}{\mathrm{a}^2}-\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1$ having eccentricity $\frac{\sqrt{5}}{2}$. If the tangent and normal at $P$...

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Q.15 Given below are two statements : Statement I : The nucleophilic addition of sodium hydrogen sulphite to an aldehyde...

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If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will...

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The total number of reagents from those given below, that can convert nitrobenzene into aniline is ______. (Integer answer)

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Consider the sulphides $\mathrm{HgS}, \mathrm{PbS}, \mathrm{CuS}, \mathrm{Sb} 2 \mathrm{~S}_3, \mathrm{As}_2 \mathrm{~S}_3$ and CdS . Number of these sulphides soluble in...

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In the following sequence of reactions,

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The Crystal Field Stabilization Energy (CFSE) and magnetic moment (spin-only) of an octahedral aqua complex of a metal ion (...

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The molarity of the solution prepared by dissolving 6.3 g of oxalic acid $\left(\mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4 .2 \mathrm{H}_2 \mathrm{O}\right)$ in...

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If the value of the integral $\int_0^5 \frac{x+[x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta$, where $a, b \in R, 5 \alpha+6 \beta=0$, and...

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Hydrogen peroxide reacts with iodine in basic medium to give :

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A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses...

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Consider the following cell reaction : $\mathrm{Cd}_{(\mathrm{s})}+\mathrm{Hg}_2 \mathrm{SO}_{4(\mathrm{~s})}+\frac{9}{5} \mathrm{H}_2 \mathrm{O}_{(\mathrm{i})} \rightleftharpoons \mathrm{CdSO}_4 \cdot \frac{9}{5} \mathrm{H}_2 \mathrm{O}_{(\mathrm{s})}+2 \mathrm{Hg}_{(\mathrm{i})}$ The value of...

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Match List – I with List - II.

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The local maximum value of the function $f(x)=\left(\frac{2}{x}\right)^{x^2}, x>0$, is

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A mixture of hydrogen and oxygen has volume $500 \mathrm{~cm}^3$, temperature 300 K , pressure 400 kPa and mass 0.76...

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In the following sequence of reactions a compound A , (molecular formula $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_2$ ) with a straight chain...

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The structure of product C, formed by the following sequence of reactions is : $...

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Choose the incorrect statement :

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Let $\mathrm{A}=\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 0\end{array}\right)$. Then $\mathrm{A}^{2025}-\mathrm{A}^{2020}$...

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The stereoisomers that are formed by electrophilic addition of bromine to trans-but-2-ene is/are :

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Identify A in the following reaction

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A bob of mass ' m ' suspended by a thread of length $l$ undergoes simple harmonic oscillations with time...

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Let $[t]$ denote the greatest integer less than or equal to $t$. Let $f(x)=x-[x], g(x)=1-x+[x]$, and $...

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The equivalent resistance of the given circuit between the terminals A and B is :

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Which one of the following given graphs represents the variation of rate constant (k) with temperature (T) for an endothermic...

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In the given chemical reaction, colors of the $\mathrm{Fe}^{2+}$ and $\mathrm{Fe}^{3+}$ ions, are respectively $$ 5 \mathrm{Fe}^{2+}+\mathrm{MnO}_4^{-}+8 \mathrm{H}^{+} \rightarrow \mathrm{Mn}^{2+}+4...

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Match List-I with List-II

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BOD values (in ppm) for clean water (A) and polluted water (B) are expected respectively :

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The magnetic field vector of an electromagnetic wave is given by $B=B \circ \frac{i+j}{\sqrt{2}} \cos (k z-\omega t)$; where $...

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Experimentally reducing a functional group cannot be done by which one of the following reagents ?

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Which one of the following 0.10 M aqueous solutions will exhibit the largest freezing point depression ?

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Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases...

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If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will...

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A man starts walking from the point $P(-3,4)$, touches the $x$-axis at $R$, and then turns to reach at the...

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Calamine and Malachite, respectively, are the ores of :

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Given below are two statements ; one is labelled as Assertion (A) and the other is labelled as Reason (R)...

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Which one of the following compounds is aromatic in nature ?

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Let $[t]$ denote the greatest integer $\leq t$. The number of points where the function $f(x)=[x]\left|x^2-1\right|+\sin \left(\frac{\pi}{[x]+3}\right)-[x+1], x \in(-2,2)$ is...

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Water sample is called cleanest on the basis of which one of the BOD values given below

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Which one of the following is the correct PV vs P plot at constant temperature for an ideal gas ?...

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Statement :1 If three forces $\vec{F}_1, \vec{F}_2$ and $\vec{F}_3$ are represented by three sides of a triangle and $\vec{F}_1+\vec{F}_2=-\vec{F}_3$, then...

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If $\mathrm{V}_{\mathrm{A}}$ and $\mathrm{V}_{\mathrm{B}}$ are the input voltages (either 5 V or 0 V ) and $\mathrm{V}_0$ is the output...

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Choose the correct name for compound given below :

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A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with...

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A bob of mass m suspended by a thread of length $l$ undergoes simple harmonic oscillations with time period T...

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Two plane mirrors $M_1$ and $M_2$ are at right angle to each other shown. A point source ' $P$ '...

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)....

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A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time,...

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Monomer units of Dacron polymer are

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Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases...

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The denticity of an organic ligand, biuret is :

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The ratio of the equivalent resistance of the network (shown in figure) between the points a and b when switch...

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)....

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A uniform heavy rod of weight $10 \mathrm{~kg} \mathrm{~ms}^{-2}$, cross-sectional area $100 \mathrm{~cm}^2$ and length 20 cm is hanging from...

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https://competishun.com/ht_jee-main-31-08-2021_s1/

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If $V_A$ and $V_B$ are the input voltages (either 5 V or 0 V ) and $V_0$ is the output...

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Given below are two statements : Statement-I : The process of producing syn-gas is called gasification of coal. Statement-II: The...

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Two thin metallic spherical shells of radii $r_1$ and $r_2\left(r_1

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Monomer of Novolac is :

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Choose the correct waveform that can represent the voltage across R of the following circuit, assuming the diode is ideal...

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An ac circuit has an inductor and a resistor of resistance $R$ in series, such that $X_L=3 R$. Now, a...

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The major product formed in the following reaction is :

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A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils...

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Match List – I with List - II.

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)....

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A free electron of 2.6 eV energy collides with a $\mathrm{H}_{+}$ion. This results in the formation of a hydrogen atom...

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A free electron of 2.6 eV energy collides with a $\mathrm{H}+$ ion. This results in the formation of a hydrogen...

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Wires $W_1$ and $W_2$ are made of same material having the breaking stress of $...

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Which one of the following lanthanides exhibits +2 oxidation state with diamagnetic nature ? $($ Given Z for $...

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A zener diode of power rating 2W is to be used as a voltage regulator. If the zener diode has...

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In the following sequence of reactions a compound A , (molecular formula $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_2$ ) with a straight chain...

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A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of...

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The major products A and B in the following set of reactions are :

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X different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states...

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A small square loop of side ' $a$ ' and one turn is placed inside a larger square loop of...

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A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the...

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Statement I: Two forces $\left(\stackrel{\Delta \stackrel{\Delta}{\mathrm{P}}+\stackrel{\Delta}{\mathrm{Q}})}{(\stackrel{\Delta}{\mathrm{P}}-\stackrel{\Delta}{\mathrm{Q}})}\right.$ and where $^{(\stackrel{\Delta}{\mathrm{P}} \perp \stackrel{\Delta}{\mathrm{Q}})}$, when act at an angle $\theta_1$ to each other,...

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Two simple harmonic motion, are represented by the equations $y_1=10 \sin \left(3 \pi t+\frac{\pi}{3}\right)$ $$ y_2=5(\sin 3 \pi t+\sqrt{3} \cos...

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Which one of the following compounds contains $\beta-\mathrm{C}_1-\mathrm{C}_4$ glycosidic linkage?

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Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^3 \mathrm{~kg}$, The inner...

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A heat engine operates between a cold reservoir at temperature $T_2=400 \mathrm{~K}$ and a hot reservoir at temperature $T_1$. It...

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In the structure of the dichromate ion, there is a :

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The major component/ingredient of Portland Cement is :

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Figure shows a rod $A B$, which is bent in a $120^{\circ}$ circular arc of radius $R$. A charge (...

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An LPG cylinder contains gas at a pressure of 300 kPa at $27^{\circ} \mathrm{C}$. The cylinder can withstand the pressure...

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The masses and radii of the earth and moon are ( $\mathrm{M} 1, \mathrm{R}_1$ ) and ( $\mathrm{M}_2, \mathrm{R}_2$ )...

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A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of...

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The light waves from two coherent sources have same intensity $l_1=l_2=l_0$. In interference pattern the intensity of light at minima...

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When 3.00 g of a substance X is dissolved in 100 g of $\mathrm{CCl}_4$, it raises the boiling point by...

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Select the graph that correctly describes the adsorption isotherms at two temperatures $T_1$ and $T_2\left(T_1>T_2\right)$ for a gas : $(x$...

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Identify A in the following reaction.

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0.8 g of an organic compound was analysed by Kjeldahl's method for the estimation of nitrogen. If the percentage of...

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The height of victoria falls is 63 m. What is the difference in temperature of water at the top and...

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A current of 1.5 A is flowing through a triangle, of side 9 cm each. The magnetic field at the...

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A body of mass $M$ moving at speed $V_0$ collides elastically with a mass ' $m$ ' at rest. After...

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The correct order of reactivity of the given chlorides with acetate in acetic acid is :

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Assuming that $\mathrm{Ba}(\mathrm{OH})_2$ is completely ionised in aqueous solution under the given conditions the concentration of $\mathrm{H}_3 \mathrm{O}^{+}$ions in 0.005...

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A coaxial cable consists of an inner wire of radius ‘a’ surrounded by an outer shell of inner and outer...

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Which one of the following given graphs represents the variation of rate constant (k) with temperature (T) for an endothermic...

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At $20^{\circ} \mathrm{C}$, the vapour pressure of benzene is 70 torr and that of methyl benzene is 20 torr. The...

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The number of significant figures in 0.00340 is ______ .

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An average person needs about 10000 kJ energy per day. The amount of glucose (molar mass $=180.0 \mathrm{~g} \mathrm{~mol}^{-1}$ )...

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For a chemical reaction $\mathrm{A} \rightarrow \mathrm{B}$, it was found that concentration of B is increased by $0.2 \mathrm{~mol} \mathrm{~L}^{-1}$...

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Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^3 \mathrm{~kg}$, The inner...

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Experimentally reducing a functional group cannot be done by which one of the following reagents ?

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Consider the above chemical reaction. The total number of stereoisomers possible for Product 'P' is _______ .

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A coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a'...

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The inactivation rate of a viral preparation is proportional to the amount of virus. In the first minute after preparation,...

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If force (F), length (L) and time (T) are taken as the fundamental quantities, Then what will be the dimension...

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Number of electrons present in 4 f orbital of $\mathrm{Ho}^{3+}$ ion is $\_\_\_\_$ (Given Atomic No. of $\mathrm{Ho}=67$ )

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Clean water could have BOD value of less than 5 ppm whereas highly polluted water could have a BOD value...

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To synthesise 1.0 mole of 2-methylpropan-2-ol from Ethylethanoate $\_\_\_\_$ equivalents of $\mathrm{CH}_3 \mathrm{MgBr}$ reagent will be required. (Integer value)

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An accelerated electron has a speed of $5 \times 10^6 \mathrm{~ms}^{-1}$ with an uncertainty of $0.02 \%$. The uncertainty in...

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Q JEE-MAIN 2021

Match List-I with List-II

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The number of nitrogen atoms in a semicarbazone molecule of acetone is _________.

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$2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_3(\mathrm{~g})$ In an equilibrium mixture, the partial pressures are $\mathrm{P}_{\mathrm{SO}_3}=43 \mathrm{kPa} ; \mathrm{Po}_{\mathrm{O}_2}=530 \mathrm{~Pa}$ and $...

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A system does 200 J of work and at the same time absorbs 150 J of heat. The magnitude of...

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A monochromatic neon lamp with wavelength of 670.5 nm illuminates a photo-sensitive material which has a stopping voltage of 0.48...

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Which among the following is the strongest acid ?

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The spin-only magnetic moment value for the complex $\left[\mathrm{Co}(\mathrm{CN})_6\right]^{4-}$ is $\_\_\_\_$ BM. [At. no. of $\mathrm{Co}=27$ ]

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A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other...

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Water sample is called cleanest on the basis of which one of the BOD values given below

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For full scale deflection of total 50 divisions, 50 mV voltage is required in galvanometer. The resistance of galvanometer if...

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Identify the process in which change in the oxidation state is five :

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The Azimuthal quantum number for the valence electrons of Ga+ ion is _______. (Atomic number of Ga = 31)

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A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and...

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What is the major product "P" of the following reaction ?

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250 mL of 0.5 M NaOH was added to 500 mL of 1 M HCl . The number of unreacted...

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The number of lone pairs of electrons on the central I atom in $\mathrm{I}_3^{-}$is $\_\_\_\_$ .

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A constant magnetic field of 1 T is applied in the x > 0 region. A metallic circular ring of...

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Match List I with List II : Choose the most appropriate answer from the options given below

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For above chemical reactions, identify the correct statement from the following:

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[where $\mathrm{Et} \Rightarrow-\mathrm{C}_2 \mathrm{H}_5{ }^{\mathrm{t}} \mathrm{Bu} \Rightarrow\left(\mathrm{CH}_3\right)_3 \mathrm{C}-$ ] Consider the above reaction sequence, Product "A" and Product "B" formed...

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If the rms speed of oxygen molecules at 0°C is 160 m/s, find the rms speed of hydrogen molecules at...

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An antenna is mounted on a 400 m tall building. What will be the wavelength of signal of signal that...

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Which among the above compound/s does/do not form Silver mirror when treated with Tollen's reagent?

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Given below are two statements : Statement I : Chlorofluoro carbons breakdown by radiation in the visible energy region and...

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The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor...

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Maleic anhydride Maleic anhydride can be prepared by :

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Identify the incorrect statement from the following

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Three capacitors $\mathrm{C}_1=2 \mu \mathrm{~F}, \mathrm{C}_2=6 \mu \mathrm{~F}$ and $\mathrm{C}_3=12 \mu \mathrm{~F}$ are connected as shown in figure. Find the...

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Which one of the following metals forms interstitial hydride easily ?

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Identify the species having one $\pi$-bond and maximum number of canonical forms from the following :

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Two discs have moments of intertia $l_1$ and $l_2$ about their respective axes perpendicular to the plane and passing through...

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Which one of the following is correct structure for cytosine ?

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The spin only magnetic moments (in BM ) for free $\mathrm{Ti}^{3+}, \mathrm{V}^{2+}$ and $\mathrm{Sc}^{3+}$ ions respectively are (At.No. Sc :...

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A reaction of benzonitrile with one equivalent $\mathrm{CH}_3 \mathrm{MgBr}$ followed by hydrolysis produces a yellow liquid " P ". The...

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Consider the above reaction, the Product "P" is :

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Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m. The...

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For a transistor $\alpha$ and $\beta$ are given as $\alpha=\frac{I_c}{I_E}$ and $\beta=\frac{I_c}{I_B}$. Then the correct relation between $\alpha$ and $\beta$...

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The correct decreasing order of densities of the following compounds is :

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The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate...

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The ionic radii of $\mathrm{F}^{-}$and $\mathrm{O}^{2-}$ respectively are $1.33 \AA$ and $1.4 \AA$, while the covalent radius of N is...

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Curved surfaces of a plano-convex lens of refractive index $\mu$1 and a plano-concave lens of refractive index $\mu$2 have equal...

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Let $\vec{a}-=2 \hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}=\hat{i}--2 \hat{j}-\hat{k}$. Let a vector $\vec{v}$ be in the plane containing $\vec{a}$ and $\vec{b}$. If...

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If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096 , then the greatest coefficient in the...

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All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R...

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Let $f(x)$ be a polynomial of degree 3 such that $f(k)=-\frac{2}{k}$ for $k=2,3,4,5$. Then the value of $52-10 f(10)$ is...

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Let the points of intersections of the lines x – y + 1 = 0, x – 2y + 3...

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If for the complex numbers $z$ satisfying $|z-2-2 i| \leq 1$, the maximum value of $|3 i z+6|$ is attained...

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Let $f(x)=x^6+2 x^4+x^3+2 x+3, x \in R$. Then the natural number $n$ for which $\lim _{x \rightarrow 1} \frac{x^n f(1)-f(x)}{x-1}=44$...

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Let X be a random variable with distribution. If the mean of $X$ is 2.3 and variance of $X$ is...

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Let $\theta$ be the acute angle between the tangents to the ellipse $\frac{x^2}{9}+\frac{y^2}{1}=1$ and the circle $x^2+y^2=3$ at their point...

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Given below are two statements: Statement I: $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-},\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$ and $\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$ are $d^2 \mathrm{sp}^3$ hybridised. Statement Il: $\left[\mathrm{MnCl}_6\right]^{3-}$ and $\left[\mathrm{FeF}_6\right]^{3-}$...

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The function $f(x)$, that satisfies the condition $f(x)=x+\int_0^{\pi / 2} \sin x \cdot \cos y f(y) d y$, is :

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Given below are two statements Statement I : Hyperconjugation is a permanent effect. Statement II : Hyperconjugation in ethyl cation...

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Let $\mathrm{a}_1, \mathrm{a}_2 \ldots \ldots, \mathrm{a}_{21}$ be an AP such that $\sum_{\mathrm{n}=1}^{20} \frac{1}{\mathrm{a}_{\mathrm{n}} \mathrm{a}_{\mathrm{n}+1}}=\frac{4}{9}$. If the sum of this AP...

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The CORRECT order of first ionisation enthalpy is :

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The range of the function, $f(x)=\log _{\sqrt{5}}\left(3+\cos \left(\frac{3 \pi}{4}+x\right)+\cos \left(\frac{\pi}{4}+x\right)+\cos \left(\frac{\pi}{4}-x\right)-\cos \left(\frac{3 \pi}{4}-x\right)\right)$ is :

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Given below are two statements one is labelled as Assertion A and the other is labelled as Reason R. Assertion...

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Let $\mathrm{P}_1, \mathrm{P}_2 \ldots \ldots, \mathrm{P}_{15}$ be 15 points on a circle. The number of distinct triangles formed by points...

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Let $S_n=1 \cdot(n-1)+2 \cdot(n-2)+3 \cdot(n-3)+\ldots \cdot+(n-1) \cdot n \geq 4$. The sum $\sum_{n=4}^{\infty}\left(\frac{2 S_n}{n!}-\frac{1}{(n-2)!}\right)$ is equal to :

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The numbers of pairs $(a, b)$ of real numbers, such that whenever $a$ is a root of the equation $...

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Consider the parabola with vertex $\left(\frac{1}{2}, \frac{3}{4}\right)$ and the directrix $y=\frac{1}{2}$. Let $P$ be the point where the parabola meets...

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The distance of line 3y – 2z – 1 = 0 = 3x – z + 4 from the point...

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The area, enclosed by the curves $y=\sin x+\cos x$ and $y=|\cos x-\sin x|$ and the lines $x=0, x=\frac{\pi}{2}$, is :

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Q JEE MAIN_2021

Match List - I with List II :

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Let $J_{n, m}=\int_0^{\frac{1}{2}} \frac{x^n}{x^m-1} d x, \forall n>m$ and $m \in N$. Consider a matrix $A=\left[a_{i j}\right]_{3 \times 3}$ where...

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The number of neutrons and electrons, respectively, present in the radioactive isotope of hydrogen is :-

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Consider the above reaction, the major product "P" formed is :-

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Which one of the following set of elements can be detected using sodium fusion extract ?

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Let $...

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If $n$ is the number of solutions of the equation $2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1, x \in[0, \pi]$...

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The term independent of ' $x$ ' in the expansion of $\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right)^{10}$, where $...

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If $\alpha, \beta$ are roots of the equation $x^2+5(\sqrt{2}) x+10=0, \alpha>\beta$ and $P_n=\alpha^n-\beta^n$ for each positive integer $n$, then the...

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There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the...

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If $y=y(x)$ is the solution curve of the differential equation $x^2 d y+\left(y-\frac{1}{x}\right) d x=0 ; x>0$ and $y(1)=1$, then...

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Let $M=\left\{A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right): a, b, c, d \in\{ \pm 3, \pm 2, \pm 1,0\}\right\}$ Difine...

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Value of KP for the equilibrium reaction $\mathrm{N}_2 \mathrm{O}_4(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2(\mathrm{~g})}$ at 288 K is 47.9. The $\mathrm{K}_{\mathrm{C}}$ for...

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Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common...

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The ratio of the coefficient of the middle term in the expansion of $(1+x)^{20}$ and the sum of the coefficients...

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Assume a cell with the following reaction $\mathrm{Cu}_{(\mathrm{s})}+2 \mathrm{Ag}^{+}\left(1 \times 10^{-3} \mathrm{M}\right) \rightarrow \mathrm{Cu}^{2+}(0.250 \mathrm{M})+2 \mathrm{Ag}_{(\mathrm{s})}$ $\mathrm{E}_{\mathrm{cell}}^{\ominus}=2.97 \mathrm{~V}$ $...

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Let $\vec{p}=2 \hat{i}+3 \hat{j}+\hat{k}$ and $\vec{q}=\hat{i}+2 \hat{j}+\hat{k}$ be two vectors. If a vector $\vec{r}=(\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k})$ is perpendicular to...

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Which of the following is equivalent to the Boolean expression $\mathrm{p} \wedge \sim \mathrm{q}$ ?

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Consider the following frequency distribution

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If the value of $\left(1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\ldots . \text { upto } \infty\right)^{\log _{1008}\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^2}+\ldots \text { uptoss }\right)}$ is $l$, then $l^2$...

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Let $y=y(x)$ be solution of the following differential equation $...

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Methylation of 10 g of benzene gave 9.2 g of toluene. Calculate the percentage yield of toluene ______. (Nearest integer)

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The total number of unpaired electrons present in $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right] \mathrm{Cl}_2$ and $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right] \mathrm{Cl}_3$ is

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Let the foot of perpendicular from a point $P(1,2,-1)$ to the straight line $L: \frac{x}{1}=\frac{y}{0}=\frac{z}{-1}$ be $N$. Let a line...

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The conditions given below are in the context of observing Tyndall effect in colloidal solutions: (A) The diameter of the...

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Let the acute angle bisector of the two planes x – 2y – 2z + 1 = 0 and 2x...

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Compound A is converted to B on reaction with $\mathrm{CHCl}_3$ and KOH . The compound B is toxic and can...

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The metal that can be purified economically by fractional distillation method is:

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Consider the system of linear equations $$ \begin{aligned} & -x+y+2 z=0 \\ & 3 x-a y+5 z=1 \\ & 2...

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In the given reaction 3-Bromo-2, 2 -dimethyl butane $\xrightarrow{\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}} \underset{\text { (Major Product) }}{'} A^{\prime}$ Product $A$ is:

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A s-block element (M) reacts with oxygen to form an oxide of the formula $\mathrm{MO}_2$. The oxide is pale yellow...

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Which one of the following 0.06 M aqueous solutions has lowest freezing point ?

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$\cos ^{-1}(\cos (-5))+\sin ^{-1}(\sin (6))-\tan ^{-1}(\tan (12))$ is equal to :

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Match List I with List II : (Both having metallurgical terms) Choose the correct answer from the options given below...

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Among the given species the Resonance stabilised carbocations are:

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An object is placed at the focus of concave lens having focal length $f$, What is the magnification and distance...

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Let $f: R \rightarrow R$ be a continuous function. Then $...

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An organic compound A $\left(\mathrm{C}_6 \mathrm{H}_6 \mathrm{O}\right)$ gives dark green colouration with ferric chloride. On treatment with $\mathrm{CHCl}_3$ and KOH,...

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An inorganic Compound ' $X$ ' on treatment with concentrated $\mathrm{H}_2 \mathrm{SO}_4$ produces brown fumes and gives dark brown ring...

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If $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1\end{array}\right]$ and $...

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Chemical nature of the nitrogen oxide compound obtained from a reaction of concentrated nitric acid and $\mathrm{P}_4 \mathrm{O}_{10}$ (in $...

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Let $A=\left\{n \in N \mid n^2 \leq n+10,000\right\}, B=\{3 k+1 \mid k \in N\}$ and $...

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A reversible engine has efficiency of $1 / 4$. If the temperature of the sink is reduced by $58^{\circ} \mathrm{C}$,...

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Given below are two statements : One is labelled as Assertion A and other is labelled as Reason R. Assertion...

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Which one of the following metal complexes is most stable?

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Thiamine and pyridoxine are also known respectively as :

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Orlon fibres are made up of :

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Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion...

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The set having ions which are coloured and paramagnetic both is -

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An electron of mass me and a proton of mass $m_p= 1836 \mathrm{~m}_{\mathrm{e}}$ are moving with the same speed. The...

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The species given below that does NOT show disproportionation reaction is :

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The set in which compounds have different nature is :

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Match List-I with List-II :

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Let an ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a^2>b^2$, passes through $\left(\sqrt{\frac{3}{2}}, 1\right)$ and has eccentricity $\frac{1}{\sqrt{3}}$. If a circle, centered at focus...

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The correct order of intensity of colors of the compounds is :

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Two particles A and B having charges $20 \mu \mathrm{C}$ and $-5 \mu \mathrm{C}$ respectively are held fixed with a...

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Match List I with List II : Choose the correct answer from the options given below :

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The number of real roots of the equation $\mathrm{e}^{6 \mathrm{x}}-\mathrm{e}^{4 \mathrm{x}}-2 \mathrm{e}^{3 \mathrm{x}}-12 \mathrm{e}^{2 \mathrm{x}}+\mathrm{e}^{\mathrm{x}}+1=0$ is $i$

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Green chemistry in day–to–day life is in the use of:

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The correct structure of Rhumann's Purple, the compound formed in the reaction of ninhydrin with proteins is :

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Let a parabola P be such that its vertex and focus lie on the positive x -axis at a distance...

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According to the valence bond theory the hybridization of central metal atom is $\mathrm{dsp}^2$ for which one of the following...

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Let 9 distinct balls be distributed among 4 boxes, $B_1, B_2, B_3$ and $B_4$. If the probability than $B_3$ contains...

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Given below are the statements about diborane (a) Diborane is prepared by the oxidation of NaBH4 with I2 (b) Each...

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In the following logic circuit the sequence of the inputs A, B are (0, 0), (0, 1), (1, 0) and...

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The values of $a$ and $b$, for which the system of equations $$ \begin{aligned} & 2 x+3 y+6 z=8 \\...

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A biodegradable polyamide can be made from:

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Let $n$ be a non-negative integer. Then the number of divisors of the form " $4 n+1$ " of the...

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When silver nitrate solution is added to potassium iodide solution then the sol produced is :

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Consider the complete combustion of butane, the amount of butane utilized to produce 72.0 g of water is $...

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A helicopter is flying horizontally with a speed ' v ' at an altitude ' h ' has to drop...

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Let $y=y(x)$ be the solution of the differential equation $d y=e^{\alpha x+y} d x ; \alpha \in N$. If $...

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When 10 mL of an aqueous solution of $\mathrm{Fe}^{2+}$ ions was titrated in the presence of dil $\mathrm{H}_2 \mathrm{SO}_4$ using...

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The number of real roots of the equation $e^{4 x}-e^{3 x}-4 e^{2 x}-e^x+1=0$ is equal to $\_\_\_\_$

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Match List-I with List-II : Choose the correct answer from the options given below :

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If $\int_0^\pi\left(\sin ^3 x\right) e^{-\sin ^2 x} d x=\alpha-\frac{\beta}{e} \int_0^1 \sqrt{t} e^t d t$, then $\alpha+\beta$ is equal to $\_\_\_\_$...

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A home owner uses $4.00 \times 10^3 \mathrm{~m}^3$ of methane $\left(\mathrm{CH}_4\right)$ gas, (assume $\mathrm{CH}_4$ is an ideal gas) in a...

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Let $E$ be an ellipse whose axes are parallel to the co-ordinates axes, having its center at $(3,-4)$, one focus...

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At 298 K , the enthalpy of fusion of a solid $(\mathrm{X})$ is $2.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and the enthalpy of...

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Consider a badminton racket with length scales as shown in the figure. If the mass of the linear and circular...

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If the real part of the complex number $z=\frac{3+2 i \cos \theta}{1-3 i \cos \theta}, \theta \in\left(0, \frac{\pi}{2}\right)$ is zero,...

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Consider the cell at $25^{\circ} \mathrm{C} \mathrm{Zn}\left|\mathrm{Zn}^{2+}(\mathrm{aq}),(1 \mathrm{M}) \| \mathrm{Fe}^{3+}(\mathrm{aq}), \mathrm{Fe}^{2+}(\mathrm{aq})\right| \mathrm{Pt}(\mathrm{s})$ The fraction of total iron present as $\mathrm{Fe}^{3+}$...

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In the following the correct bond order sequence is:

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The distance of the point $\mathrm{P}(3,4,4)$ from the point of intersection of the line joining the points. $\mathrm{Q}(3,-4,-5)$ and $R(2,-3,1)$...

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For the reaction $A+B \rightleftharpoons 2 C$ the value of equilibrium constant is 100 at 298 K . If the...

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White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation...

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Isotope(s) of hydrogen which emits low energy $\beta^{-}$ particles with $t_{1 / 2}$ value > 12 years is/are

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Let $\vec{a}=\hat{i}-\alpha \hat{j}+\beta \hat{k}, \vec{b}=3 \hat{i}+\beta \hat{j}+\alpha \hat{k}$ and $\vec{c}=-\alpha \hat{i}+2 \hat{j}+\hat{k}$, where $\alpha$ and $\beta$ are integers. If $...

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$\mathrm{CO}_2$ gas is bubbled through water during a soft drink manufacturing process at 298 K . If $\mathrm{CO}_2$ exerts a...

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Two travelling waves produces a standing wave represented by equation, $\mathrm{y}=1.0 \mathrm{~mm} \cos \left(1.57 \mathrm{~cm}^{-1}\right) \times \sin \left(78.5 \mathrm{~s}^{-1}\right) \mathrm{t}$....

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Let $f:(\mathrm{a}, \mathrm{b}) \rightarrow \mathrm{R}$ be twice differentiable function such that $\mathrm{f}(\mathrm{x})=\int_{\mathrm{a}}^{\mathrm{x}} \mathrm{g}(\mathrm{t}) \mathrm{dt}$ for a differentiable function $\mathrm{g}(\mathrm{x})$. If...

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A source of monochromatic radiation of wavelength 400 nm provides 1000 J of energy in 10 seconds. When this radiation...

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Two short magnetic dipoles $m_1$ and $m_2$ each having magnetic moment of $1 \mathrm{Am}^2$ are placed at point $O$ and...

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Let $f:[0, \infty) \rightarrow[0, \infty)$ be defined as $f:(x)=\int_0^x[y] d y$ where $[x]$ is the greatest integer less than or...

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Let $A$ and $B$ be two $3 \times 3$ real matrices such that $\left(A^2-B^2\right)$ is invertible matrix. If $A^5=B^5$ and...

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Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three vectors such that $\vec{a}=\vec{b} \times(\vec{b} \times \vec{c})$. If magnitudes of the vectors $...

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Match List-I with List-II Choose the correct answer from the options given below :

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Three moles of AgCl get precipitated when one mole of an octahedral co-ordination compound with empirical formula $...

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An amplitude modulated wave is represented by $$ C_m(t)=10(1+0.2 \cos 12560 t) \sin \left(111 \times 10^4 t\right) \text { volts....

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Potassium chlorate is prepared by electrolysis of KCl in basic solution as shown by following equation. $...

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Let $\mathrm{g}: \mathrm{N} \rightarrow \mathrm{N}$ be defined as $$ \begin{aligned} & g(3 n+1)=3 n+2 \\ & g(3 n+2)=3 n+3 \\...

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Q JEE MAIN 2021 S2

Consider a circle $C$ which touches the $y$-axis at $(0,6)$ and cuts off an intercept $6 \sqrt{5}$ on the $x$-axis....

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The number of sigma bonds in is ................

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A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius...

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An aqueous solution of $\mathrm{NiCl}_2$ was heated with excess sodium cyanide in presence of strong oxidizing agent to form $\left[\mathrm{Ni}(\mathrm{CN})_6\right]^{2-}$....

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The sum of all values of $x$ in $[0,2 \pi]$, for which $\sin x+\sin 2 x+\sin 3 x+\sin 4 x=0$,...

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An organic compound ' A ' $\mathrm{C}_4 \mathrm{H}_8$ on treatment with $\mathrm{KMnO}_4 / \mathrm{H}^{+}$yields compound $...

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Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred...

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Which of the following compounds does not exhibit resonance?

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The area (in sq. units) of the region, given by the set $...

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Let $N$ be the set of natural numbers and a relation $R$ on $N$ be defined by $...

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Which of the following compounds will provide a tertiary alcohol on reaction with excess of CH3MgBr followed by hydrolysis?

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$\mathrm{PCl}_5(\mathrm{~g}) \rightarrow \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g})$ In the above first order reaction the concentration of $\mathrm{PCl}_5$ reduces from initial concentration $50 \mathrm{~mol} \mathrm{~L}^{-1}$...

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In the leaching of alumina from bauxite, the ore expected to leach out in the process by reacting with NaOH...

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The Boolean expression $(P \Rightarrow q) \wedge(q \Rightarrow \sim p)$ is equivalent to:

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Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction...

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Let $f:[0, \infty) \rightarrow[0,3]$ be a function defined by $...

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Which one of the following compounds will liberate $\mathrm{CO}_2$, when treated with $\mathrm{NaHCO}_3$ ?

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Let $y=y(x)$ be the solution of the differential equation $\frac{d}{d x}=1+x e^{y-x},-\sqrt{2}

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Let $\alpha=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$ and $...

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A source and a detector move away from each other in absence of wind with a speed of $...

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When 0.15 g of an organic compound was analyzed using Carius method for estimation of bromine, 0.2397 g of AgBr...

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The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that...

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Two sides of a parallelogram are along the lines $4 x+5 y=0$ and $7 x+2 y=0$. If the equation of...

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If $b$ is very small as compared to the value of $a$, so that the cube and other higher powers...

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Which one of the following chemical agent is not being used for dry–cleaning of clothes?

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The electric field in a plane electromagnetic wave is given by $$ \overrightarrow{\mathrm{E}}-=200 \cos \left[\left(\frac{0.5 \times 10^3}{\mathrm{~m}}\right) \mathrm{x}-\left(1.5 \times 10^{11}...

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An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length...

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4 g equimolar mixture of NaOH and $\mathrm{Na}_2 \mathrm{CO}_3$ contains x g of NaOH and y g of $\mathrm{Na}_2 \mathrm{CO}_3$....

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The value of $\lim _{x \rightarrow 0}\left(\frac{x}{\sqrt[8]{1-\sin x}-\sqrt[8]{1+\sin x}}\right)$ is equal to:

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The correct order of following 3d metal oxides, according to their oxidation numbers is : (a) $\mathrm{CrO}_3$ (b) $\mathrm{Fe}_2 \mathrm{O}_3$...

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The value of the definite integral $\int_{\pi / 24}^{5 \pi / 24} \frac{d x}{1+\sqrt[3]{\tan 2 x}}$ is :

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The vapour pressures of $A$ and $B$ at $25^{\circ} \mathrm{C}$ are 90 mm Hg and 15 mm Hg respectively. If...

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For the given circuit, the power across zener diode is ............ mW.

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A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter laying on...

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Let $y=y(x)$ be the solution of the differential equation $\left(x-x^3\right) d y=\left(y+y x^2-3 x^4\right) d x, x>2$. If $y(3)=3$, then...

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Which purification technique is used for high boiling organic liquid compound (decomposes near its boiling point)?

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Given below are two statements : Srtatement II : Solubility of alkaline earth metal hydroxides in water increases down the...

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A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the...

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Which one of the following statements for D.I. Mendeleeff, is incorrect?

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The area of the region bounded by $y-x=2$ and $x^2=y$ is equal to :-

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Two simple harmonic motions are represented by the equations $x_1=5 \sin \left(2 \pi t+\frac{\pi}{4}\right)$ and $...

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The wavelength of electrons accelerated from rest through a potential difference of 40 kV is $x \times 10^{-12} \mathrm{~m}$. The...

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Statement-I : By doping silicon semiconductor with pentavalent material, the electrons density increases. Statement-II : The n-type semiconductor has net...

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A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed...

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The water having more dissolved O2 is :

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The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a...

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For a given chemical reaction $\mathrm{A} \rightarrow \mathrm{B}$ at 300 K the free energy change is $-49.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and...

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Q JEE MAIN 2021 S2

If $\tan \left(\frac{\pi}{9}\right), x, \tan \left(\frac{7 \pi}{18}\right)$ are in arithmetic progression and $\tan \left(\frac{\pi}{9}\right), y, \tan \left(\frac{5 \pi}{18}\right)$ are also...

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A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability....

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If the maximum value of accelerating potential provided by a ratio frequency oscillator is 12 kV. The number of revolution...

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Let be the set of all complex numbers. Let $$ \begin{aligned} & S_1=\{z \in \mathbb{C}:|z-2| \leq 1\} \text { and...

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The material filled between the plates of a parallel plate capacitor has resistivity $200 \Omega \mathrm{~m}$. The value of capacitance...

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A source of light is placed in front of a screen. Intensity of light on the screen is $I$. Two...

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If $E, L, M$ and $G$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then...

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Let $f: R-R$ be defined as $f(x+y)+f(x-y)=2 f(x) f(y), f\left(\frac{1}{2}\right)=-1$. Then, the value of $\sum_{k=1}^{20} \frac{1}{\sin (k) \sin (k+f(k))}$ is...

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Two waves are simultaneously passing through a string and their equations are $y_1=A_1 \sin k(x-v t), y_2=A_2 \sin k\left(x-v t+x_0\right)$....

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The initial mass of a rocket is 1000 kg . Calculate at what rate the fuel should be burnt so...

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For real numbers $\alpha$ and $\beta \neq 0$, if the point of intersection of the straight lines $\frac{x-\alpha}{1}=\frac{y-1}{2}=\frac{z-1}{3}$ and $\frac{x-4}{\beta}=\frac{y-6}{3}=\frac{z-7}{3}$,...

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What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to...

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Which one among the following resonating structures is not correct?

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Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley....

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Which one of the following compounds of Group–14 elements is not known?

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In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed....

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The ionic radii of $\mathrm{K}^{+}, \mathrm{Na}^{+}, \mathrm{Al}^{3+}$ and $\mathrm{Mg2}^{+}$are in the order :

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If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is:

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The correct order of their reactivity towards hydrolysis at room temperature is :

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The rms speeds of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are $\mathrm{V}_{\mathrm{H}}$, $\mathrm{V}_0$ and $\mathrm{V}_c$...

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The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in...

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Which one of the products of the following reactions does not react with Hinsberg reagent to form sulphonamide?

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In the given circuit the AC source has $\omega=100 \mathrm{rad} \mathrm{s}^{-1}$. Considering the inductor and capacitor to be ideal, what...

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The $\mathrm{K}_\alpha$ X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atoms with a K electron...

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A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius...

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For the following graphs, Choose from the options given below, the correct one regarding order of reaction is :

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Which one of the following gases is reported to retard photosynthesis ?

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Match List-I with List-II

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A small block slides down from the top of hemisphere of radius R = 3 m as shown in the...

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Four NOR gates are connected as shown in figure. The truth table for the given figure is :

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Given below are two statements, one is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (R)...

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In Carius method, halogen containing organic compound is heated with fuming nitric acid in the presence of :

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An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V supply. Calculate...

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$\mathrm{Cu}^{2+}$ salt reacts with potassium iodide to give

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The given reaction can occur in the presence of : Choose the correct answer from the options given below :

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In the given figure, the emf of the cell is 2.2 V and if internal resistance is $0.6 \Omega$. Calculate...

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For the circuit shown, the value of current at time t = 3.2 s will be _____A.

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Major product P of above reaction, is

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A refrigerator consumes an average 35 W power to operate between temperature –10°C to 25°C. If there is no loss...

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Consider the above reaction, compound B is :

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Consider the given reaction, the product 'X' is:

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A transmitting antenna at top of a tower has a height of 50 m and the height of receiving antenna...

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In a photoelectric experiment ultraviolet light of wavelength 280 nm is used with lithium cathode having work function $\phi=2.5 \mathrm{eV}$....

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A swimmer wants to cross a river from point A to point B. Lint AB makes an angle of 30º...

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At 298.2 K the relationship between enthalpy of bond dissociation (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) for hydrogen (EH) and its isotope,...

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Benzene on nitration gives nitrobenzene in presence of $\mathrm{HNO}_3$ and $\mathrm{H}_2 \mathrm{SO}$ mixture, where

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A particle executes simple harmonic motion represented by displacement function as $x(t)=A \sin (\omega t+\varphi)$ If the position and velocity...

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The water soluble protein is :

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Sodium stearate $\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{16} \mathrm{COO}^{-} \mathrm{Na}^{+}$is an anionic surfactant which forms micelles in oil. Choose the correct statement for it from...

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A particular hydrogen like ion emits radiation of frequency $2.92 \times 10^{15} \mathrm{~Hz}$ when it makes transition from $n=3$ to...

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Bakelite is a cross-linked polymer of formaldehyde and :

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A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the...

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Let $f: R \rightarrow R$ be defined as $...

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Consider the above reaction, the major product 'P' is:

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A parallel - plate capacitor with plate area $A$ has separation $d$ between the plates. Two dielectric slabs of dielectric...

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The hybridisations of the atomic orbitals of nitrogen in $\mathrm{NO}_2^{-}, \mathrm{NO}_2^{+}$andN $\mathrm{NH}_4^{+}$respectively are.

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A possible value of ' $x$ ', for which the ninth term in the expansion of $...

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Identify the logic operation carried out by the given circuit

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In the given figure the magnetic flux through the loop increases according to the relation $\varphi_{\mathrm{B}}(\mathrm{t})=10 \mathrm{t}^2+20 \mathrm{t}$, where $\varphi_{\mathrm{B}}$...

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Let the vectors $(2+a+b) \hat{i}+(a+2 b+c) \hat{j}-(b+c) \hat{k},(1+b) \hat{i}+2 b \hat{j}-b \hat{k}$ and $...

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Which one of the following species responds to an external magnetic field?

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The point P (a,b) undergoes the following three transformations successively : (a) reflection about the line $\mathrm{y}=\mathrm{x}$.: (b) translation through...

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The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of...

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The maximum amplitude for an amplitude modulated wave is found to be 12V while the minimum amplitude is found to...

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is a repeating unit for :

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A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance $\mathrm{R}=3 \mathrm{k} \Omega$,...

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The difference in the number of waves when yellow light propagates through air vacuum columns of the same thickness is...

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Which one of the following species doesn't have a magnetic moment of 1.73 BM, (spin only value) ?

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If you are provided a set of resistances $2 \Omega, 4 \Omega, 6 \Omega$ and $8 \Omega$. Connect these resistances...

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The locus of the centroid of the triangle formed by any point $P$ on the hyperbola $...

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Q JEE MAIN 2021 S2

If the lines $\frac{x-k}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x+1}{3}=\frac{y+2}{2}=\frac{z+3}{1}$ are co-planar, then the value of $k$ is

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The difference between bond orders of CO and $\mathrm{NO}^{\oplus}$ is $\frac{\mathrm{x}}{2}$ where $\mathrm{x}=$ $\_\_\_\_$ . (Round off to the Nearest...

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An inductor coil stores 64 J of magnetic field energy and dissipates energy at the rate of 640 W when...

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$\mathrm{PC}_1 \rightleftharpoons \mathrm{PCl}_3+\mathrm{Cl}_3 \mathrm{~K}_{\mathrm{c}}=1.844$ 3.0 moles of $\mathrm{PCl}_5$ is introduced in a 1 L closed reaction vessel at 380 K...

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In the given figure, two wheels P and Q are connected by a belt B. The radius of P is...

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The two thin coaxial rings, each of radius 'a' and having charges +Q and –Q respectively are separated by a...

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Spin only magnetic moment of an octahedral complex of $\mathrm{Fe}^{2+}$ in the presence of a strong field ligand in BM...

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An electric appliance supplies $6000 \mathrm{~J} / \mathrm{min}$ heat to the system. If the system delivers a power of 90...

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The resistance of a conductor at 15ºC is 16 $\Omega$ at 100ºC is 20$\Omega$ What will be the temperature coefficient...

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A light beam is described by $E=800 \sin \omega\left(t-\frac{x}{c}\right)$. An electron is allowed to move normal to the propagation of...

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For water at $100^{\circ} \mathrm{C}$ and $1 \mathrm{bar}, \Delta_{\text {vap }} \mathrm{H}-\Delta_{\text {vap }} \mathrm{U}=$ $\_\_\_\_$ $\times 10^2 \mathrm{~J} \mathrm{~mol}^{-1}$....

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Let $S_n$ be the sum of the first $n$ terms of ah arithmetic progression. If $S_{3 n}=3 S_{2 n}$, then...

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Metallic sodium does not react normally with :

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If the co-efficient of $x^7$ and $x^8$ in the expansion of $\left(2+\frac{x}{3}\right)^n$ are equal, then the value of $n$ is...

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Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at...

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In gaseous triethyl amine the "–C–N–C–" bond angle is ________ degree.

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A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies...

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A fair coin is tossed $n$-times such that the probability of getting at least one head is at least 0.9...

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The angle between vector $(\vec{A})$ and $(\vec{A}-\vec{B})$ is :-

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Outermost electronic configuration of a group 13 element, E , is $4 \mathrm{~s}^2, 4 \mathrm{p}^1$. The electronic configuration of an...

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The number of geometrical isomers possible in triamminetrinitrocobalt (III) is X and in trioxalatochromate (III) is Y. Then the value...

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Let $f(x)=3 \sin ^4 x+10 \sin ^3 x+6 \sin ^2 x-3, x \in\left[-\frac{\pi}{6}, \frac{\pi}{2}\right]$. Then, $f$ is -

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If $a+b+c=1, a b+b c+c a=2$ and $a b c=3$, then the value of $a 4+b 4+c 4$ is equal...

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An organic compound is subjected to chlorination to get compound A using 5.0 g of chlorine. When 0.5 g of...

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Let a curve $y=f(x)$ pass through the point $\left(2,\left(\log _e 2\right)^2\right)$ and have slope $\frac{2 y}{x \log _e x}$ for...

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1.46 g of a biopolymer dissolved in a 100 mL water at 300 K exerted an osmotic pressure of $...

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Inside a uniform spherical shell : (a) the gravitational field is zero (b) the gravitational potential is zero (c) the...

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A spherical gas balloon of radius 16 meter subtends an angle $60^{\circ}$ at the eye of the observer A while...

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A solution is 0.1 M in $\mathrm{Cl}^{-}$and 0.001 M in $\mathrm{CrO}_4^{-2}$. Solid $\mathrm{AgNO}_3$ is gradually added to it Assuming that...

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Q JEE MAIN 2021 S2

If $(\vec{a}+3 \vec{b})$ is perpendicular to $(7 \vec{a}-5 \vec{b})$ and $(\vec{a}-4 \vec{b})$ is perpendicular to $(7 \vec{a}-2 \vec{b})$, then the...

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The conductivity of a weak acid HA of concentration $0.001 \mathrm{~mol} \mathrm{~L}^{-1}$ is $2.0 \times 10^{-5} \mathrm{~S} \mathrm{~cm}^{-1}$. If $...

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The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital...

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$\mathrm{CO}_2$ gas adsorbs on charcoal following Freundlich adsorption isotherm. For a given amount of charcoal, the mass of $\mathrm{CO}_2$ adsorbed...

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Consider two chemical reactions (A) and (B) that take place during metallurgical process : (A) $\mathrm{ZnCO}_{3(\mathrm{~s})} \xrightarrow{\Delta} \mathrm{ZnO}_{(\mathrm{s})}+\mathrm{CO}_{2(\mathrm{~g})}$ (B) $...

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The density of NaOH solution is $1.2 \mathrm{~g} \mathrm{~cm}^{-3}$. The molality of this solution is $\_\_\_\_$ m. (Round off to...

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Car B overtakes another car A at a relative speed of $40 \mathrm{~ms}^{-1}$. How fast will the image of car...

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An automobile of mass ‘m’ accelerates starting from origin and initially at rest, while the engine supplies constant power P....

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Given below are two statements : One is labelled as Assertion A and the other labelled as Reason R. Assertion...

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The single largest industrial application of dihydrogen is :

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A physical quantity ‘y’ is represented by the formula $y=m^2 r^{-4} g^x l^{-\frac{3}{2}}$ . If the percentage errors found in...

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The correct order of stability of given carbocation is :

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The major product (P) in the following reaction is :

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The magnitude of vectors $\overrightarrow{\mathrm{OA}}, \overrightarrow{\mathrm{OB}}$ and $\overrightarrow{\mathrm{OC}}$ in the given figure are equal. The direction of $\overrightarrow{\mathrm{OA}}+\overrightarrow{\mathrm{OB}}-\overrightarrow{\mathrm{OC}}$ with $x$-axis...

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What will be the magnitude of electric field at point O as shown in figure? Each side of the figure...

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Match List - I with List - II : Choose the most appropriate answer from the options given below

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In the above reactions, product A and product B respectively are :

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The fractional change in the magnetic field intensity at a distance ' $r$ ' from centre on the axis of...

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Staggered and eclipsed conformers of ethane are :

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If a rectangle is inscribed in an equilateral triangle of side length $2 \sqrt{2}$ as shown in the figure, then...

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The equation of a circle is $\operatorname{Re}\left(z^2\right)+2(\operatorname{lm}(z))^2+2 \operatorname{Re}(z)=0$, where $z=x+i y$. A line which passes through the center of the...

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A cylindrical container of volume $4.0 \times 10^{-3} \mathrm{~m}^3$ contains one mole of hydrogen and two moles of carbon dioxide....

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A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in...

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The de-Broglie wavelength of a particle having kinetic energy E is $\lambda$. How much extra energy must be given to...

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The temperature of equal masses of three different liquids x,y and z are 10ºC, 20ºC and 30ºC respectively. The temperature...

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An engine is attached to a wagon through a shock absorber of length 1.5 m . The system with a...

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A carrier wave with amplitude of 250 V is amplitude modulated by a sinusoidal base band signal of amplitude 150...

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A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and...

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A steel rod with $\mathrm{y}=2.0 \times 10^{11} \mathrm{Nm}^{-2}$ and $\alpha=10^{-5^{\circ}} \mathrm{C}^{-1}$ of length 4 m and area of cross-section 10...

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A uniform heating wire of resistance 36 Ω is connected across a potential difference of 240 V. The wire is...

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The average translational kinetic energy of N2 gas molecules at ...........°C becomes equal to the K.E. of an electron accelerated...

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When a body slides down from rest along a smooth inclined plane making an angle of 30° with the horizontal,...

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Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour...

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If the matrix $\mathrm{A}=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 2 & 0 \\ 3 & 0 & -1\end{array}\right]$...

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Consider the following statements : A. Atoms of each element emit characteristics spectrum. B. According to Bohr’s Postulate, an electron...

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Which one of the following pairs of isomers is an example of metamerism ?

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The compound 'A' is a complementary base of __________ in DNA stands.

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oportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is x : 4 where...

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Consider the above reaction and identify the Product P :

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The temperature of 3.00 mol of an ideal diatomic gas is increased by 40.0 °C without changing the pressure of...

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Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their...

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The statement that is INCORRECT about Ellingham diagram is

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Let $X_1, X_2, \ldots \ldots X_{18}$ be eighteen observations such that $\sum_{i=1}^{18}\left(x_i-\alpha\right)=36$ and $\sum_{i=1}^{18}\left(x_i-\beta\right)^2=90$, where $\alpha$ and $\beta$ are distinct...

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Electric field of plane electromagnetic wave propagating through a non–magnetic medium is given by $...

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Consider the function $$ \begin{array}{ll} f(x)=\frac{P(x)}{\sin (x-2)}, & x \neq 2 \\ =7 & x=2 \end{array} $$ Where $\mathrm{P}(\mathrm{x})$ is...

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Match List-I with List-II : Choose the most appropriate match :

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Figure A and B shown two long straight wires of circular cross-section (a and b with a < b), carrying...

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The nuclear activity of a radioactive element becomes $\left(\frac{1}{8}\right)^{\text {th }}$ of its initial value in 30 years. The half-life...

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Let a be an integer such that all the real roots of the polynomial $2 x^5+5 x^4+10 x^3+10 x^2+10 x+10$...

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Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational...

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Let $n \in N$ and $[x]$ denote the greatest integer less than or equal to $x$. If the sum of...

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In a semiconductor, the number density of intrinsic charge carriers at $27^{\circ} \mathrm{C}$ is $1.5 \times 10^{16} / \mathrm{m}^3$. If...

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Find the truth table for the function Y of A and B represented in the following figure.

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Which one among the following chemical tests is used to distinguish monosaccharide from disaccharide ?

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A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm...

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A capacitor is connected to a 20 V battery through a resistance of 10Ω. It is found that the potential...

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Presence of which reagent will affect the reversibility of the following reaction, and change it to a irreversible reaction :

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A force of $\mathrm{F}=(5 \mathrm{y}+20) \mathrm{j} \mathrm{N}$ acts on a particle. The workdone by this force when the particle is...

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Let $L$ be a common tangent line to the curves $4 x^2+9 y^2=36$ and $(2 x)^2+(2 y)^2=31$. Then the square...

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A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed...

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From the given data, the amount of energy required break the nucleus of aluminium ${ }_{13}^{27} \mathrm{Al}$ is $\_\_\_\_$ $...

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Given below are two statements : Statement I : Rutherford's gold foil experiment cannot explain the line spectrum of hydrogen...

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An object of mass 'm' is being moved with a constant velocity under the action of an applied force of...

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Which one of the following statements is NOT correct ?

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Two circuits are shown in the figure (a) & (b). At a frequency of ________rad/s the average power dissipated in...

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Let $y=y(x)$ be the solution of the differential equation $x d y=\left(y+x^3 \cos x\right) d x$ with $y(\pi)=0$, then $y\left(\frac{\pi}{2}\right)$...

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The number of geometrical isomers found in the metal complexes $\left[\mathrm{PtCl}_2\left(\mathrm{NH}_3\right)_2\right],\left[\mathrm{Ni}(\mathrm{CO})_4\right],\left[\mathrm{Ru}\left(\mathrm{H}_2 \mathrm{O}\right)_3 \mathrm{Cl}_3\right]$ and $\left[\mathrm{CoCl}_2\left(\mathrm{NH}_3\right)_4\right]^{+}$respectively, are :

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For the given circuit the current i through the battery when the key in closed and the steady state has...

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A $16 \Omega$ wire is bend to form a square loop. A 9 V supply having internal resistance of $...

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The type of hybridisation and magnetic property of the complex $\left[\mathrm{MnCl}_6\right]^{3-}$, respectively, are :

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The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is

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A message signal of frequency 20 kHz and peak voltage of 20 volt is used to modulate a carrier wave...

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In the given figure, each diode has a forward bias resistance of 30 Ω and infinite resistance in reverse bias....

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Two Carnot engines A and B operate in series such that engine A absorbs heat at $\mathrm{T}_1$ and rejects heat...

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A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV , placed...

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If ${ }^n P_r={ }^n P_{r+1}$ and ${ }^n C_r={ }^n C_{r+1}$, then the value of $r$ is equal to:

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Given below are two statements : Statement I : Aniline is less basic than acetamide. Statement II : In aniline,...

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A system consists of two types of gas molecules $A$ and $B$ having same number density $...

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A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water (μ...

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A simple pendulum of mass ‘m’ length ‘l’ and charge ‘+q’ suspended in the electric field produced by two conducting...

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Let the equation of the pair of lines, $y=p x$ and $y=q x$, can be written as $(y-p x)(y-q x)=0$....

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For a reaction of order n, the unit of the rate constant is :

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Following plots show Magnetization (M) vs Magnetising field (H) and Magnetic susceptibility (χ) vs temperature (T) graph :

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If the arithmetic mean and geometric mean of the $p^{\text {th }}$ and $q^{\text {th }}$ terms of the sequence...

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Two vectors $\vec{X}$ and $\vec{Y}$ have equal magnitude. The magnitude of $(\vec{X}-\vec{Y})$ is $n$ times the magnitude of $(\vec{X}+\vec{Y})$. The...

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The oxidation states of ' $\mathrm{P}^{\prime}$ in $\mathrm{H}_4 \mathrm{P}_2 \mathrm{O}_7, \mathrm{H}_4 \mathrm{P}_2 \mathrm{O}_5$ and $\mathrm{H}_4 \mathrm{P}_2 \mathrm{O}_6$, respectively, are :

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The half life period of radioactive element x is same as the mean life time of another radioactive element y....

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A 100 $\Omega$ resistance, a 0.1 $\mu \mathrm{F}$ capacitor and an inductor are connected in series across a 250 V...

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The parameters of the unit cell of a substance are $a=2.5, b=3.0, c=4.0, \alpha=90^{\circ}, \beta=120^{\circ} \gamma=90^{\circ}$. The crystal system of...

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When radiation of wavelength $\lambda$ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V...

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Two resistors $\mathrm{R}_1=(4 \pm 0.8) \Omega$ and $\mathrm{R}_2=(4 \pm 0.4) \Omega$ are connected in parallel. The equivalent resistance of their...

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A ray of light entering from air into a denser medium of refractive index $\frac{4}{3}$, as shown in figure. The...

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Given below is the plot of a potential energy function U (x) for a system, in which a particle is...

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If $I_{m, n}=\int_0^1 x^{m-1}(1-x)^{n-1} d x$, for $m, n \geq 1$ and $...

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Due to cold weather a 1 m water pipe of cross–sectional area 1 cm2 is filled with ice at –10°C....

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The instantaneous velocity of a particle moving in a straight line is given as $\mathrm{v}=\alpha \mathrm{t}+\beta \mathrm{t}^2$, where $\alpha$ and...

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Let $\alpha$ and $\beta$ be two real numbers such that $\alpha+\beta=1$ and $\alpha \beta=-1$. Let $p_n=(\alpha)^n+(\beta)^n, P_{n-1}=11$ and $p_{n+1}=29$ for...

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The product obtained from the electrolytic oxidation of acidified sulphate solutions, is :

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A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The...

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Match List I with List II. Choose the correct answer from the options given below

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An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of...

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Let the normals at all the points on a given curve pass through a fixed point $(a, b)$. If the...

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The ranges and heights for two projectiles projected with the same initial velocity at angles 42° and 48° with the...

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The given potentiometer has its wire of resistance $10 \Omega$. When the sliding contact is in the middle of the...

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Which one of the following compounds will give orange precipitate when treated with 2,4-dinitrophenyl hydrazine ?

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An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T)...

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A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of $0.8 \sqrt{g h}$...

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Let zbe those complex numbers which satisfy $|z+5| \leq 4$ and $z(1+i)+\bar{z}(1-i) \geq-10, i-\sqrt{-1}$. If the maximum value of $|z+1|^2$...

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The force is given in terms of time t and displacement x by the equation F = A cos Bx...

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The temperature of an ideal gas in 3-dimensions is 300 K. The corresponding de-Broglie wavelength of the electron approximately at...

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Let $f:[0,3] \rightarrow R$ be defined by $f(x)=\min \{x-[x], 1+[x]-x\}$ where $[x]$ is the greatest integer less than or equal...

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If $y=y(x), y \in\left[0, \frac{\pi}{2}\right)$ is the solution of the dirrential equation $\sec y \frac{d y}{d x}-\sin x(x+y)-\sin (x-y)=0$, with...

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A square loop of side 20 cm and resistance 1Ω is moved towards right with a constant speed v0. The...

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A seven-digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed...

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Two spherical soap bubbles of radii $r_1$ and $r_2$ in vacuum combine under isothermal conditions. The resulting bubble has a...

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Let S={1,2,3,4,5,6,7}. Then the number of possible functions $f: S \rightarrow S$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for...

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A cube is placed inside an electric field, $\overrightarrow{\mathrm{E}}-=150 \mathrm{y}^2 \hat{\mathrm{j}}$. The side of the cube is 0.5 m and...

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Two ideal electric dipoles $A$ and $B$ having their dipole moment $p_1$ and $p_2$ respectively are placed on a plane...

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One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27^{\circ} \mathrm{C}$ to...

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Let a plane $P$ pass through the point $(3,7,-7)$ and contain the line, $\frac{x-2}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$. If distance of the plane P...

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Let A_1 be the area of the region bounded by the curves $y=\sin x, y=\cos x$ and $y$-axis in the...

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Consider a planet in some solar system which has a mass double the mass of earth and density equal to...

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A particle of mass ' $m$ ' is moving in time ' $t$ ' on a trajectory given by $$...

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Let $F:[3,5] \rightarrow R$ be a twice differentiable function on $(3,5)$ such that $F(x)=e^{-x} \int_3^x\left(3 t^2+2 t+4 F^{\prime}(t)\right) d t$...

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Let $f(x)=\int_0^x e^t f(t) d t+e^x$ be a differentiable function for all $x \in R$. Then $f(x)$ equals :

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If $\mathrm{g}_{\mathrm{f}}$ is the free charge on the capacitor plates and $\mathrm{g}_{\mathrm{b}}$ is the bound charge on the dielectric slab...

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A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The...

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A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above...

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Let $...

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Let the domain of the function $f(x)=\log _4\left(\log _5\left(\log _3\left(18 x-x^2-77\right)\right)\right)$ be $(a, b)$. Then the value of the integral...

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A balloon was moving upwards with a uniform velocity of $10 \mathrm{~m} / \mathrm{s}$. An object of finite mass is...

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If $\log _3 2, \log _3\left(2^x-\frac{7}{2}\right)$ are in an arithmetic progression, then the value of $x$ is equal to $\_\_\_\_$...

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An electric bulb rated as 200 W at 100 V is used in a circuit having 200 V supply. The...

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If the mirror image of the point $(1,3,5)$ with respect to the plane $4 x-5 y+2 z=8$ is $...

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Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}$ and $\vec{c}=\hat{j}-\hat{k}$ be three vectors such that $\vec{a} \times \vec{b}=\vec{c}$ and $\vec{a} \cdot \vec{b}=1$. If the length...

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The expected graphical representation of the variation of angle of deviation ‘δ’ with angle of incidence ‘i’ in a prism...

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A $10 \Omega$ resistance is connected across $220 \mathrm{~V}-50 \mathrm{~Hz} \mathrm{AC}$ supply. The time taken by the current to change...

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For real numbers $\alpha$ and $\beta$, consider the following system of linear equations: $x+y-z=2, x+2 y+\alpha z=1,2 x-y+z=\beta$. If the...

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A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at...

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An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV....

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Let $...

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The value of aluminium susceptibility is $2.2 \times 10^{-5}$. The percentage increase in the magnetic field if space within a...

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Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform...

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Let $A(1,4)$ and $B(1,-5)$ be two points. Let $P$ be a point on the circle $(x-1)^2+(y-1)^2=1$ such that $...

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In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the...

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In the given potentiometer circuit arrangement, the balancing length AC is measured to be 250 cm . When the galvanometer...

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A circular conducting coil of radius 1 m is being heated by the change of magnetic field $\vec{B}$ passing perpendicular...

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Let $f(x)$ be a differentiable function at $x=a$ with $f^{\prime}(a)=2$ and $f(a)=4$. Then $\lim _{x \rightarrow 0} \frac{x f(a)-a f(x)}{x-a}$...

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a heat engine has an efficiency of $\frac{1}{6}$. When the temperature ofsink is reduced by $62^{\circ} \mathrm{C}$ its efficiency get...

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The probability that a randomly selected 2 -digit number belongs to the set $\left\{n \in N:\left(2^n-2\right)\right.$ is a multiple of...

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An inductor of 10 mH is connected to a 20 V battery through a resistor of $10 \mathrm{k} \Omega$ and...

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A prism of refractive index μ and angle of prism A is placed in the position of minimum angle of...

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The sum of the series $\sum_{n=1}^{\infty} \frac{n^2+6 n+10}{(2 n+1)!}$ is equal to:

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Let $\alpha, \beta$ be two roots of the equation $x^2+(20)^{1 / 4} x+(5)^{\frac{1}{2}}=0$. Then $\alpha^8+\beta^8$ is equal to

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A force $\overrightarrow{\mathrm{F}}=(40 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}) \mathrm{N}$ acts on a body of mass 5 kg . If the body starts from...

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22. Student A and student B used two screw gauges of equal pitch and 100 equal circular divisions to measure...

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Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes...

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In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the...

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If $0

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A body of mass 2 kg moving with a speed of $4 \mathrm{~m} / \mathrm{s}$. makes an elastic collision with...

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Let $f: R \rightarrow R$ be a function such that $f(2)=4$ and $f(2)=1$. Then, the value of $...

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The relation between time $t$ and distance $x$ for a moving body is given as $t=m x^2+n x$, where $m$...

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Two tangents are drawn from the point $P(-1,1)$ to the circle $x^2+y^2-2 x-6 y+6=0$. If these tangents touch the circle...

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The minimum and maximum distances of a planet revolving around the Sun are $x_1$ and $x_2$. If the minimum speed...

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Consider the following system of equations : $$ \begin{aligned} & x+2 y-3 z=a \\ & 2 x+6 y-11 z=b \\...

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Let the plane passing through the point (–1, 0, –2) and perpendicular to each of the planes 2x + y...

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Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th...

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Let $y=y(x)$ be solution of the differential equation $\log _e\left(\frac{d y}{d x}\right)=3 x+4 y$, with $y(0)=0$. If $...

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Q JEE MAIN 2021

In 5 minutes, a body cools from 75ºC to 65ºC at room temperature of 25ºC. The temperature of body at...

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Let $f:\left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \rightarrow R$ be defined as $f(x)=\left\{\begin{array}{cc}(1+|\sin x|)^{\frac{3 a}{|\sin x|}}, & -\frac{\pi}{4}

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If the locus of the mid-point of the line segment from the point $(3,2)$ to a point on the circle,...

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Three students $S_1, S_2$ and $S_3$ perform an experiment for determining the acceleration due to gravity (g) using a simple...

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In amplitude modulation, the message signal $...

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Let $A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]$. If $A^{-1}=\alpha I+\beta A, \alpha, \beta \in R, I$ is a $...

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Q JEE MAIN 2021

If $\sin \theta+\cos \theta=\frac{1}{2}$, then $16(\sin (2 \theta)+\cos (4 \theta)+\sin (6 \theta))$ is equal to :

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The area of cross-section of a railway track is $0.01 \mathrm{~m}^2$. the temperature variation is $10^{\circ} \mathrm{C}$. Coefficient of linear...

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In the given figure, there is a circuit of potentiometer of length AB = 10 m. The resistance per unit...

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Q JEE MAIN 2021

The compound statement $(P \vee Q) \wedge(\sim P) \Rightarrow Q$ is equivalent of:

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A ray of light passing through a prism $(\mu=\sqrt{3})$ suffers minimum deviation. It is found that the angle of incidence...

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A linearly polarized electromagnetic wave in vacuum is $\mathrm{E}=3.1 \cos \left[(1.8) \mathrm{z}-\left(5.4 \times 10^6\right) \mathrm{t}\right] \hat{\mathrm{iN}} / \mathrm{C}$ is incident...

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The centre of a wheel rolling on a plane surface moves with a speed $v_0$. A particle on the rim...

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If the coefficients of $x^7$ in $\left(x^2+\frac{1}{b x}\right)^{11}$ and $x^{-7}$ in $\left(x-\frac{1}{b x^2}\right)^{11}, b \neq 0$, are equal, then the...

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Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The...

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Q JEE MAIN 2021

Let $F_1(A, B, C)=(A \wedge \sim B) \vee[\sim C \wedge(A \vee B)] \vee \sim A$ and $...

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Three particles P, Q and R are moving along the vectors $\vec{A}=\hat{i}+\hat{j}, \vec{B}=\hat{j}+\hat{k}$ and $\vec{C}=-\hat{i}+\hat{j}$ respectively. They strike on a...

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A ray of light through $(2,1)$ is reflected at a point $P$ on the $y$-axis and then passes through the...

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In the Young's double slit experiment, the distance between the slits varies in time as $d(t)=d_0+a_0 \sin \omega t$; where...

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The total charge enclosed in an incremental volume of $2 \times 10^{-9} \mathrm{~m}^3$ located at the origin is $\_\_\_\_$ $...

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Let $L$ be a line obtained from the intersection of two planes $x+2 y+z=6$ and $y+2 z=4$. If point $...

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In an electric circuit, a call of certain emf provides a potential difference of 1.25 V across a load resistance...

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The position of the centre of mass of a uniform semi-circular wire of radius ' $R$ ' placed in $x-y$...

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In a given circuit diagram, a 5 V zener diode along with a series resistance is connected across a 50...

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Let $E_1: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$. Let $E_2$ be ahother ellipse such that it touches the end points of major axis of...

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If a tangent to the ellipse $x^2+4 y^2=4$ meets the tangents at the extremities of its major axis at $B$...

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Let a line $L$ : $2 x+y=k, k>0$ be a tangent to the hyperbola $x^2-y^2=3$. If $L$ is also a...

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Let $x$ be a random variable such that the probability function of a distribution is given by $...

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Let $f: R \rightarrow R$ be defined as $...

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If $P=\left[\begin{array}{cc}1 & 0 \\ 1 / 2 & 1\end{array}\right]$, then $P^{50}$ is :

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If the domain of the function $f(x)=\frac{\cos ^{-1} \sqrt{x^2-x+1}}{\sqrt{\sin ^{-1}\left(\frac{2 x-1}{2}\right)}}$ is the interval $(\alpha, \beta]$, then $\alpha+\beta$ is equal...

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Consider function $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ and $\mathrm{g}: \mathrm{B} \rightarrow \mathrm{C}(\mathrm{A}, \mathrm{B}, \mathrm{C} \subseteq \mathrm{R})$ such that (gof) ${ }^{-1}$...

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The number of solutions of $\sin ^7 x+\cos ^7 x=1, x \in[0,4 \pi]$ is equal to

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The number of real solutions of the equation, $\mathrm{x}^2-|\mathrm{x}|-12=0$ is:

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Let $n$ denote the number of solutions of the equation $z^2+3 \bar{z}=0$, where $z$ is a complex number. Then the...

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If $|\vec{a}|=2, \mid \vec{b}=5$ and $|\vec{a} \times \vec{b}|=8$, then $|\vec{a} \cdot \vec{b}|$ is equal to:

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The number of distinct real roots of $...

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Let the circle $\mathrm{S} ; 36 x^2+36 y^2-108 x+120 y+C=0$ be such that it neither intersects nor touches the coordinate...

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If $[x]$ be the greatest integer less than or equal to $x$, then $\sum_{n=8}^{100}\left[\frac{(-1)^n n}{2}\right]$ is equal to:

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Let $[x]$ denote the greatest integer less than or equal to $x$. Then, the values of $x \in R$ satisfying...

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Let $a, b$ and $c$ be distinct positive numbers. If the vectors $a-a \hat{i}+a \hat{j}+c \hat{k}, \hat{i}+\hat{k}$ and $...

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Let $A=\left[a_i\right]$ be a real matrix of order $3 \times 3$, such that $a_{i 1}+a_{i 2}+a_{i 3}=1$, for $i=1,2,3$. Then,...

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Q JEE MAIN _2021_

Which of the following Boolean expressions is not a tautology?

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The value of the integral $\int_{-1}^1 \log \left(x+\sqrt{x^2+1}\right) d x$ is :

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The lowest integer which is greater than $\left(1+\frac{1}{10^{100}}\right)^{10^{100}}$ is

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If the shortest distance between the straight lines $3(x-1)=6(y-2)=2(z-1)$ and $4(x-2)=2(y-\lambda)=(z-3)$, $\lambda \in \mathrm{R}$ is $\frac{1}{\sqrt{38}}$, then the integral value...

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The value of $\cot \frac{\pi}{24}$ is :

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The values of $\lambda$ and $\mu$ such that the system of equations $x+y+\mid z=6,3 x+5 y+5 z=26, x+2 y+\lambda z=\mu$...

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Consider the statement "The match will be played only if the weather is good and ground is not wet". Select...

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If the greatest value of the term independent of ' $x$ ' in the expansion of $...

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If $f(x)=\left\{\begin{array}{cc}\int_0^x(5+|1-t|) d t, & x>2 \\ 5 x+1, & x \leq 2\end{array}\right.$, then

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What will be the magnitude of electric field at point O as shown in figure? Each side of the figure...

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the first of the two samples in a group has 100 items with mean 15 and standard deviation 3 ....

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Consider the following statements : A. Atoms of each element emit characteristics spectrum. B. According to Bohr’s Postulate, an electron...

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The sum of all those terms which are rational numbers in the expansion of $\left(2^{1 / 3}+3^{1 / 4}\right)^{12}$ is:

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Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their...

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If the value of $\lim _{x \rightarrow 0}(2-\cos x \sqrt{\cos 2 x})^{\left(\frac{x+2}{x^2}\right)}$ is equal to $e^a$, then a is equal...

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Let $y=m x+c, m>0$ be the focal chord of $y^2=-64 x$, which is tangent to $(x+10)^2+y^2=4$. Then, the value of...

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Figure A and B shown two long straight wires of circular cross-section (a and b with a < b), carrying...

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There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are...

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Let $a, b, c, d$ be in arithmetic progression with common difference $\lambda$. If $...

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Find the truth table for the function Y of A and B represented in the following figure.

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Let $T$ be the tangent to the ellipse $E: x^2+4 y^2=5$ at the point $P(1,1)$. If the area of the...

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Two Carnot engines A and B operate in series such that engine A absorbs heat at $T_1$ and rejects heat...

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A carrier wave $V_c(t)=160 \sin \left(2 \pi \times 10^6 t\right)$ volts is made to vary between $V_{\max }=200 \mathrm{~V}$ and...

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Two billard balls of equal mass 30 g strike a rigid wall with same speed of 108 kmph (as shown)...

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If the area of the bounded region $...

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The half-life of ${ }^{198} \mathrm{Au}$ is 3 days. If atomic weight of ${ }^{198} \mathrm{Au}$ is $...

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Let C be the set of all complex numbers. Let $...

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A simple pendulum of mass ' m' length ' l ' and charge ' $+q$ ' suspended in the electric...

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The frequency of a car horn encountered a change from 400 Hz to 500 Hz. When the car approaches a...

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A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to...

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The value of the definite integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{\left(1+e^{x \cos x}\right)\left(\sin ^4 x+\cos ^4 x\right)}$ is equal to :

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Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the material...

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Let $\vec{a}=\hat{i}+\hat{j}+2 \hat{k}$ and $\vec{b}=-\hat{i}+2 \hat{j}+3 \hat{k}$. Then the vector product $(\vec{a}+\vec{b}) \times((\vec{a} \times((\vec{a}-\vec{b}) \times \vec{b})) \times \vec{b})$ is equal...

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Q JEE MAIN 2021

an electric dipole is placed on $x$-axis in proximity to a line charge of linear charge density $...

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A ray of laser of a wavelength 630 nm is incident at an angle of 30º at the diamond-air interface....

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If the shortest distance between the lines $\vec{r}_1=\alpha \hat{i}+2 \hat{j}+2 \hat{k}+\lambda(\hat{i}-2 \hat{j}+2 \hat{k}), \lambda \in R, \alpha>0$ and $...

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Q JEE MAIN 2021

The value of $\lim _{x \rightarrow \infty} \frac{1}{n} \sum_{j=1}^n \frac{(2 j-1)+8 n}{(2 j-1)+4 n}$ is equal to :

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A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with a frictionless pistion. The gas...

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The number of rational terms in the binomial expansion of $\left(4^{\frac{1}{4}}+5^{\frac{1}{6}}\right)^{120}$

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If the mean and variance of the following data : $6,10,7,13, a, 12, b, 12$ are 9 and $\frac{37}{4}$ respectively,...

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A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm'...

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A $100 \Omega$ resistance, a $0.1 \mu \mathrm{~F}$ capacitor and an inductor are connected in series across a 250 V...

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Let $P$ be a plane passing through the points $(1,0,1),(1,-2,1)$ and $(0,1,-2)$. Let a vector $\overrightarrow{\mathbf{a}}=\alpha \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}+\gamma \hat{\mathbf{k}}$ be...

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In a uniform magnetic field, the magnetic needle has a magnetic moment $9.85 \times 10^{-2} \mathrm{~A} / \mathrm{m}^2$ and moment...

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A parallel plate capacitor with plate area ‘A’ and distance of separation ‘d’ is filled with a dielectric. What is...

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let $A=\left(\begin{array}{ccc}1 & -1 & 0 \\ 0 & 1 & -1 \\ 0 & 0 & 1\end{array}\right)$ and $...

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Q JEE MAIN 2021

Given below is the plot of a potential energy function $\mathrm{U}(\mathrm{x})$ for a system, in which a particle is in...

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The amplitude of upper and lower side bands of A.M. wave where a carrier signal with frequency 11.21 MHz ,...

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Intensity of sunlight is observed as $0.092 \mathrm{Wm}^{-2}$ at a point in free space. What will be the peak value...

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Let $\vec{a}, \vec{b}, \vec{c}$-be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle $\theta$, with...

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Q JEE-MAIN 2021

Match List I with List II

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A transistor is connected in common emitter circuit configuration, the collector supply voltage is 10 V and the voltage drop...

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Let the tangent to the parabola $\mathrm{S}: \mathrm{y}^2=2 \mathrm{x}$ at the point $\mathrm{P}(2,2)$ meet the x -axis at Q and...

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A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross...

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What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?

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Some muclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of...

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The probability of selecting integers $a \in[-5,30]$ such that $x^2+2(a+4) x-5 a+64>0$, for all $x \in R$, is :

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A prism of refractive index $n_1$ and another prism of refractive index $n_2$ are stuck together (as shown in the...

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In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the...

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What should be the height of transmitting antenna and the population covered if the television telecast is to cover a...

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Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that...

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Q JEE MAIN 2021

Match List I with List II.

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A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero...

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Match List-I with List-II : Choose the correct answer from the options given below :

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SOLVE THE FIG

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Let ' $a$ ' be a real number such that the function $f(x)=a x^2+6 x-15, x \in R$ is increasing...

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What should be the order of arrangement of de-Broglie wavelength of electron ( $\lambda_{\mathrm{e}}$ ), an $\alpha$-particle ( $\lambda_\alpha$ )...

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An electron of mass me and a proton of mass $\mathrm{m}_{\mathrm{p}}$ are accelerated through the same potential difference. The ratio...

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An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period $(\mathrm{T})$...

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Let $y=y(x)$ be the solution of the differential equation $e^x \sqrt{1-y^2} d x+\left(\frac{y}{x}\right) d y=0, y(1)=-1$. Then the value of...

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Q JEE-MAIN 2021

Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R....

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The number of real roots of the equation $\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{4}$ is :

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Q JEE MAIN 2021

Let $\vec{a}-=2 \hat{i}+\hat{j}-2 \hat{k}$ and $\vec{b}-=\hat{i}+\hat{j}$. If $\vec{c}-$ is a vector such that $\vec{a} \cdot \vec{c}=|\vec{c}|,|\vec{c}-\vec{a}|=2 \sqrt{2}$ and the angle...

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Q JEE MAIN 2021

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27^{\circ} \mathrm{C}$ to...

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A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the...

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Let P be an arbitrary point having sum of the squares of the distance from the planes $\mathrm{x}+\mathrm{y}+\mathrm{z}=0, l \mathrm{x}-\mathrm{nz}=0$...

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Q JEE MAIN 2021

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ______ $\pi \mathrm{J}$.

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Let $A=\left[a_{i j}\right]$ be a $3 \times 3$ matrix, where $...

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Let $\vec{x}$ be a vector in the plane containing vectors $\vec{a}=2 \hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}+2 \hat{j}-\hat{k}$. If the vector $\vec{x}$ is...

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Q JEE MAIN 2021

A body having specific charge 8 $\mu \mathrm{C} / \mathrm{g}$ is resting on a frictionless plane at a distance 10...

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Q JEE MAIN 2021

The coefficien of $x^{256}$ in the expansion of $(1-x)^{101}\left(x^2+x+1\right)^{100}$ is :

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Q JEE-MAIN 2021

Let $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ and $B=\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]$ such that $A B=B$ and...

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Q JEE MAIN 2021

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above...

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Let the coefficients of third, fourth and fifth terms in the expansion of $\left(x+\frac{a}{x^2}\right)^n, x \neq 0$ be in the...

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Q JEE MAIN 2021

The amplitude of wave disturbance propagating in the positive x-direction is given by $y=\frac{1}{(1+x)^2}$ at time t = 0 and...

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Q JEE-MAIN 2021

Consider a set of 3n numbers having variance 4. In this set, the mean of first 2n numbers is 6...

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Let $\tan \alpha, \tan \beta$ and $\tan \gamma, \alpha, \beta, \gamma \neq \frac{(2 \mathrm{n}-1) \pi}{2}, \mathrm{n} \in \mathrm{N}$ be the...

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Q JEE MAIN 2021

In an LCR series circuit, an inductor 30 mH and a resistor $1 \Omega$ are connected to an AC source...

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Q JEE-MAIN 2021

Let $f:[-3,1] \rightarrow R$ given as $$ f(x)=\left\{\begin{array}{cc} \min \left\{(x+6), x^2\right\}, & -3 \leq x \leq 0 \\ \max \left\{\sqrt{x},...

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Q JEE MAIN 2021

Let $y=y(x)$ be the solution of the differential equation $...

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The expected graphical representation of the variation of angle of deviation ' $\delta$ ' with angle of incidence ' i...

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Let $f:[-1,1] \rightarrow R$ be defined as $f(x)=a x^2+b x+c$ for all $x \in[-1,1]$ where $a, b, c \in R$...

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Q JEE MAIN 2021

In a spring gun having spring constant 100 N/m a small ball 'B' of mass 100 g is put in...

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If $1, \log _{10}\left(4^x-2\right)$ and $\log _{10}\left(4^x+\frac{18}{5}\right)$ are in arithmetic progression for a real number $x$, then the value of...

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A particle of mass $9.1 \times 10^{-31} \mathrm{~kg}$ travels in a medium with a speed of $10^6 \mathrm{~m} / \mathrm{s}$...

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An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV....

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A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance $200 \mu \mathrm{~F}$...

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In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius $0.5 \AA$. If the...

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The radiation corresponding to 32 transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons...

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Suppose two planets (spherical in shape) of radii $R$ and $2 R$, but mass $M$ and $9 M$ respectively have...

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Consider an electrical circuit containing a two way switch ' $S$ '. Initially $S$ is open and then $T_1$ is...

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A body takes 4 min . to cool from $61^{\circ} \mathrm{C}$ to $59^{\circ} \mathrm{C}$. If the temperature of the surroundings...

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Let $[x]$ denote the greatest integer $\leq x$, where $x \in R$. If the domain of the real valued function...

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The entropy of any system is given by $\mathrm{S}=\alpha^2 \beta 1 \mathrm{n}\left[\frac{\mu \mathrm{kR}}{\mathrm{J} \beta^2}+3\right]$ Where $\alpha$ and $\beta$ are the...

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Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the...

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A nucleus with mass number 184 initially at rest emits an $\alpha$-particle. If the Q value of the reaction is...

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Two identical tennis balls each having mass ' $m$ ' and charge ' $q$ ' are suspended from a fixed...

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Consider a situation in which reverse biased current of a particular P-N junction increases when it is exposed to a...

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A 0.07 H inductor and a $12 \Omega$ resistor are connected in series to a $220 \mathrm{~V}, 50 \mathrm{~Hz}$ ac...

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The value of $\int_{-2}^2\left|3 x^2-3 x-6\right| d x$ is $\_\_\_\_$ .

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Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined...

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The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then...

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Q JEE MAIN 2021

Choose the correct option :

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If the curve, $y=y(x)$ represented by the solution of the differential equation $\left(2 x y^2-y\right) d x+x d y=0$, passes...

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A carrier wave with amplitude of 250 V is amplitude modulated by a sinusoidal base band signal of amplitude 150...

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For the circuit shown below, calculate the value of $\mathrm{I}_z:$

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An engine is attached to a wagon through a shock absorber of length 1.5 m . The system with a...

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If $\lim _{x \rightarrow 0} \frac{a x-\left(e^{4 x}-1\right)}{a x\left(e^{4 x}-1\right)}$ exists and is equal to $b$, then the value of...

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If in a triangle $A B C, A B=5$ units, $\angle B=\cos ^{-1}\left(\frac{3}{5}\right)$ and radius of circumcircle of $...

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The value of tension in a long thin metal wire has been changed from $\mathrm{T}_1$ to $\mathrm{T}_2$. The lengths of...

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A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and...

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A ball is thrown up with a certain velocity so that it reaches a height ' $h$ '. Find the...

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A bullet of ' 4 g ' mass is fired from a gun of mass 4 kg . If the...

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A line is a common tangent to the circle $(x-3)^2+ y^2=9$ and the parabola $y^2=4 x$. If the two points...

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Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is...

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A butterfly is flying with a velocity $4 \sqrt{2} \mathrm{~m} / \mathrm{s}$ in North-East direction. Wind is slowly blowing at...

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Statement I : The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet. Statement II : At high...

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If ' $f$ ' denotes the ratio of the number of nuclei decayed $\left(N_d\right)$ to the number of nuclei at...

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A ray of light passes from a denser medium to a rarer medium at an angle of incidence $i$. The...

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A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic...

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If $z$ and $\omega$ are two complex numbers such that $|z \omega|=1$ and arg $(z)-\arg (\omega) \frac{3 \pi}{2}$, then $...

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A steel rod with $y=2.0 \times 10^{11} \mathrm{Nm}^{-2}$ and $\alpha=10^{-5} \mathrm{C}^{-1}$ of length 4 m and area of cross-section $...

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To is the time period of a simple pendulum at a place. If the length of the pendulum is reduced...

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A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area...

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Consider a mixture of gas molecule of types A, B and C having masses $\mathrm{m}_{\mathrm{A}}

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If the remainder when x is divided by 4 is 3 , then the remainder when $(2020+\mathrm{x})^{2022}$ is divided by...

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A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance...

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Let $A=\left[\begin{array}{ll}2 & 3 \\ a & 0\end{array}\right], a \in R$ be written as $P+Q$ where $P$ is a symmetric...

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Assertion $\mid \mathrm{A}$ : If $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are four points on a semi-circular arc with centre at '...

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Let ${ }^{\mathrm{a}}=\hat{\mathrm{i}}+\alpha \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{b}}=3 \hat{\mathrm{i}}+\alpha \hat{\mathrm{j}}+\hat{\mathrm{k}}$. If the area of the parallelogram whose adjacent sides are represented...

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What will be the projection of vector $\overrightarrow{\mathrm{A}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\mathrm{k}$ on vector $\overrightarrow{\mathrm{B}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$ ?

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A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm2 is joined with a similar Aluminium (Al)...

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A uniform heating wire of resistance 36 Ω is connected across a potential difference of 240 V. The wire is...

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A function $f$ is defined on $[-3,3]$ as $$ f(x)=\left\{\begin{array}{cc} \min \left\{|x|, 2-x^2\right\}, & -2 \leq x \leq 2 \\...

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In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas....

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A current of 5 A is passing through a non-linear magnesium wire of cross-section $0.04 \mathrm{~m}^2$ . At every point...

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Let three vectors $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ be such that $\overline{\mathrm{a}} \times \overline{\mathrm{b}}=\overline{\mathrm{c}}, \overline{\mathrm{b}} \times-\overline{\mathrm{c}}=\overline{\mathrm{a}}$ and $|\overline{\mathrm{a}}|=2$. Then which one...

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In Young’s double slit experiment, if the source of light changes from orange to blue then :

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In a circuit consisting of a capacitance and a generator with alternating emf $\mathrm{E}_9=\mathrm{E}_{90} \sin \omega t, \mathrm{~V}_c$ and $\mathrm{I}_c$...

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The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for...

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The total number of two digit numbers ' n ', such that $3^n+7^n$ is a multiple of 10 , is...

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If $\int_0^{100 \pi} \frac{\sin ^2 x}{e^{\left(\frac{x}{\pi}-\left[\frac{x}{\pi}\right]\right)}} d x=\frac{\alpha \pi^3}{1+4 \pi^2}, \alpha \in R$ where $[x]$ is the greatest integer less...

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If $\alpha$ and $\beta$ are the distinct roots of the equation $x^2+(3)^{1 / 4} x+3^{1 / 2}=0$, then the value...

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In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor....

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The average translational kinetic energy of $\mathrm{N}_2$ gas molecules at $\_\_\_\_$ ${ }^{\circ} \mathrm{C}$ becomes equal to the K.E. of...

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The following system of linear equations 2x + 3y + 2z = 9 3x + 2y + 2z = 9...

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Let a vector $\bar{a}$ be coplanar with vectors $\bar{b}=2 \hat{i}+\hat{j}+\hat{k}$ and $\bar{c}=\hat{i}-\hat{j}+\hat{k}$. If $\bar{a}$ is perpendicular to $...

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A capacitor of capacitance $\mathrm{C}=1 \mu \mathrm{~F}$ is suddenly connected to a battery of 100 volt through a resistance $...

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The value of the integral $\int_{-1}^1 \log _e(\sqrt{1-x}+\sqrt{1+x}) d x$ is equal to :

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A certain charge Q is divided into two parts q and (Q–q). How should the charges Q and q be...

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Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 × 2 matrices. The...

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Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of...

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Let x denote the total number of one-one functions from a set A with 3 elements to a set B...

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Let $y=y(x)$ be the solution of the differential equation $...

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Choose the correct answer from the options given below :

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A nucleus of mass M emits -ray photon of frequency ‘v’. The loss of internal energy by the nucleus is...

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The relative permittivity of distilled water is 81 . The velocity of light in it will be : (Given $\left.\mu_r=1\right)$

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Let $f: R \rightarrow R$ be defined as $...

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When a body slides down from rest along a smooth inclined plane making an angle of $30^{\circ}$ with the horizontal,...

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The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are...

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The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean...

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Let $a$ and $\beta$ be the roots of $x^2-6 x-2=0$. If $\alpha_n=\alpha^n -\beta^n$ for $n \geq 1$, then the value...

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Let a be a positive real number such that $\int_0^a e^{x-[x]} d x=10 e-9$ where $[x]$ is the greatest integer...

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In the given figure, a battery of emf E is connected across a conductor PQ of length ' I '...

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Let $S_n$ denote the sum of first $n$-terms of an arithmetic progression. If $S_{10}=530, S_5=140$, then $S_{20}-S_6$ is equal to

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A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let rd and $\mathbf{r}_\alpha$...

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Let $L$ be the line of intersection of planes $\vec{r} \cdot(\hat{i}-\hat{j}+2 \hat{k})=2$ and $\vec{r} \cdot(2 \hat{i}+\hat{j}-\hat{k})=2$. If $P(\alpha, \beta, \gamma)$...

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Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that...

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Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour...

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Let $y=y(x)$ be the solution of the differential equation $x d y-y d x=\sqrt{\left(x^2-y^2\right)} d x, x \geq 1$, with...

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Let $P$ be $a$ plane containing the line $\frac{x-1}{3}=\frac{y+6}{4}=\frac{z+5}{2}$ and parallel to the line $\frac{x-3}{4}=\frac{y-2}{-3}=\frac{z+5}{7}$. If the point $(1,-1, \alpha)$...

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If $\vec{A}$ and $\vec{B}$ are two vectors satisfying the relation $\vec{A} \cdot \vec{B}=|\vec{A} \times \vec{B}|$. Then the value of $|\vec{A}-\vec{B}|$...

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Q JEE MAIN 2021

The Boolean expression $(p \wedge \sim q) \Rightarrow(q \vee \sim p)$ is equivalent to :

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$\lim _{n \rightarrow \infty}\left[\frac{1}{n}+\frac{n}{(n+1)^2}+\frac{n}{(n+2)^2}+\ldots . .+\frac{n}{(2 n-1)^2}\right]$ is equal to

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If $(2021)^{3762}$ is divided by 17 , then the remainder is $\_\_\_\_$ .

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Let ${ }^n C_r$ denote the binomial coefficient of $\underline{X^r}$ in the expansion of $(1+\mathrm{x})^{\mathrm{n}}$. If $...

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Let $f: R \rightarrow R$ satisfy the equation $f(x+y)=f(x)$. $f(y)$ for all $x, y \in R$ and $f(x) \neq 0$...

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Let the mirror image of the point $(1,3, a)$ with respect to the plane $\overrightarrow{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})-\mathrm{b}=0$ be $(-3,5$, 2)....

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Q JEE MAIN 2021

Proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is x : 4 where...

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Let $P(x)$ be real polynomial of degree 3 which vanishes at $x=-3$. Let $P(x)$ have local minima at $x=1$, local...

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$$ \text { If } I_n=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \cot ^n x   d x, \text { then : } $$

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If the equation of plane passing through the mirror image of a point $(2,3,1)$ with respect to line $\frac{x+1}{2}=\frac{y-3}{1}=\frac{z+2}{-1}$ and...

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If $\lim _{x \rightarrow 0} \frac{\alpha x e^x-\beta \log _e(1+x)+\gamma x^2 e^{-x}}{x \sin ^2 x}=10, \alpha, \beta, \gamma \in R$,...

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If the Boolean expression $(p \wedge q)(p \otimes q)$ is a tautology, then and $\otimes$ are respectively given by

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The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from $0^{\circ} \mathrm{C}$...

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Let $\left\{a_n\right\}_{n=1}^{\infty}$ be a sequence such that $a_1=1, a_2=1$ and $a_{n+2}=2 a_{n+1}+a_n$ for all $n \geq 1$. Then the value...

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The minimum value of $f(x)=a^{a x}+a^{1-a x}$, where $a, x \in R$ and $a>0$, is equal to :

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The term independent of x in the expansion of $\left[\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right]^{10}, x \neq 1$ is...

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The temperature of 3.00 mol of an ideal diatomic gas is increased by $40.0^{\circ} \mathrm{C}$ without changing the pressure of...

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For $k \in N$, let $\frac{1}{\alpha(\alpha+1)(\alpha+2) \ldots .(\alpha+20)}=\sum_{K=0}^{20} \frac{A_k}{\alpha+k}$, where $\alpha>0$. Then the value of $100\left(\frac{A_{14}+A_{15}}{A_{13}}\right)^2$ is equal to $\_\_\_\_$...

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Let the tangent to the circle $x^2+y^2=25$ at the point $R(3,4)$ meet $x$-axis and $y$-axis at point $P$ and $Q$,...

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If $\sum_{r=1}^{10} r!\left(r^3+6 r^2+2 r+5\right)=\alpha(11!)$ then the value of $\alpha$ is equal to $\_\_\_\_$ .

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Let $I$ be an identity matrix of order $2 \times 2$ and $P=\left[\begin{array}{ll}2 & -1 \\ 5 & -3\end{array}\right]$. Then...

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A radioactive substance decays to $\left(\frac{1}{16}\right)^{\text {th }}$ of its initial activity in 80 days. The half life of the...

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Let a function $\mathrm{g}:[0,4] \rightarrow R$ be defined as $...

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There are two infinitely long straight current carrying conductors and they are held at right angles to each other so...

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If $f(x)$ and $g(x)$ are two polynomials such that the polynomial $P(x)=f\left(x^3\right)+x g\left(x^3\right)$ is divisible by $x^2+x$ +1 , then...

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The value of the limit $\lim _{\theta \rightarrow 0} \frac{\tan \left(\pi \cos ^2 \theta\right)}{\left(2 \pi \sin ^2 \theta\right)}$ equal to:

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A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The...

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Let $f: R \rightarrow R$ be a function defined as $...

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A certain metallic surface is illuminated by monochromatic radiation of wavelength $\lambda$. The stopping potential for photoelectric current for this...

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Let $L$ be a tangent line to the parabola $y^2=4 x-20$ at $(6,20)$. If $L$ is also a tangent to...

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If for the matrix, $A=\left[\begin{array}{cc}1 & -\alpha \\ \alpha & \beta\end{array}\right], A A^{\top}=I_2$, then the value of $\alpha^4+\beta^4$ is :

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Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region...

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One mole of an ideal gas at $27^{\circ} \mathrm{C}$ is taken from A to B as shown in the given...

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The area bounded by the curve $4 y^2=x^2(4-x)(x-2)$ is equal to:

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Consider the function $f: R \rightarrow R$ defined by $$ f(x)=\left\{\begin{array}{cl} \left(2 \sin \left(\frac{1}{x}\right)\right)|x|, & x \neq 0 \\ 0...

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A function $f(x)$ is given by $f(x)=\frac{5^x}{5^x+5}$, then the sum of the series $$ f\left(\frac{1}{20}\right)+f\left(\frac{2}{20}\right)+f\left(\frac{3}{20}\right)+\ldots \ldots+f\left(\frac{39}{20}\right) $$ is equal to:

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If $15 \sin ^4 \alpha+10 \cos ^4 \alpha=6$, for some $\alpha \in \mathrm{R}$, then then value of $...

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A series LCR circuit of R $=5 \Omega, \mathrm{~L}=20 \mathrm{mH}$ and $\mathrm{C}=0.5 \mu \mathrm{~F}$ is connected across an AC supply...

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AC voltage V(t) = 20 $\sin \omega t$ of frequency 50 Hz is applied to a parallel plate capacitor. The...

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A pole stands vertically inside a triangular park $A B C$. Let the angle of elevation of the top of...

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For the forward biased diode characteristics shown in the figure, the dynamic resistance at $\mathrm{I}_{\mathrm{D}}=3 \mathrm{~mA}$ will be $\_\_\_\_$ $\Omega$

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Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by $...

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Define a relation $R$ over a class of $n \times n$ real matrices $A$ and $B$ as "ARB iff there...

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Let O be the origin. Let $\overline{\mathrm{OP}}=x \hat{\mathrm{i}}+y \hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overline{\mathrm{PQ}}=\sqrt{20} \overline{\mathrm{OQ}}=-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 x \hat{\mathrm{k}}, x, y \in \mathrm{R}, x>0$,...

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Q JEE MAIN 2021

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The...

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Let a tangent be drawn to the ellipse $\frac{x^2}{27}+y^2=1$ at $(3 \sqrt{3} \cos \theta, \sin \theta)$ where $\theta \in\left(0, \frac{\pi}{2}\right)$....

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Q JEE-MAIN 2021

If $x, y, z$ are in arithmetic progression with common difference $d, x 3 d$, and the determinant of the...

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Q JE MAIN 2021

Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational...

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Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and...

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In the given figure switches $S_1$ and $S_2$ are in open condition. The resistance across ab when the switches $S_1$...

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If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then...

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The contrapositive of the statement "If you will work, you will earn money" is :

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Let $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ be two non-zero vectors perpendicular to each other and $|\overline{\mathrm{a}}|=|\overline{\mathrm{b}}|$. If $|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|=|\overline{\mathrm{a}}|$, then the...

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In the curve y = y (x) is the solution of the differential equation $...

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A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on...

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A body of mass 'm ' is launched up on a rough inclined plane making an angle of $30^{\circ}$ with...

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Let $S_1: x^2+y^2=9$ and $S_2:(x-2)^2+y^2=1$. Then the locus of center of a variable circle $S$ which touches $S_1$ internally and...

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A zener diode having zener voltage 8 V and power dissipation rating of 0.5 W is connected across a potential...

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Let $S_1, S_2$ and $S_3$ be three sets defined as $$ \begin{aligned} & S_1=\{z \in \mathbb{C}:|z-1| \leq \sqrt{2}\} \\ &...

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Let in a series of $2 n$ observations, half of them are equal to a and remaining half are equal...

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A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively....

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If the curve $x^2+2 y^2=2$ intersects the line $x+y=1$ at two points $P$ and $Q$, then the angle subtended by...

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Let a complex number be $\mathrm{w}=1-\sqrt{3} i$. Let another complex number $z$ be such that $|z w d|=1$ and $...

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The number of solutions of the equation $x+2 \tan x=\frac{\pi}{2}$ in the interval $[0,2 \pi]$ is :

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The magnetic susceptibility of a material of a rod is 499 . Permeability in vacuum is $...

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Let $S_1$ be the sum of first $2 n$ terms of an arithmetic progression. Let $S_2$ be the sum of...

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The normal reaction ‘N’ for a vehicle of 800 kg mass, negotiation a turn on a $30^{\circ}$ banked road at...

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A capacitor is connected to a 20 V battery through a resistance of $10 \Omega$. It is found that the...

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Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability...

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Let $g(x)=\int_0^x f(t) d t$, where $f$ is continuous function in $[0,3]$ such that $\frac{1}{3} \leq f(t) \leq 1$ for...

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Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total...

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$\operatorname{cosec}\left[2 \cot ^{-1}(5)+\cos ^{-1}\left(\frac{4}{5}\right)\right]$ is equal to :

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The number of solutions of the equation $$ \sin ^{-1}\left[x^2+\frac{1}{3}\right]+\cos ^{-1}\left[x^2-\frac{2}{3}\right]=x^2 $$ for $x \in[-1,1]$ and $[x]$ denotes the greatest...

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The Value of current in the $6 \Omega$ resistance is :

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Two vectors $\vec{P}$ and $\vec{Q}$ have equal magnitudes. If the magnitude of $\vec{P}+\vec{Q}$ is $n$ times magnitude of $\vec{P}-\vec{Q}$, then...

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The value of $\lim _{n \rightarrow \infty} \frac{[r]+[2 r]+\ldots \ldots+[n r]}{n^2}$ where $r$ is non-zero real number and $[r]$ denotes...

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In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140...

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A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance...

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A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed...

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The value of $\sum_{\mathrm{r}=0}^6\left({ }^6 \mathrm{C}_{\mathrm{r}} \cdot{ }^6 \mathrm{C}_{6-\mathrm{r}}\right)$ is equal to :

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At an angle of 30° to the magnetic meridian, the apparent dip is 45°. Find the true dip :

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Let y = y (x) be the solution of the differential equation

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Consider a binary star system of star $A$ and star $B$ with masses $m_A$ and $m_B$ revolving in a circular...

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If P and Q are two statements, then which of the following compound statement is a tautology ?

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For a certain radioactive process the graph between In R and t(sec) is obtained as shown in the figure. Then...

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An object of mass 'm' is being moved with a constant velocity under the action of an applied force of...

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Consider a hyperbola $H_{\text {in }} x^2 2 y^2=4$. Let the tangent at a point $\mathrm{P}(4, \sqrt{6})$ meet the x...

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The correct relation between the degrees of freedom f and the ratio of specific heat

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If the integral $\int_0^{10} \frac{[\sin 2 \pi x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta e^{-\frac{1}{2}}+\gamma$, where, $\alpha, \beta, \gamma$ are integers and $[x]$...

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If time (t), velocity (v), and angular momentum (l) are taken as the fundamental units. Then the dimension of mass...

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Let $f: R \rightarrow R$ be defined as $f(x)=e^{-x} \sin x$. If $F:[0,1] \rightarrow R$ is a differentiable function such...

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For the given circuit the current i through the battery when the key in closed and the steady state has...

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A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic...

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An electron having de- Broglie wavelength $\lambda$ is incident on a target in a X-ray tube. Cut – off wavelength...

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In the given figure, each diode has a forward bias resistance of $30 \Omega$ and infinite resistance in reverse bias....

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A particle is making simple harmonic motion along the X -axis. If at a distances $\mathrm{X}_1$ and $\mathrm{X}_2$ from the...

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Consider the reaction. The percentage yield of amide product is _______. (Round off to the Nearest Integer). (Given : Atomic...

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Which of the following graphs represent the behavior of an ideal gas ? Symbols have their usual meaning

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For a series LCR circuit with R $=100 \Omega, \mathrm{~L}=0.5 \mathrm{mH}$ and $\mathrm{C}=0.1 \mathrm{pF}$ connected across $220 \mathrm{~V}-50 \mathrm{~Hz} \mathrm{AC}$...

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Consider the reaction $\mathrm{N}_2 \mathrm{O}_4(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_2(\mathrm{~g})$. The temperature at which $\mathrm{KC}=20.4$ and $\mathrm{K}_{\mathrm{P}}=600.1$, is $\_\_\_\_$ K. (Round off...

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KBr is doped with $10^{-5}$ mole percent of $\mathrm{SrBr}_2$. The number of cationic vacancies in 1 g of KBr crystal...

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If the equation of the plane passing through the line of intersection of the planes $...

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The number of chlorine atoms in 20 mL of chlorine gas at STP is_____$10^2$. (Round off to the Nearest Integer)....

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The minimum distance between any two points $P_1$ and $P_2$ while considering point $P_1$ on one circle and point $P_2$...

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A plane passes through the points $\mathrm{A}(1,2,3), \mathrm{B}(2$, $3,1)$ and $\mathrm{C}(2,4,2)$. If O is the origin and P is (...

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In an electromagnetic wave the electric field vector and magnetic field vector are given as $\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{\mathrm{i}}$ and $\overrightarrow{\mathrm{B}}=\mathrm{B}_0$ respectively....

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If [ ] represents the greatest integer function, then the value of

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A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water (...

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In the ground state of atomic Fe(Z = 26), the spin-only magnetic moment is ______ × $10^{-1}$ BM. (Round off...

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The length of a metal wire is $\ell_1$, when the tension in it is $\mathrm{T}_1$ and is $\ell_2$ when the...

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Q JEE MAIN_2021_1

IF A is

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A 1 molal $\mathrm{K}_4 \mathrm{Fe}(\mathrm{CN})_6$ solution has a degree of dissociation of 0.4 . Its boiling point is equal to...

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With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890...

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Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral...

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Following plots show Magnetization (M) vs Magnetising field (H) and Magnetic susceptibility ( $\alpha$ ) vs temperature (T) graph :...

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If $\bar{a}=\alpha \hat{i}+b \hat{j}+3 \hat{k}, \bar{b}=\beta \hat{i}-\alpha \hat{j}-\hat{k}$ and $\bar{c}=\hat{i}-2 \hat{j}-\hat{k}$ such that $\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=1$ and $\overline{\mathrm{b}} \cdot \overline{\mathrm{c}}=-3$...

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The total number of C–C sigma bond/s in mesityl oxide $\left(\mathrm{C}_6 \mathrm{H}_{10} \mathrm{O}\right)$ is_____. (Round off to the Nearest Integer).

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A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into...

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Let there be three independent events $\mathrm{E}_1, \mathrm{E}_2$ and $E_3$. The probability that only $E_1$ occurs is $\alpha$, only $E_2$...

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A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in...

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The reaction 2A + $\mathrm{B}_2$ 2AB is an elementary reaction. For a certain quantity of reactants, if the volume of...

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Let $f: R-\{3\} \rightarrow R-\{1\}$ be defined by $f(x)=\frac{x-2}{x-3}$. Let $g: R \rightarrow R$ be given as $g(x)=2 x$ -3...

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If $f(x)=\sin \left(\cos ^{-1}\left(\frac{1-2^{2 x}}{1+2^{2 x}}\right)\right)$ and its firs t derivative with respect to $x$ is $-\frac{b}{a} \log _e 2$...

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Let the system of linear equations $...

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On complete reaction of FeCl3 with oxalic acid in aqueous solution containing KOH, resulted in the formation of product A....

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If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in...

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If the function $f(x)=\frac{\cos (\sin x)-\cos x}{x^4}$ is continuous at each point in its domain and $f(0)=\frac{1}{k}$, then $k$ is...

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Consider a triangle having vertices $\mathrm{A}(-2,3), \mathrm{B}(1,9)$ and $\mathrm{C}(3,8)$. If a line L passing through the circum-centre of triangle $...

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A hyperbola passes through the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and its transverse and conjugate axes coincide with major and...

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The maximum value of z in the following equation $z=6 x y+y^2$, where $3 x+4 y \leq 100$ and $...

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A KCl solution of conductivity $0.14 \mathrm{~S} \mathrm{~m}^{-1}$ shows a resistance of $4.19 \Omega$ in a conductivity cell. If the...

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In a triangle ABC, if $|\overrightarrow{\mathrm{BC}}|=8,|\overrightarrow{\mathrm{CA}}|=7,|\overrightarrow{\mathrm{AB}}|=10$, then the projection of the vector $\overrightarrow{\mathrm{AB}}$ on $\overrightarrow{\mathrm{AC}}$ is equal to:

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For $\mathrm{p}>0$, a vector $\overrightarrow{\mathrm{v}}_2=2 \hat{\mathrm{i}}+(\mathrm{p}+1) \hat{\mathrm{j}}$ is obtained by rotating the vector $\overrightarrow{\mathrm{v}}_1=\sqrt{3} p \hat{\mathrm{i}}+\hat{\mathrm{j}}$ by an angle $\theta$...

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10. The half life period of radioactive element x is same as the mean life time of another radioactive element...

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Let $f: R \rightarrow R$ and $g \mid: R \rightarrow R$ be defined as $$ \begin{aligned} & f(x)=\left\{\begin{array}{ll} x+a, &...

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During which of the following processes, does entropy decrease ?

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Let $P=\left[\begin{array}{ccc}3 & -1 & -2 \\ 2 & 0 & \alpha \\ 3 & -5 & 0\end{array}\right]$, where $...

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The value of

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Let a curve $y=y(x)$ be given by the solution of the differential equation $$ \cos \left(\frac{1}{2} \cos ^{-1}\left(e^{-x}\right)\right) d x=\sqrt{e^{2...

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Choose the correct statement regarding the formation of carbocations A and B given :-

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Let $\mathrm{B}_i(\mathrm{i}=1,2,3)$ be three independent events in a sample space. The probability that only $\mathrm{B}_1$ occur is $\alpha$, only $\mathrm{B}_2$...

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Which of the following is true for y (x) that satisfies the differential equation

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If $a, \beta \in R$ are such that $1-2 i$ (here $i^2=-1$ ) is a root of $z^2+\alpha z+\beta=0$, then...

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The number of solutions of the equation $\log _{(x+1)}\left(2 x^2+7 x+5\right)+\log _{(2 x+5)}(x+1)^2-4=0, x>0$, is

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Let $A=\left[\begin{array}{l}a_1 \\ a_2\end{array}\right]$ and $B=\left[\begin{array}{l}b_1 \\ b_2\end{array}\right]$ be two $2 \times 1$ matrices with real entries such that $\mathrm{A}=\mathrm{XB}$,...

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Which of the following statements is incorrect for the function $\mathrm{g}(\mathrm{a})$ for $\alpha \in \mathrm{R}$ such that

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Let three vectors $\vec{a}, \vec{b}$ and $\vec{c}$ be such that $\vec{c}$ is coplanar with $\vec{a}$ and, $\vec{b}, \vec{a} \cdot \vec{c}=7$...

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Two resistors $\mathrm{R}_1=(4 \pm 0.8) \Omega$ and $\mathrm{R}_2=(4 \pm 0.4) \Omega$ are connected in parallel. The equivalent resistance of their...

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Let $\mathrm{A}=\left\{\mathrm{a}_{\mathrm{ij}}\right\}$ be a $3 \times 3$ matrix, where $\mathrm{a}_{\mathrm{ij}}=\left\{\begin{array}{cll}(-1)^{\mathrm{j}-\mathrm{i}} & \text { if } & \mathrm{i}\mathrm{j},\end{array}\right.$, hen $...

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Consider the above reaction where 6.1 g of benzoic acid is used to get 7.8 g of m -bromo benzoic...

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$\lim _{n \rightarrow \infty} \tan \left\{\sum_{r=1}^n \tan ^{-1}\left(\frac{1}{1+r+r^2}\right)\right\}$ is equal to $\_\_\_\_$ .

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10.0 ml of $\mathrm{Na}_2 \mathrm{CO}_3$ solution is titrated against 0.2 M HCI solution. The following titre values were obtained in...

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Choose the incorrect statement about the two circles whose equations are given below. $$ \begin{aligned} & x^2+y^2-10 x-10 y+41=0 \text...

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The minimum value of a for which the equation $\frac{4}{\sin x}+\frac{1}{1-\sin x}=\alpha$ has at least one solution in $\left(0, \frac{\pi}{2}\right)$...

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A student determined Young's Modulus of elasticity using the formula $Y=\frac{\mathrm{MgL}^3}{4 \mathrm{bd}^3 \delta}$. The value of g is taken to...

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In a triangle ABC , if $|\overrightarrow{\mathrm{BC}}|=3,|\overrightarrow{\mathrm{CA}}|=5$ and $|\overrightarrow{\mathrm{BA}}|=7$, then the projection of the vector $\overrightarrow{\mathrm{BA}}$ on $\overrightarrow{\mathrm{BC}}$ is equal...

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A solute a dimerizes in water. The boiling point of a 2 molar solution of A is $100.52^{\circ} \mathrm{C}$. The...

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VALUE OF

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The solubility of $\mathrm{CdSO}_4$ in water is $8.0 \times 10^{-4} \mathrm{~mol} \mathrm{L}^{-1}$. Its solubility in $0.01 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4$ solution...

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If the distance of the point $(1,-2,3)$ from the plane $x+2 y-3 z+10=0$ measured parallel to the line, $\frac{x-1}{3}=\frac{2-y}{m}=\frac{z+3}{1}$ is...

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If sum of the first 21 terms of the series $...

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If one of the diameters of the circle $x^2+y^2-2 x-6 y+6=0$ is a chord of another circle ' $C$ ',...

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Which of the following statement(s) is (are) incorrect reason for eutrophication ? (A) excess usage of fertilisers (B) excess usage...

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Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a...

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The value of $k \in R$, for which the following system of linear equations $$ \begin{aligned} & 3 x-y+4 z=3...

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In Tollen's test for aldehyde, the overall number of electron(s) transferred to the Tollen's reagent formula $\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]_{\sim}^{+}$per aldehyde group to...

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Let $\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}$ and $\vec{b}=2 \hat{i}-3 \hat{j}+5 \hat{k}$ If $\vec{r} \times \vec{a}=\vec{b} \times \vec{r} \cdot(a \hat{i}+2 \hat{j}+\hat{k})=3$ and $...

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Let M be any 3 × 3 matrix with entries from the set {0, 1, 2}. The maximum number of...

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Let $P$ be a variable point on the parabola $y=4 x^2+1$. Then, the locus of the mid-point of the point...

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The line 2x – y + 1 = 0 is a tangent to the circle at the point (2, 5)...

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The integral $...

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For the coagulation of a negative sol, the species below, that has the highest flocculating power is :

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Let C 1 be the curve obtained by the solution of differential equation $2 x y \frac{d y}{d x}=y^2-x^2, x>0$....

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The gas phase reaction $2 \mathrm{~A}(\mathrm{~g}) \rightleftharpoons \mathrm{A}_2(\mathrm{~g})$ at $400 \mathrm{~K}_{\text {has }} \Delta \mathrm{G}^0=+25.2 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The equilibrium constant...

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The area of the triangle with vertices A (z), B (iz) and C (z + iz) is :

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Let $g(t)=\int_{-\pi / 2}^{\pi / 2}\left(\cos \frac{\pi}{4} t+f(x)\right) d x$, where $f(x)=\log _e\left(x+\sqrt{x^2+1}\right), x \in R$. Then which one of...

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A xenon compound 'A' upon partial hydrolysis gives $\mathrm{XeO}_2 \mathrm{~F}_2$. The number of lone pair of electrons present in compound...

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If the foot of the perpendicular from point $(4,3,8)$ on the line $\mathrm{L}_1: \frac{\mathrm{x}-\mathrm{a}}{\ell}=\frac{\mathrm{y}-2}{3}=\frac{\mathrm{z}-\mathrm{b}}{4}, \ell \neq 0$ is $(3,5$, 7),...

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The sum of possible values of $x$ for $\tan ^{-1}(x+1)+\cot ^{-1}\left(\frac{1}{x-1}\right)=\tan ^{-1}\left(\frac{8}{31}\right)$ is :

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Let $A$ be a $3 \times 3$ matrix with $\operatorname{det}(A)=4$. Let $R_i$ denote the ith row of $A$. If a...

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-If the mean and variance of six observations $7,10,11,15, a, b$ are 10 and $\frac{20}{3}$, respectively, then the value of...

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The number of species below that have two lone pairs of electrons in their central atom is $\_\_\_\_$ (Round off...

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Consider the line $L$ given by the equation $\frac{x-3}{2}=\frac{y-1}{1}=\frac{z-2}{1}$. Let $Q$ be the mirror image of the point $(2,3$, -1)...

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The molar conductivities at infinite dilution of barium chloride, sulphuric arid and hydrochloric acid are 280,860 and $426 \mathrm{Scm}^2 \mathrm{~mol}^{-1}$...

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In a school, there are three types of games to be played. Some of the students play two types of...

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Let $\mathrm{P}(\mathrm{x})=\mathrm{x}^2+\mathrm{bx}+\mathrm{c}$ be a quadratic polynomial with real coefficients such that $=\int_0^1 P(x) d x=1$ and $\mathrm{P}(\mathrm{x})$ leaves remainder 5...

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A reaction has a half life of 1 min. The time required for 99.9% completion of the reaction is ______...

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Let $y=y(x)$ satisfies the equation $\frac{d y}{d x}-|A|=0$, for all $x>0$ where $...

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Due to cold weather a 1 m water pipe of cross-sectional area $1 \mathrm{~cm}_2$ is filled with ice at $...

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A hard substance melts at high temperature and is an insulator in both solid and in molten state. This solid...

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The unit cell of copper corresponds to a face centered cube of edge length $3.596 A $ with one copper...

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Let $f: S \rightarrow$ Swhere $S=(0, \infty)$ be a twice differentiable function such that $\mathrm{f}(\mathrm{x}+1)= \mathrm{xf}(\mathrm{x})$. If $...

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In the following molecules, Hybridisation of carbon a, b and c respectively are :

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Let in a right angled triangle, the smallest angle be $\theta$. If a triangle formed by taking the reciprocal of...

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Match list-I with list-II : Choose the most appropriate answer from the option given below :

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Let $f$ be a real valued funditon, defined on $R-\{-1$, $1\}$ and given by $$ f(x)=3 \log _e\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1} $$ Then...

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The sum of all the local minimum values of the twice differentiable function $f: R \rightarrow R$ defined by $...

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Copper reduces $\mathrm{NO}_3^{-}$into NO and $\mathrm{NO}_2$ depending upon the concentration of $\mathrm{HNO}_3$ in solution. (Assuming fixed $\left[\mathrm{Cu}^{2+}\right]$ and $\mathrm{P}_{\mathrm{NO}}=\mathrm{P}_{\mathrm{NO} 2}$...

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A block of mass $m$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The...

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Given below are two statements : Statement I : Non-biodegradable wastes are generated by the thermal power plants. Statement II...

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Let $A, B$ and $C$ be three events such that the probability that exactly one of $A$ and $B$ occurs...

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Let $A(-1,1), B(3,4)$ and $C(2,0)$ be given three points. A line $y=m x, m>0$, intersects lines $A C$ and BC...

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If $f: R \rightarrow R$ is given by $f(x)=x+1$, then the value of $\lim _{n \rightarrow \infty}\left[f(x)+f\left(\frac{5}{n}\right)+f\left(\frac{10}{n}\right)+\ldots+f\left(\frac{5(n-1)}{n}\right)\right]$, is :

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Lef $f: R-\left\{\frac{\alpha}{6}\right\} \rightarrow R$ be defined by $f(x)=\frac{5 x+3}{6 x-\alpha}$. Then the value of $\alpha$ for which (fof) $(x)=x$,...

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Match list-I with list-II : Choose the most appropriate answer the option given below :

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The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the...

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If the real part of the complex number $(1-\cos \theta+2 i \sin \theta)^{-1}$ is $\frac{1}{5}$ for $\theta \in(0, \pi)$, then...

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(A) "X" and "Y" respectively are :

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Consider the above reaction, the product 'X' and 'Y' respectively are :

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Match List - I with List - II :

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One of the by-products formed during the recovery of NH3 from Solvay process is :

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If $\int_{-a}^a(|x|+|x-2|) d x=22(a>2)$ and $[x]$ denotes the greatest integer $\leq x$, then $\int_a^{-a}(x+[x]) d x$ is equal to $\_\_\_\_$...

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A body of mass ' $m$ ' dropped from a height ' $h$ ' reaches the ground with a speed...

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Given that the inverse trigonometric functions take principal values only. Then, the number of real values of $x$ which satisfy...

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Five moles of an ideal gas at 293 K is expanded isothermally from an initial pressure of 2.1 MPa to...

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In the reactions, the enzyme A and enzyme B respectively are : –

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If the least and the largest real values of $a$, for which the equation $z+\alpha|z-1|+2 i=0(z \in C$ and $i=\sqrt{-1})$...

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If the point of intersections of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the circle $x^2+y^2=4 b, b>4$ lie on the curve $...

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The locus of the mid-point of the line segment joining the focus of the parabola $y^2=4 a x$ to a...

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Amongst the following, the linear species is

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The temperature of an ideal gas in 3-dimensions is 300 K . The corresponding de-Broglie wavelength of the electron approximately...

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Consider a rectangle ABCD having $5,7,6,9$ points in the interior of the line segments $...

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Consider titration of NaOH solution versus 1.25M oxalic acid solution. At the end point following burette readings were obtained.(i) 4.5...

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Nitrogen can be estimated by Kjeldahl's method for which of the following compound ?

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If $e^{\left(\cos ^2 x+\cos ^4 x+\cos ^6 x+-\infty\right) \log _4 2}$ satisfies the equation $t^2-9 t+8=0$, then the value of...

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The least value of $|z|$ where $z$ is complex number which satisfies the inequality $$ \exp \left(\frac{(|z|+3)(|z|-1)}{||z|+1|} \log _e 2\right)...

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Given below are two statements : Statement-I : 2-methylbutane on oxidation with $\mathrm{KMnO}_4$ gives 2-methylbutan-2-ol. Statement-II : n-alkanes can be...

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A square loop of side 20 cm and resistance $1 \Omega$ is moved towards right with a constant speed vo....

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Match List-I with List-II :

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The charges on the colloidal CdS sol and $\mathrm{TiO}_2$ sol are, respectively :

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Let the lengths of intercepts on $x$-axis and $y$-axis made by the circle $x^2+y^2+a x+2 a y+c=0,(a< 0)$ be $...

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$\lim _{x \rightarrow 0} \frac{\int_0^{x^2}(\sin \sqrt{t}) d t}{x^3}$ is equal to :

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Consider the given reaction, percentage yield of :

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The common positive oxidation states for an element with atomic number 24, are :

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Electromagnetic radiation of wavelength 663 nm is just sufficient to ionise the atom of metal A . The ionization energy...

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Two vertical poles are 150 m apart and the height of one is three times that of the other. If...

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Given below are two statements : Statement I : Bohr's theory accounts for the stability and line spectrum of Li+...

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Let $A \mid=\{2,3,4,5, \ldots ., 30\}$ and ${ }^{\prime} \simeq$ ' be an equivalence relation on $\mathrm{A} \times \mathrm{A}$, defined...

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Primary, secondary and tertiary amines can be separated using :-

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The secondary valency and the number of hydrogen bonded water molecule(s) in $\mathrm{CuSO}_4 .5 \mathrm{H}_2 \mathrm{O}$, respectively, are :

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Match List-I with List-II :

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Let $p$ and $q$ be two positive numbers such that $p+q=2$ and $p^4+q^4=272$. Then $p$ and $q$ are roots of...

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The spin only magnetic moment of a divalent ion in aqueous solution (atomic number 29) is _______ BM.

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If $y=y(x)$ is the solution of the differential equation $\frac{d y}{d x}+(\tan x) y=\sin x, 0 \leq x \leq \frac{\pi}{3}$,...

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The first ionization energy of magnesium is smaller as compared to that of elements X and Y, but higher than...

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A cube is placed inside an electric field, ${ }^{\hat{\mathrm{E}}-=150 \mathrm{y}^2 \mathrm{j}}$. The side of the cube is 0.5 m...

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An organic compound "A" on treatment with benzene sulphonyl chloride gives compound B. B is soluble in dil. NaOH solution....

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Let C be the locus of the mirror image of a point on the parabola $\mathrm{y}^2=4 \mathrm{x}$ with respect to...

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Among the following, number of metal/s which can be used as electrodes in the photoelectric cell is _______ (Integer answer)

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Deficiency of vitamin K causes :

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Consider the integral $$ \int_0^{10} \frac{[x] e^{[x]}}{e^{x-1}} d x $$ where $[x]$ denotes the greatest integer less than or equal...

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Main Products formed during a reaction of 1-methoxy naphthalene with hydroiodic acid are:

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The set that represents the pair of neutral oxides of nitrogen is :

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The rate constant of a reaction increases by five times on increase in temperature from $27^{\circ} \mathrm{C}$ to $52^{\circ} \mathrm{C}$....

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The area (in sq. units) of the part of the circle $x^2+y^2=36$, which is outside the parabola $y^2=9 x$, is...

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The oxide that shows magnetic property is :

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The correct pair(s) of the ambident nucleophiles is (are) :

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If $(x, y, z)$ be an arbitrary point lying on a plane $P$ which passes through the point $(42,0,0),(0,42,0)$ and...

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In the reaction of hypobromite with amide, the carbonyl carbon is lost as :

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A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and...

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Match List-I and List-II :

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The number of compound/s given below which contain/s –COOH group is _______.

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In basic medium, $\mathrm{H}_2 \mathrm{O}_2$ exhibits which of the following reactions? (A) $\mathrm{Mn}^{2+} \rightarrow \mathrm{Mn}^{4+}$ (B) $\mathrm{I}_2 \rightarrow \mathrm{I}^{-}$ (C)...

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An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2...

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The oxidation states of nitrogen in NO, NO2, N2O and $\mathrm{NO}_3^{-}$are in the order of :

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The functional groups that are responsible for the ion-exchange property of cation and anion exchange resins, respectively, are :

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Let $f ; \mathrm{R} \rightarrow \mathrm{R}$ be defined as $f(\mathrm{x})=2 \mathrm{x}-1$ and $\mathrm{g}: \mathrm{R}-\{1\} \rightarrow \mathrm{R}$ be defined as $\mathrm{g}(\mathrm{x})=\frac{\mathrm{x}-\frac{1}{2}}{\mathrm{x}-1}$...

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If a compound AB dissociates to the extent of $75 \%$ in an aqueous solution, the molality of the solution...

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Let $\alpha \in \mathrm{R}$ be such that the function $$ f(x)= \begin{cases}\frac{\cos ^{-1}\left(1-\{x\}^2\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^3}, & x \neq 0 \\...

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A galaxy is moving away from the earth at a speed of $286 \mathrm{kms}^{-1}$. The shift in the wavelength of...

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Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions,...

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The set of elements that differ in mutual relationship from those of the other sets is :

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Two wires of same length and thickness having specific resistances $6 \Omega \mathrm{~cm}$ and $3 \Omega \mathrm{~cm}$ respectively are connected...

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The function $f(x)=\frac{4 x^3-3 x^2}{6}-2 \sin x+(2 x-1) \cos x:$

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Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on...

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An infinite number of point charges, each carrying $1 \mu \mathrm{C}$ charge, are placed along the y -axis at $...

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The maximum value of $$ f(x)=\left|\begin{array}{ccc} \sin ^2 & 1+\cos ^2 x & \cos 2 x \\ 1+\sin ^2 x...

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The radius of a sphere is measured to be $(7.50 \pm 0.85) \mathrm{cm}$. Suppose the percentage error in its volume...

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If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $...

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If the fourth term in the expansion of $\left(x+x^{\log _2 x}\right)^7$ is 4480 , then the value of $x$ where...

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Two dices are rolled. If both dices have six faces numbered 1,2,3,5,7 and 11, then the probability that the sum...

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If the Boolean expression $(p=q) \Leftrightarrow\left(q^*(\sim p)\right)$ is a tautology, then the Boolean expression $\mathrm{p}^*(\sim \mathrm{q})$ is equivalent toni

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The lines $x=a y-1=z-2$ and $x=3 y-2=b z-2,(a b \neq 0)$ are coplanar, if .

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If $A=\left(\begin{array}{cc}0 & \sin \alpha \\ \sin \alpha & 0\end{array}\right)$ and $\operatorname{det}=\left(A^2-\frac{1}{2} I\right)=0$ then a possible value of $\alpha$ is

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Consider the following three statements : (A) If 3 + 3 = 7 then 4 + 3 = 8. (B)...

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The equation of the plane which contains the y-axis and passes through the point (1, 2, 3) is :

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Let $r_1$ and $r_2$ be the radii of the largest and smallest circles, respectively, which pass through the point $(-4,1)$...

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If $\cot ^{-1}(\alpha)=\cot ^{-1} 2+\cot ^{-1} 8+\cot ^{-1} 18+\cot ^{-1} 32+$ sum Upto 100 terms, then $\alpha$ is is

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The value of $\left(2 \tan ^{-1}\left(\frac{3}{5}\right)+\sin ^{-1}\left(\frac{5}{13}\right)\right)$ is equal to:

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The system of equations $\mathrm{kx}+\mathrm{y}+\mathrm{z}=1, \mathrm{x}+\mathrm{ky}+\mathrm{z} =k$ and $x+y+z k=k^2$ has no solution if $k$ is equal to i

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For the natural numbers $m, n$, if $(1-y)^m(1+y)^n=1+a_1 y+a_2 y^2+\ldots . .+a_{m+n} y^{m+n}$ and $a_1=a_2=10$, then the value of $(m+n)$...

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In a triangle PQR , the co-ordinates of the points P and $Q$ are ( $-2,4$ ) and ( $4,-2$...

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The number of the real roots of the equation $(x+1)^2+|x-5|=\frac{27}{4}$ is $\_\_\_\_$ .

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Let $\vec{a}=2 \hat{i}-3 \hat{j}+4 \hat{k}$ and $\vec{b}=7 \hat{i}+\hat{j}-6 \hat{k}$ If $\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{a}}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{r}} \cdot(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})=-3$ then $...

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Let $\mathrm{i}=\sqrt{-1}$. If $\frac{(-1+\mathrm{i} \sqrt{3})^{21}}{(1-\mathrm{i})^{24}}+\frac{(1+\mathrm{i} \sqrt{3})^{21}}{(1+\mathrm{i})^{24}}=\mathrm{k}$, and $\mathrm{n}=$ [| $\mathrm{k} \mid]$ be the greatest integral part of $|\mathrm{k}|$. Then $\sum_{j=0}^{n+5}(j+5)^2-\sum_{j=0}^{n+5}(j+5)$...

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The inverse of $y=5^{\log x}$ is :

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The students $S_1, S_{2, \ldots \ldots}, S_{10}$ are to be divided into 3 groups $\mathrm{A}, \mathrm{B}$ and C such that...

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The sum of first four terms of a geometric progression (G.P.) is $\frac{65}{12}$ and the sum of their respective reciprocals...

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If the variance of 10 natural numbers 1, 1, 1,...., 1, k is less than 10, then the maximum possible...

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If the area of the triangle formed by the positive xaxis, the normal and the tangent to the circle (...

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Let a point P be such that its distance from the point $(5,0)$ is thrice the distance of P from...

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If $a+\alpha=1, b+\beta=2$ and $a f(x)+\alpha f\left(\frac{1}{x}\right)=b x+\frac{\beta}{x}, x \neq 0$, then the value of expression $\frac{f(x)+f\left(\frac{1}{x}\right)}{x+\frac{1}{x}}$ is $\_\_\_\_$ .

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Let $\lambda$ be an interger. If the shortest distance between the lines $x-\lambda=2 y-1=-2 z$ and $x=y+ 2 \lambda=z-\lambda$ is...

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For integers $n$ and $r$, let $...

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A TV transmission tower antenna is at a height of 20 m. Suppose that the receiving antenna is at. (i)...

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The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in...

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The pressure exerted by a non-reactive gaseous mixture of 6.4 g of methane and 8.8 g of carbon dioxide in...

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Consider a water tank as shown in the figure. It's cross-sectional area is $0.4 \mathrm{~m}^2$. The tank has an opening...

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For the system of linear equations : $$ x-2 y=I, x-y+k z=-2, k y+4 z=6, k \in R, $$ consider...

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The oxygen dissolved in water exerts a partial pressure of 20 kPa in the vapour above water. The molar solubility...

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The typical output characteristics curve for a transistor working in the common-emitter configuration is shown in the figure. The estimated...

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Let $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be in arithmetic progression. Let the centroid of the triangle with vertices $(\mathrm{a}, \mathrm{c}),(2, \mathrm{~b})$ and...

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A ball of mass 4 kg , moving with a velocity of 10 $\mathrm{ms}^{-1}$, collides with a spring of length...

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Let $A$ and $B$ be $3 \times 3$ real matrices such that $A$ is symmetric matrix and $B$ is skew-symmetric...

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15 mL of aqueous solution of $\mathrm{Fe}^{2+}$ in acidic medium completely reacted with 20 mL of 0.03 M aqueous $...

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The projectile motion of a particle of mass 5 g is shown in the figure. The initial velocity of the...

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Let $f(x)$ be a differentiable function defined on $[0,2]$ such that $f^{\prime}(x)=f^{\prime}(2-x)$ for all $x \in(0,2), f(0)=1$ and $f(2)=e^2$. Then...

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The standard enthalpies of formation of $\mathrm{Al}_2 \mathrm{O}_3$ and CaO are $-1675 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $-635 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. For...

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If a curve $y=f(x)$ passes through the point $(1,2)$ and satisfies $x \frac{d y}{d x}+y=b x^4$, then for what value...

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The area of the region : $$ R=\left\{(x, y): 5 \times 2 \leq y \leq 2 x^2+9\right\} \text { is...

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The speed of electrons in a scanning electron microscope is $1 \times 10^7 \mathrm{~ms}^{-1}$. If the protons having the same...

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If the curve $y=a x^2+b x+c, x \in R$, passes through the point $(1,2)$ and the tangent line to this...

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Consider a sample of oxygen behaving like an ideal gas. At 300 K , the ratio of root mean square...

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For a certain first order reaction 32\% of the reactant is left after 570 s . The rate constant of...

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The mole fraction of a solute in a 100 molal aqueous solution $\_\_\_\_$ $\times 10^{-2}$. (Round off to the Nearest...

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An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one...

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The negative of the statement $\sim p \wedge(p \vee q)$ is

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A particle of mass $m$ moves in a circular orbit under the central potential field, $U(r)=\frac{-C}{r}$, where C is a...

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$\left[\mathrm{Ti}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}$ absorbs light of wavelength 498 nm during a $\mathrm{d}-\mathrm{d}$ transition. The octahedral splitting energy for the avove complex...

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A possible value of $\tan \left(\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}\right)$ is :

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In the above reaction, 3.9 g of benzene on nitration gives 4.92 g of nitrobenzene. The percentage yield of nitrobenzene...

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The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R,...

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The value of the integral, $\int_1^3\left[x^2-2 x-2\right] d x$, where $[x]$ denotes the greatest integer less than or equal to...

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At $25^{\circ} \mathrm{C}, 50 \mathrm{~g}$ of iron reacts with HCl to form $\mathrm{FeCl}_2$. The evolved hydrogen gas expands against a...

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A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined...

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For which of the following curves, the line $x+\sqrt{3} y=2 \sqrt{3}$ is the tangent at the point $...

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A certain orbital has $\mathrm{n}=4$ and $\mathrm{m}_{\varepsilon}=-3$. The number of radial nodes in this orbital is $\_\_\_\_$ . (Round off...

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Let $f$ be a twice differentiable function defined on $R$ such that $f(0)=1, f^{\prime}(0)=2$ and $f^{\prime}(x) \neq 0$ for all...

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The function of time representing a simple harmonic motion with a period of $\frac{\pi}{\omega}$ is :

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Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as, $$ f(x)= \begin{cases}-55 x, & \text { if } x4\end{cases} $$ Let...

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0.01 moles of a weak acid HA $\left(K_a=2.0 \times 10^{-6}\right)$ is dissolved in 1.0 L of 0.1 M HCl solution....

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The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is $\overrightarrow{\mathrm{L}}$. The...

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If $n \geq 2$ is a positive integer, then the sum of the series $...

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The reaction of white phosphorus on boiling with alkali in inert atmosphere resulted in the formation of product ' A...

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In a series LCR circuit, the inductive reactance $\left(X_L\right)$ is $10 \Omega$ and the capacitive reactance $\left(\mathrm{X}_{\mathrm{c}}\right)$ is $4 \Omega$....

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The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight...

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The point of intersection and sudden increase in the slope, in the diagram given below, respectively, indicates :

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The decay of a proton to neutron is :

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If $P$ is a point on the parabola $y=x^2+4$ which is closest to the straight line $y=4 x-1$, then the...

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If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration...

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Given below are two statements : Statement-I : Retardation factor (Rf) can be measured in meter/centimeter. Statement-II : Rf value...

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The vector equation of the plane passing through the intersection of the planes $\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=1$ and $\vec{r} \cdot(\hat{i}-2 \hat{j})=-2$, and...

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Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a...

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Let $\mathrm{a}, \mathrm{b} \in \mathrm{R}$. If the mirror image of the point $\mathrm{P}(\mathrm{a}, 6$, 9) with respect to the line...

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What is the spin-only magnetic moment value (BM) of a divalent metal ion with atomic number 25, in it's aqueous...

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The correct relation between $\alpha$ (ratio of collector current to emitter current) and $\beta$ (ratio of collector current to base...

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For the statements p and q, consider the following compound statements :\ Then which of the following statements is correct?

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When 35 mL of 0.15 M lead nitrate solution is mixed with 20 mL of 0.12 M chromic sulphate solution,...

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The velocity-displacement graph of a particle is shown in the figure. The acceleration-displacement graph of the same particle is represented...

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Sulphurous acid $\left(\mathrm{H}_2 \mathrm{SO}_3\right)$ has $\mathrm{Ka}_1=1.7 \times 10^{-2}$ and $\mathrm{Ka}_2=6.4 \times 10^{-8}$. The pH of $0.588 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_3$ is...

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Assuming ideal behaviour, the magnitude of $\log \mathrm{K}$ for the following reaction at $25^{\circ} \mathrm{C}$ is $\mathrm{x} \times 10^{-1}$. The...

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Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia...

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At 363 K, the vapour pressure of A is 21 kPa and that of B is 18 kPa. One mole...

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A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $(\vec{E})$ and magnetic field $(\vec{B})$...

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The number of orbitals with $\mathrm{n}=5, \mathrm{~m}_1=+2$ is $\_\_\_\_$ . (Round off to the Nearest Integer).

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A proton and an a-particle, having kinetic energies $\mathrm{K}_{\mathrm{a}}$ and $\mathrm{K}_{\mathrm{a}}$, respectively, enter into a magnetic field at right angles....

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In Duma's method of estimation of nitrogen, 0.1840 g of an organic compound gave 30 mL of nitrogen collected at...

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1.86 g of aniline completely reacts to form acetanilide. 10\% of the product is lost during purification. Amount of acetanilide...

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For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $\gamma$ is...

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A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min respectively. Starting from an equimolar...

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An object of mass $m_1$ collides with another object of mass $m_2$, which is at rest. After the collision the...

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A $5.0 \mathrm{~m} \mathrm{~mol} \mathrm{dm}^{-3}$ aqueous solution of KCl has a conductance of 0.55 mS when measured in a cell...

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Which of the following statements are correct? (A) Electric monopoles do not exist whereas magnetic monopoles exist. (B) Magnetic field...

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Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g...

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The exact volumes of 1 M NaOH solution required to neutralize 50 mL of $1 \mathrm{M} \mathrm{H}_3 \mathrm{PO}_3$ solution and...

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The correct order of conductivity of ions in water is:

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The number of solutions of the equation $|\cot x|=\cot x+\frac{1}{\sin x}$ in the interval $[0,2 \pi]$ is

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Arrange the following metal complex/compounds in the increasing order of spin only magnetic moment. Presume all the three, high spin...

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The INCORRECT statement(s) about heavy water is (are) (A) used as a moderator in nuclear reactor (B) obtained as a...

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A square $A B C D$ has all its vertices on the curve $x^2 y^2=1$. The midpoints of its sides...

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If $f(x)=\int \frac{5 x^8+7 x^6}{\left(x^2+1+2 x^7\right)^2} d x,(x \geq 0), f(0)=0$ and $f(1) =\frac{1}{\mathrm{~K}}$, then the value of K is

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A colloidal system consisting of a gas dispersed in a solid is called a/an :

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The INCORRECT statements below regarding colloidal solutions is :

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The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60...

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The equation of the planes parallel to the plane x – 2y + 2z – 3 = 0 which are...

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Let $z_1, z_2$ be the roots of the equation $z^2+a z+12 =0$ and $\mathrm{Z}_1, \mathrm{Z}_2$ form an equilateral triangle with...

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Q

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The missing value in the following figure is

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Which of the following reaction is an example of ammonolysis?

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The characteristics of elements X,Y and Z with atomic numbers, respectively, 33, 53 and 83 are :

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Let $f(x)$ and $g(x)$ be two functions satisfying $f\left(x^2\right)+ g(4-x)=4 x^3$ and $g(4-x)+g(x)=0$, then the value of $...

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Mesityl oxide is a common name of :

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Which of the following is least basic?

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Let the plane $a x+b y+c z+d=0$ bisect the line joining the points $(4,-3,1)$ and $(2,3,-5)$ at the right angles....

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The number of times the digit 2 will be written when listing the integers from 1 to 1000 is

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An unsaturated hydrocarbon X on ozonolysis gives A. Compound A when warmed with ammonical silver nitrate forms a bright silver...

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Hoffmann bromomide degradation of benzamide gives product A , which upon heating with $\mathrm{CHCl}_3$ and NaOH gives product B ....

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The value of $3+\frac{1}{4+\frac{1}{3+\frac{1}{4+\frac{1}{3+\infty}}}}$ is equal to

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Ammon lysis of Alkyl halides followed by the treatment with Nao solution can be used to prepare primary, secondary and...

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Reducing smog is a mixture of:

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Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of 3.33 h...

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The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3...

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The correct statements about $\mathrm{H}_2 \mathrm{O}_2$ are : (A) used in the treatment of effluents. (B) used as both oxidising...

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Let $A+2 B=\left[\begin{array}{ccc}1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1\end{array}\right]$ and...

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If $\quad f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} ; & |x| \geq 1 \\ a x^2+b ; & |x|

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The INCORRECT statement regarding the structure of $\mathrm{C}_{60}$ is :

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The magnitude of the change in oxidising power of the $\mathrm{MnO}_4^{-} / \mathrm{Mn}^{2+}$ couple is $\mathrm{x} \times 10^{-4} \mathrm{~V}$, if...

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Statement I : Sodium hydride can be used as an oxidising agent. Statement II : The lone pair of electrons...

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Fructose is an example of :-

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Seawater at a frequency $f=9 \times 10^2 \mathrm{~Hz}$, has permittivity $\varepsilon=80 \varepsilon_0$ and resistivity $r=0.25 \Omega \mathrm{~m}$. Imagine a parallel...

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$\mathrm{C}_6 \mathrm{H}_6$ freezes at $5.5^{\circ} \mathrm{C}$. The temperature at which a solution 10 g of $\mathrm{C}_4 \mathrm{H}_{10}$ in 200 g...

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Which of the following polymer is used in the manufacture of wood laminates?

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A $2 \mu \mathrm{~F}$ capacitor $\mathrm{C}_1$ is first charged to a potential difference of 10 V using a battery. Then...

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$F_2 x_2$ and $F e y_3$ are known when $x$ and $y$ are :

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The volume occupied by 4.75 g of acetylene gas at 50°C and 740 mmHg pressure is _____ L. (Rounded off...

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The image of an object placed in air formed by a convex refracting surface is at a distance of 10...

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$\frac{1}{3^2-1}+\frac{1}{5^2-1}+\frac{1}{7^2-1}+\ldots \ldots+\frac{1}{(201)^2-1}$ is equal to

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The disc of mass $M$ with uniform surface mass density $s$ is shown in the figure. The centre of mass...

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The secondary strtucture of protein is stabilised by:

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The electric field in a region is given by $\vec{E}=\frac{2}{5} E_0 \hat{i}+\frac{3}{5} E_0 \hat{j}$ with $E_0=4.0 \times 10^3 \frac{N}{C}$. The...

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The real valued function $f(x)=\frac{\operatorname{cosec}^{-1} x}{\sqrt{x-[x]}}$, where $[\mathrm{x}]$ denotes the greatest integer less than or equal to x , is...

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The formula of a gaseous hydrocarbon which requires 6 times of its own volume of $\mathrm{O}_2$ for complete oxidation and...

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A particle of mass $m$ moves in a circular orbit in a central potential field $U(r)=U_0 r^4$. If Bohr's quantization...

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If $\alpha, \beta$ are natural numbers such that $100^\alpha-199 \beta=$ (100) $(100)+(99)(101)+(98)(102)+\ldots . .+(1)$ (199), then the slope of the...

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A boy of mass 4 kg is standing on a piece of wood having mass 5kg. If the coefficient of...

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For the four circles $\mathrm{M}, \mathrm{N}, \mathrm{O}$ and P , following four equations are given : Circle $\mathrm{M}: \mathrm{x}^2+\mathrm{y}^2=1$ Circle...

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A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction...

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If the equation $\mathrm{a}|\mathrm{z}|^2+\overline{\alpha \overline{\mathrm{z}}+\alpha \overline{\mathrm{z}}}+\mathrm{d}=0$ represents a circle where $a, d$ are real constant when which of the following...

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Among the following allotropic forms of sulphur, the number of allotropic forms, which will show paramagnetism is (A) $\alpha$-sulphur (B)...

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A vector $\vec{a}$ has components $3 p$ and 1 with respect to a rectangular cartesian system. This system is rotated...

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The electric field intensity produced by the radiation coming from a 100 W bulb at a distance of 3 m...

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Which of the following reduction reaction CANNOT be carried out with coke ?

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A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of $1 \mathrm{~ms}^{-1}$ goes...

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If $\lim _{x \rightarrow 0} \frac{\sin ^{-1} x-\tan ^{-1} x}{3 x^2}$ is equal to $L$, then the value of $...

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The total number of amines among the following which can be synthesized by Gabriel synthesis is

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The equation of one of the straight lines which passes through the point $(1,3)$ and makes an angles $...

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The correct set from the following in which both pairs are in correct order of melting point is

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What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved ?

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The diazonium salt of which of the following compounds will form a coloured dye on reaction with $\beta-$Naphthol in NaOH...

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Two identical photocathodes receive the light of frequencies $f_1$ and $f_2$ respectively. If the velocities of the photo-electrons coming out...

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The green house gas/es is (are) : (A) Carbon dioxide (B) Oxygen (C) Water vapour (D) Methane Choose the most...

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in...

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The correct shape and I-I-I bond angles respectively in $\mathrm{I}_3^{-}$ion are :-

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Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a...

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For an ideal heat engine, the temperature of the source is 127°C. In order to have 60% efficiency the temperature...

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The incorrect statement among the following is :-

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The integral $\int \frac{(2 x-1) \cos \sqrt{(2 x-1)^2+5}}{\sqrt{4 x^2-4 x+6}} d x$ is equal to (where c is a constant...

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A solid disc of radius ' $a$ ' and mass ' $m$ ' rolls down without slipping on an inclined...

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Match list I with List II

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Let $\alpha, \beta, \gamma$ be the real roots of the equation, $\mathrm{x}^2+\mathrm{ax}^2 +b x+c=0,(a, b, c \in R$ and $...

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A closed organ pipe of length $L$ and an open organ pipe contain gases of densities $\rho_1$ and $\rho_2$ respectively....

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Two particles A and B of equal masses are suspended from two massless springs of spring constants $K_1$ and $K_2$...

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Choose the correct statement about two circles whose equation are given below : $...

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Given below are two statements :- Statement I : The value of the parameter "Biochemical Oxygen Demand (BOD)" is important...

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The solutions of the equation

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The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of $15 \Omega$ resistance...

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A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6...

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What is the correct order of the following elements with respect to their density ?

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s $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}) \mathrm{N}$. It starts from rest and was at the origin initially. After 4s, its new...

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Which one of the following compounds is nonaromatic

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A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the...

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A deviation of 2° is produced in the yellow ray when prism of crown and flint glass are achromatically combined....

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Let $\left(1+x+2 x^2\right) 20=a_0+a_1 x+a_2 x_2+\ldots+a_{40} x^{40}$. then $\mathbf{a}_1+\mathbf{a}_3+\mathbf{a}_5+\ldots+\mathbf{a}_{37}$ is equal to

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The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y...

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If one wants to remove all the mass of the earth to infinity in order to break it up completely....

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Match List-I with List-II C hoose the correct answer from the options given below :

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The differential equation satisfied by the system of parabolas $y^2=4 a(x+a)$ is :

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A force $\vec{F}-=4 \hat{i}+3 \hat{j}+4 \hat{k}$ is applied on an intersection point of $x=2$ plane and $x$-axis. The magnitude of...

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Two cells of emf 2E and E with internal resistance r1 and r2 respectively are connected in series to an...

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Complete combustion of 3 g of ethane gives $x \times 10^{22}$ molecules of water. The value of $x$ is $\_\_\_\_$...

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In a parallel plate capacitor set up, the plate area of capacitor is $2 \mathrm{~m}^2$ and the plates are separated...

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For the reaction $2 \mathrm{Fe}^{3+}(\mathrm{aq})+2 \mathrm{I}^{-}(\mathrm{aq}) \rightarrow 2 \mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{I}_2(\mathrm{~s})$ the magnitude of the standard molar free energy change, $\Delta_{\mathrm{r}} \mathrm{G}_{\mathrm{m}}^0=-$...

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A carrier signal $C(t)=25 \sin \left(2.512 \times 10^{10} t\right)$ is amplitude modulated by a message signal $...

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The energy dissipated by a resistor is 10 mJ in 1 s when an electric current of 2 mA flows...

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Match List-I and List-II.

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Red light differs from blue light as they have:

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The velocity of a particle is $\mathrm{v}=\mathrm{v}_0+\mathrm{gt}+\mathrm{Ft}^2$. Its position is $\mathrm{x}=0$ at $\mathrm{t}=0$; then its displacement after time $(\mathrm{t}=1)$ is...

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2 molal solution of a weak acid HA has a freezing point of $3.885^{\circ} \mathrm{C}$. The degree of dissociation of...

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Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

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The total number of unpaired electrons present in the complex $\mathrm{K}_3\left[\mathrm{Cr}(\text { oxalate })_3\right]$ is $\_\_\_\_$ .

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Which one is the correct option for the two different thermodynamic processes ?

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Which of the following reagent is suitable for the preparation of the product in the above reaction ?

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A reaction of 0.1 mole of Benzylamine with bromomethane gave 23 g of Benzyl trimethyl ammonium bromide. The number of...

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Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500g, Decay constant...

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$\_\_\_\_$ grams of 3-Hydroxy propanal (MW=74) must be dehydrated to produce 7.8 g of acrolein $(\mathrm{MW}=56)\left(\mathrm{C}_3 \mathrm{H}_4 \mathrm{O}\right)$ if the...

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A sound wave of frequency 245 Hz travels with the speed of 300 ms–1 along the positive x-axis. Each point...

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The magnetic field in a region is given by $\overrightarrow{\mathrm{B}}-=\mathrm{B}_0\left(\frac{\mathrm{x}}{\mathrm{a}}\right) \hat{\mathrm{k}}$. A square loop of side d is placed with...

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In polymer Buna-S: 'S' stands for :-

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For the reaction $\mathrm{C}_2 \mathrm{H}_6 \longrightarrow \mathrm{C}_2 \mathrm{H}_4+\mathrm{H}_2$ the reaction enthalpy $\Delta_{\mathrm{r}} \mathrm{H}=$ $\_\_\_\_$ $\mathrm{kJ} \mathrm{mol}^{-1}$. (Round off to the...

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A geostationary satellite is orbiting around an arbitary planet 'P' at a height of 11R above the surface of 'P'...

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Which one of the following carbonyl compounds cannot be prepared by addition of water on an alkyne in the presence...

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$2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NOCl}(\mathrm{s})$ This reaction was studied at $-10^{\circ} \mathrm{C}$ and the following data was obtained $[\mathrm{NO}]_0$ and...

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An object is located at 2 km beneath the surface of the water. If the fractional compression $\frac{\Delta V}{V}$ is...

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Which one of the following will be the output of the given circuit ?

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A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude of 12...

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If one mole of the polyatomic gas is having two vibrational modes and b is the ratio of molar specific...

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A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising...

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Let $z$ and $\omega$ be two complex numbers such that $\omega=z \bar{z}-2 z+2,\left|\frac{z+i}{z-3 i}\right|=1$ and $\operatorname{Re}(\omega)$ has minimum value. Then,...

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Which of the following compound CANNOT act as a Lewis base?

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The absolute value of the electron gain enthalpy of halogens satisfies:

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The above reaction requires which of the following reaction conditions?

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Which of the following is correct structure of tyrosine ?

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Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should...

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Given below are two statements: Statement I : Potassium permanganate on heating at 573 K forms potassium manganate. Statement II...

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Statement I : A cyclist is moving on an unbanked road with a speed of 7 kmh–1 and takes a...

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A central atom in a molecule has two lone pairs of electrons and forms three single bonds. The shape of...

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n order to prepare a buffer solution of pH 5.74, sodium acetate is added to acetic acid. If the concentration...

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A resistor develops 500 J of thermal energy in 20s when a current of 1.5 A is passed through it....

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The produce "A" in the above reaction is :

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AX is a covalent diatomic molecule where A and X are second row elements of periodic table. Based on Molecular...

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The chemical that is added to reduce the melting point of the reaction mixture during the extraction of aluminium is...

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A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher...

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Which of the following is an aromatic compound?

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In a binary compound, atoms of element A form a hcp structure and those of element M occupy 2/3 of...

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The number of ionisable hydrogens present in the product obtained from a reaction of phosphorus trichloride and phosphonic acid is:

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Let the curve $y=y(x)$ be the solution of the differential equation, $\frac{d y}{d x}=2(x+1)$. If the numerical value of area...

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With respect to drug-enzyme interaction, identify the wrong statement:

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Match List-I with List-II : Choose the correct answer from the options given below :

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Given below are two statements: One is labelled as Assertion $A$ and the other labelled as reason $R$ Assertion A...

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If the normal to the curve $y(x)=\int_0^x\left(2 t^2-15 t+10\right) d t$ at a point $(a, b)$ is parallel to the...

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The refractive index of a converging lens is 1.4 . What will be the focal length of this lens if...

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Let

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Match List-I with List-II Choose the most appropriate answer from the options given below –

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Calculate the value of mean free path ( $\lambda$ ) for oxygen molecules at temperature $27^{\circ} \mathrm{C}$ and pressure $...

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The total number of 3 × 3 matrices A having enteries from the set (0, 1, 2, 3) such that...

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Considering the above chemical reaction, identify the product "X" :

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If $\lim _{x \rightarrow 0} \frac{a e^x-b \cos x+c e^{-x}}{x \sin x}=2$, then $a+b+c$ is equal to $\_\_\_\_$ .

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The half-life of $\mathrm{Au}^{198}$ is 2.7 days. The activity of 1.50 mg of $\mathrm{Au}^{198}$ if its atomic weight is $...

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A certain orbital has no angular nodes and two radial nodes. The orbital is :

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Let A B C D be a square of side of unit length. Let a circle $C_1$ centered at $A$...

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For the given circuit, comment on the type of transformer used :

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The correct structures of trans- $\left[\mathrm{NiBr}_2\left(\mathrm{PPh}_3\right)_2\right]$ and meridonial- $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3\left(\mathrm{NO}_2\right)_3\right]$, respectively, are

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Let $f:(0,2) \rightarrow \mathbb{R}$ be defined as

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Compound with molecular formula $\mathrm{C}_3 \mathrm{H}_6 \mathrm{O}$ can show :

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The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100...

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Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26,...

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Let $S_k=\sum_{r=1}^k \tan ^{-1}\left(\frac{6^r}{2^{2 r+1}+3^{2 r+1}}\right)$. Then $\lim _{k \rightarrow \infty} S_k$ is equal to :

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Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the...

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The number of roots of the equation, $$ (81)^{\sin ^2 x}+(81)^{\cos ^2 x}=30 $$ in the interval $[0, \pi]$ is...

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The locus of the midpoints of the chord of the circle, $x^2+y^2=25$ which is tangent to the hyperbola, $\frac{x^2}{9}-\frac{y^2}{16}=1$ is...

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What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18...

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If $y=y(x)$ is the solution of the differential equation, $\frac{d y}{d x}+2 y \tan x=\sin x, y\left(\frac{\pi}{3}\right)=0$, then the maximum...

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A charge $Q$ is moving $\overline{\operatorname{dI}}$ distance in the magnetic field $\vec{B}$ - Find the value of work done by...

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Let $[x]$ denote greatest integer less than or equal to $x$. If for $n \in \mathbb{N},\left(1-x+x^3\right)^n=\sum_{j=0}^{3 n} a_j x^j m$...

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The calculated magnetic moments (spin only value) for species $\left[\mathrm{FeCl}_4\right]^{2-},\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$ and $\mathrm{MnO}_4^{2-}$ respectively are :

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A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The...

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Match list - I and List - II Choose the correct answer from the options given below :

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A large block of wood of mass $\mathrm{M}=5.99 \mathrm{~kg}$ is hanging from two long massless cords. A bullet of mass...

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Match List-I with List-II Choose the most appropriate answer from the options given below :

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The range of $a \in \mathbb{R}$ for which the function $$ f(x)=(4 a-3)\left(x+\log _e 5\right)+2(a-7) \cot \left(\frac{x}{2}\right) \sin ^2\left(\frac{x}{2}\right) $$...

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According to Bohr's atomic theory :- (1) Kinetic energy of electron is $\propto \frac{\mathrm{Z}^2}{\mathrm{n}^2}$. (2) The product of velocity (v)...

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Let $P$ be a plane $l x+m y+n z=0$ containing the line, $\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}$. IF plane $P$ divides the line segment...

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The following logic gate is equivalent to :

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The correct order of the following compounds showing increasing tendency towards nucleophilic substitution reaction is :-

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The statements that are TRUE : (A) Methane leads to both global warming and photochemical smog (B) Methane is generated...

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If $n$ is the number of irrational terms in the expansion of $\left(3^{1 / 4}+5^{1 / 8}\right)^{60}$, then $(n-1)$ is...

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Let a complex number $\mathrm{z},|\mathrm{z}| \neq 1$, satisfy $\log _{\frac{1}{\sqrt{2}}}\left(\frac{|z|+11}{(|z|-1)^2}\right) \leq 2$. Then, the largest value of $|z|$ is equal...

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Which of the following Boolean expression is a tautology ?

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Match List-I with List-II : List-I (Chemicals) (a) Alcoholic potassium hydroxide (b) $\mathrm{Pd} / \mathrm{BaSO}_4$ (c) BHC (Benzene hexachloride) (d)...

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Most suitable salt which can be used for efficient clotting of blood will be :-

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Match List-I with List-II Choose the most appropriate answer from the options given below :

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Let the functions $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be defined as

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Consider the above chemical reaction and identify product "A"

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If $\sqrt{3}\left(\cos ^2 x\right)=(\sqrt{3}-1) \cos x+1$, the number of solutions of the given equation when $\mathrm{x} \in\left[0, \frac{\pi}{2}\right]$ is

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What is the correct sequence of reagents used for converting nitrobenzene into m-dibromobenzene

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Let the position vectors of two points $P$ and $Q$ be $3 \hat{i}+\hat{j}+2 \hat{k}$ and $\hat{i}+2 \hat{j}-4 \hat{k}$, respectively. Let...

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Q JEE MAIN 2021

Match the list -I with list – II

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If the three normasl drawn to the prabola, $y^2=2 x$ pass through the point $(a, 0) a \neq 0$, then...

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An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength...

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A non-reducing sugar "A" hydrolyses to give two reducing mono saccharides. Sugar A is-

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The value of the integral $\int_0^\pi|\sin 2 x| d x$ is

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Let $A=\left[\begin{array}{cc}i & -i \\ -i & i\end{array}\right], i=\sqrt{-1}$ Then, the system of linear equation $A^8=\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}8 \\ 64\end{array}\right]$...

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Reagent, 1-naphthylamine and sulphanilic acid in acetic acid is used for the detection of

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The area bounded by the lines y = ||x – 1| – 2| is

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If for $x \in\left(0, \frac{\pi}{2}\right), \log _{10} \sin x+\log _{10} \cos x=-1$ and $\log _{10}(\sin x+\cos x)=\frac{1}{2}\left(\log _{10} n-1\right), n>0$,...

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Let $(\lambda, 2,1)$ be a point on the plane which passes through the point $(4,-2,2)$. If the plane is perpendicular...

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The ionic radius of $\mathrm{Na}+$ ions is 1.02 Å.. The ionic radii (in Å. ) of $\mathrm{Mg}^{2+}$ and $\mathrm{Al}^{3+}$, respectively,...

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Consider three observations a, b and c such that b = a + c. If the standard deviation of a...

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If $y=y(x)$ is the solution of the equation $...

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Considering the above reaction, X and Y respectively are:

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Let $m, n \in N$ and $\operatorname{gcd}(2, n)=1$, If $$ 30\binom{30}{0}+29\binom{30}{1}+\ldots+2\binom{30}{28}+1\binom{30}{29}=n \cdot 2^m $$ then $n+m$ is equal to (Here...

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A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after...

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The sum of 162th power of the roots of equation $x^3-2 x^2+2 x-1=0$ is

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An npn transistor operates as a common emitter amplifier with a power gain of $10^6$. The input circuit resistance is...

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The number of solutions of the equation $\log _4(x-1)=\log _2(x-3)$ is

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If for $\mathrm{a}>0$, the feet of perpendiculars from the points $\mathrm{A}(\mathrm{a},-2 \mathrm{a}, 3)$ and $\mathrm{B}(0,4,5)$ on the plane $l \mathrm{x}+\mathrm{my}+\mathrm{nz}=0$...

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As shown in the figure, a particle of mass 10 kg is placed at a point $A$. When the particle...

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The number of integral values of ' k ' for which the equation $3 \sin x+4 \cos x=k+1$ has a...

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A ball of mass 10 kg moving with a velocity $10 \sqrt{3} \mathrm{~m} / \mathrm{s}$ along the x-axis, hits another...

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The difference between degree and order of a differential equation that represents the family of curves given by $y^2=a\left(x+\frac{\sqrt{a}}{2}\right), a>0$...

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Let a vector $\alpha \hat{i}+\beta \hat{j}$ be obtained by rotating the vector $\sqrt{3} \hat{i}+\hat{j}$ by an angle $45^{\circ}$ about the...

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Let R = {(P,Q) | P and Q are at the same distance from the origin} be a relation, then...

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The value of $\int_{-\pi / 2}^{\pi / 2} \frac{\cos ^2 x}{1+3 x} d x$ is

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A parallel plate capacitor has plate area $100 \mathrm{~m}^2$ and plate separation of 10 m . The space between the...

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The value of $$ \left|\begin{array}{lll} (a+1)(a+2) & a+2 & 1 \\ (a+2)(a+3) & a+3 & 1 \\ (a+3)(a+4) & a+4...

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Consider the three planes $$ \begin{aligned} & P_1: 3 x+15 y+21 z=9 \\ & P_2: x \cdot 3 y \cdot...

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If $2.5 \times 10^{-6} \mathrm{~N}$ average force is exerted by a light wave on a non-reflecting surface of $30 \mathrm{~cm}^2$...

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Two blocks $(\mathrm{m}=0.5 \mathrm{~kg}$ and $\mathrm{M}=4.5 \mathrm{~kg})$ are arranged on a horizontal frictionless table as shown in figure. The coefficient...

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A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference $...

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The following bodies, (1) a ring (2) a disc (3) a solid cylinder (4) a solid sphere, of same mass...

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Consider two identical springs each of spring constant k and negligible mass compared to the mass $M$ as shown. Fig....

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The radius in kilometer to which the present radius of earth (R = 6400 km) to be compressed so that...

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Four identical rectangular plates with length, $l=2$ cm and breadth, $\mathrm{b}=\frac{3}{2} \mathrm{~cm}$ are arranged as shown in figure. The equivalent...

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The equivalent resistance of series combination of two resistors is 's'. When they are connected in parallel, the equivalent resistance...

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Q JEE_MAIN_2021

The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of...

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For VHF signal broadcasting, $\_\_\_\_$ $\mathrm{km}^2$ of maximum service area will be covered by an antenna tower of height 30...

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A current of 10 A exists in a wire of crosssectional area of $5 \mathrm{~mm}^2$ with a drift velocity of...

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Two ideal polyatomic gases at temperatures $\mathrm{T}_1$ and $\mathrm{T}_2$ are mixed so that there is no loss of energy. If...

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Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

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A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of $20 \mathrm{~ms}^{-1}$. The ball...

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Q JEE MAIN 2021

What is 'X' in the given reaction?

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The output of the given combination gates represents :

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The thickness at the centre of a plano convex lens is 3 mm and the diameter is 6 cm ....

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A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The...

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The major product of the following reaction is: $$ \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}=\mathrm{CH}_2 \xrightarrow[\text { Rh catalyst }]{\mathrm{H}_2 / \mathrm{CO}} $$

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Q JEE_MAIN_2021

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?

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A mass M hangs on a massless rod of length $l$ which rotates at a constant angular frequency. The mass...

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Given below are two statements : Statement 1 : The identification of $\mathrm{Ni}^{2+}$ is carried out by dimethyl glyoxime in...

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The triangle of maximum area that can be inscribed in a given circle of radius ' r ' is :

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A person is swimming with a speed of $10 \mathrm{~m} / \mathrm{s}$ at an angle of $120^{\circ}$ with the flow...

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Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to...

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The intersection of three lines x – y = 0, x + 2y = 3 and 2x + y =...

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The voltage across the $10 \Omega$ resistor in the given circuit is $x$ volt. he value of 'x' to the...

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Let $f(x)=\sin ^{-1} x$ and $g(x)=\frac{x^2-x-2}{2 x^2-x-6}$. If $g(2)=\lim _{x \rightarrow 2} g(x)$, then the domain of the function fog...

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The value of ${ }^{-15} C_1+2 .{ }^{15} C_2-3 .{ }^{15} C_3+\ldots \ldots$. $...

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A solenoid of 1000 turns per mettes has a core with relative permeability 500. Insulated windings of the solenoid carry...

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The circuit shown in the figure consists of a charged capacitor of capacity $3 \mu \mathrm{~F}$ and a charge of...

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The maximum slope of the curve $y=\frac{1}{2} x^4-5 x^3+ 18 x^2-19 x$ occurs at the point

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Which one of the following statements is FALSE for hydrophilic sols ?

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A natural number has prime factorization given by $\mathrm{n}=2^{\mathrm{x}} 3^{\mathrm{y}} 5^{\mathrm{z}}$, where y and z are such that $\mathrm{y}+\mathrm{z}=5$ and...

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A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover...

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Let f be any function defined on R and let it satisfy the condition : $$ |f(x)-f(y)| \leq\left|(x-y)^2\right|, \forall(x, y)...

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The time period of a satellite in a circular orbit of radius R is T. The period of another satellite...

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A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect...

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For $x>0$, if $f(x)=\int_1^x \frac{\log _e t}{(1+t)} d t$ then $f(e)+f\left(\frac{1}{e}\right)$ is equal to

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Your friend is having eye sight problem. She is not able lo see clearly a distant uniform window mesh and...

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Which of the following compound is added to the sodium extract before addition of silver nitrate for testing of halogens?

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The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits...

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An AC source rated 220 V, 50 Hz is connected to a resistor. The time taken by the current to...

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Let $f: R \rightarrow R$ be defined as $$ f(x)=\left\{\begin{array}{cc} 2 \sin \left(-\frac{\pi x}{2}\right), & \text { if } x1...

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In a scries LCR resonance circuit, if we change the resistance only, from a lower to higher value :

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In which of the following order the given complex ions are arranged correctly with respect to their decreasing spin only...

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If $\int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x=a \sin ^{-1}\left(\frac{\sin x+\cos x}{b}\right)+c$, where $c$ is a constant of integration,...

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In the experiment of Ohm's law, a potential difference of 5.0 V is applied across the end of a conductor...

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If the tangent to the curve $y=x^3$ at the point $P\left(t, t^3\right)$ meets the curve again at $Q$, then the...

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Let $A=\{1,2,3, \ldots, 10\}$ and $f: A \rightarrow A$ be defined as $...

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The major components of German Silver are :

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If vectors $\vec{a}_1=x \hat{i}-\hat{j}+\hat{k}$ and $\vec{a}_2=\hat{i}+y \hat{j}+z \hat{k}$ are collinear, then a possible unit vector parallel to the vector $...

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Given below are two statements : Statement I : The pH of rain water is normally ~5.6. Statement II :...

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The pH of ammonium phosphate solution, if $\mathrm{pk}_{\mathrm{a}}$ of phosphoric acid and $\mathrm{pk}_{\mathrm{b}}$ of ammonium hydroxide are 5.23 and 4.75...

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The correct order of bond dissociation enthalpy of halogens is :

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The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :

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A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle...

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In Young's double slit arrangement, slits are separated by a gap of 0.5 mm, and the screen is placed at...

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The number of stereoisomers possible for $\left[\mathrm{Co}(\mathrm{ox})_2(\mathrm{Br})\left(\mathrm{NH}_3\right)\right]^{2-}$ is $\_\_\_\_$ [ox = oxalate]

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The P-V diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done...

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In mildly alkaline medium, thiosulphate ion is oxidized by $\mathrm{MnO}_4^{-}$to " A ". The oxidation state of sulphur in "...

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The correct order of acid character of the following compounds is :

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A radioactive sample disintegrate via two independent decay processes having half lives $T_{1 / 2}^{(1)}$ and $T_{1 / 2}^{(2)}$ respectively....

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A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant...

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The number of octahedral voids per lattice site in a lattice is _____.(Rounded off to the nearest integer)

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What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium...

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A ball weighing 10 g is moving with a velocity of $90 \mathrm{~ms}^{-1}$. If the uncertainty in its velocity is...

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If $(1,5,35),(7,5,5),(1, \lambda, 7)$ and $(2 \lambda, 1,2)$ are coplanar, then the sum of all possible values of $\lambda$ is

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A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The...

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The time period of a pendulum is given by $\mathrm{T}=2 \pi \sqrt{\frac{l}{g}}$. The measured value of the length of pendulum...

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The average $\mathrm{S}-\mathrm{F}$ bond energy in $\mathrm{kJ} \mathrm{mol}^{-1}$ of $\mathrm{SF}_6$ is $\_\_\_\_$ (Rounded off to the nearest integer) [Given :...

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The rate of growth of bacteria in a culture is proportional to the number of bacteris present and the bacteria...

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Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If...

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When 12.2 g of benzoic acid is dissolved in 100 g of water, the freezing point of solution was found...

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Water does not produce CO on reacting with:

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The maximum value of the term independent of ' t ' in the expansion of $\left(t^{\frac{1}{5}}+\frac{(1-x)^{\frac{1}{10}}}{t}\right)^{10}$ where $x \in (0,1)$...

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A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with an angular speed $\omega$....

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Emf of the following cell at 298 K in V is $\mathrm{x} \times 10^{-2} . \mathrm{Zn}\left|\mathrm{Zn}^{2+}(0.1 \mathrm{M})\right|\left|\mathrm{Ag}^{+}(0.01 \mathrm{M})\right| \mathrm{Ag}$. The...

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A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the $x$-direction. At a particular point in...

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The value of $\lim _{h \rightarrow 0} 2\left\{\frac{\sqrt{3} \sin \left(\frac{\pi}{6}+h\right)+\cos \left(\frac{\pi}{6}+h\right)}{\sqrt{3} h(\sqrt{3} \cos h-\sin h)}\right\}$ is

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Imagine that the electron in a hydrogen atom is replaced by a muon $(\mu)$. The mass of muon particle is...

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Match List – I with List-II List- I (a) 10 km height over earth's surface (b) 70 km height over...

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The distance of the point $(1,1,9)$ from the point of intersection of the line $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}$ and the plane $x+y+z=17$ is

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The sum of the infinite series $1+\frac{2}{3}+\frac{7}{3^2}+\frac{12}{3^3}+\frac{17}{3^4}+\frac{22}{3^5}+\ldots$ is equal to

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Choose the correct answer from the options given below

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An oil drop of radius 2 mm with a density $3 \mathrm{~g} \mathrm{~cm}^{-3}$ his held stationary under a constant electric...

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The correct sequence of reagents used in the preparation of 4-bromo-2-nitroethyl benzene from benzene is :

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In the circle given below, let $\mathrm{OA}=1$ unit, $\mathrm{OB}=13$ unit and $\mathrm{PQ} \perp \mathrm{OB}$. Then, the area of the triangle...

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The nature of charge on resulting colloidal particles when $\mathrm{FeCl}_3$ is added to excess of hot water is :

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If $f: \mathrm{R} \rightarrow \mathrm{R}$ is a function defined by $f(\mathrm{x})=[\mathrm{x}-1] \cos \left(\frac{2 \mathrm{x}-1}{2}\right) \pi$, where $[$.$...

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A modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius...

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In a increasing geometric series, the sum of the second and the sixth term is $\frac{25}{2}$ and the product of...

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The system of linear equations 3x – 2y – kz = 10 2x – 4y – 2z = 6 x...

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The major product of the following reaction is:

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Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of...

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The locus of the point of intersection of the lines $(\sqrt{3}) k x+k y-4 \sqrt{3}=0$ and $\sqrt{3 x}-y-4(\sqrt{3}) k=0$ is...

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If the system of equations kx + y + 2z = 1 3x – y – 2z = 2 –2x...

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The population $P=P(t)$ at time ' $t$ ' of a certain species follows the differential equation $\frac{d P}{d t}=0.5 P-450$....

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The number of elements in the set $\{x \in \mathbb{R}:(|x|-3)|x+4|=6\}$ is equal to

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A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to...

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Let $\vec{a}=\hat{i}+2 \hat{j}-\hat{k}, \vec{b}=\hat{i}-\hat{j}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$ be three given vectors. If $\vec{r}$ is a vector such that $...

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Which of the following is correct structure of α-anomer of maltose ?

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The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3,...

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The equation of the plane passing through the point (1, 2, –3) and perpendicular to the planes 3x + y...

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The decomposition of formic acid on gold surface follows first order kinetics. If the rate constant at 300 K is...

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If $A=\left[\begin{array}{cc}0 & -\tan \left(\frac{\theta}{2}\right) \\ \tan \left(\frac{\theta}{2}\right) & 0\end{array}\right]$ and $\left(I_2+A\right)\left(I_2-A\right)^{-1}= \left[\begin{array}{cc}a & -b \\ b & a\end{array}\right]$, then...

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If $\vec{a} \quad$ and $\vec{b}$ are perpendicular, then $\overrightarrow{\mathbf{a}} \times(\overrightarrow{\mathbf{a}} \times(\overrightarrow{\mathbf{a}} \times(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}})))$ is equal to.

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A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line...

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Let $A=\left[\begin{array}{lll}x & y & z \\ y & z & x \\ z & x & y\end{array}\right]$, where $...

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A certain element crystallises in a bcc lattice of unit cell edge length 27 Å. If the same element under...

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Let $\mathrm{A}_1, \mathrm{~A}_2, \mathrm{~A}_3$, $\_\_\_\_$ be squares such that for each $n \geq 1$, the length of the side of...

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Two salts $A_2 X$ and $M X$ have the same value of solubility product of $4.0 \times 10^{-12}$. The ratio...

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Number of bridging CO ligands in $\left[\mathrm{Mn}_2(\mathrm{CO})_{10}\right]$ is $\_\_\_\_$ .

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Identify A in the given reaction.

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The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points...

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The statement among the following that is a tautology is :

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When light of wavelength 248 nm falls on a metal of threshold energy 3.0 eV, the de-Broglie wavelength of emitted...

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3.12 g of oxygen is adsorbed on 1.2 g of platinum metal. The volume of oxygen adsorbed per gram of...

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The number of points, at which of function $f(x)=|2 x+1|-3|x+2|+\left|x^2+x-2\right|, x \in R$ is not differentiable, is $\_\_\_\_$

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Gaseous cyclobutene isomerizes to butadiene in a first order process which has a ' k ' value of $...

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considering the above reaction, the major product among the following is :

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224 mL of $\mathrm{SO}_{2(\mathrm{~g})}$ at 298 K and 1 atm is passed through 100 mL of 0.1 M NaOH solution....

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let $f(x)$ be polynomial of degree 6 in $x$, in which the coefficient of $x^6$ is unity and it has...

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A 6.50 molal solution of KOH (aq.) has a density of $1.89 \mathrm{~g} \mathrm{~cm}^{-3}$. The molarity of the solution is...

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The coordination number of an atom in a bodycentered cubic structure is _______. [Assume that the lattice is made up...

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If Rolle's theorem holds for the function $f(x)=x^3-a x^2+b x-4, x \in[1,2]$ with $f^{\prime}\left(\frac{4}{3}\right)=0$, then ordered pair $(a, b)$ is...

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The equivalents of ethylene diamine required to replace the neutral ligands from the coordination sphere of the trans-complex of $...

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The stepwise formation of $\left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\right]^{2+}$ is given below $...

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Calgon is used for water treatment. Which of the following statement is NOT true about Calgon?

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$\mathrm{AB}_2$ is $10 \%$ dissociated in water to $\mathrm{A}^{2+}$ and $\mathrm{B}^{-}$. The boiling point of a 10.0 molal aqueous solution...

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A homogeneous ideal gaseous reaction $\mathrm{AB}_{2(\mathrm{~g})} \rightleftharpoons \mathrm{A}_{(\mathrm{g})}+2 \mathrm{~B}_{(\mathrm{g})}$ is carried out in a 25 litre flask at $27^{\circ} \mathrm{C}$....

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A proton and a $\mathrm{Li}^{3+}$ nucleus are accelerated by the same potential. If $\lambda_{\mathrm{Li}}$ and $\lambda_P$ denote the de Broglie...

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$2 \mathrm{MnO}_4^{-}+\mathrm{bC}_2 \mathrm{O}_4^{2-}+\mathrm{cH}^{+} \rightarrow \mathrm{xMn}^{2+}+\mathrm{yCO}_2+\mathrm{z} \mathrm{H}_2 \mathrm{O}$ If the above equation is balanced with integer coefficients, the value of c...

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Which among the following species has unequal bond lengths ?

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Identify A in the following chemical reaction

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A certain gas obeys $\mathrm{P}\left(\mathrm{V}_{\mathrm{m}}-\mathrm{b}\right)=\mathrm{RT}$. The value of $\left(\frac{\partial \mathrm{Z}}{\partial \mathrm{P}}\right)_{\mathrm{T}}$ is $\frac{\mathrm{xb}}{\mathrm{RT}}$. The value of x is $\_\_\_\_$ ....

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For the reaction $\mathrm{A}_{(\mathrm{g})} \rightarrow(\mathrm{B})_{(\mathrm{g})}$, the value of the equilibrium constant at 300 K and 1 atm is equal to...

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Complete combustion of 750 g of an organic compound provides 420 g of $\mathrm{CO}_2$ and 210 g of $\mathrm{H}_2 \mathrm{O}$....

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The statement $A \rightarrow(B \rightarrow A)$ is equivalent to :

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Identify A in the given chemical reaction

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An AC current is given by $\mathrm{I}=\mathrm{I} 1$ sincet +I 2 cosest. A hot wire ammeter will give a reading.

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An exothermic reaction $X \rightarrow Y$ has an activation energy $30 \mathrm{~kJ} \mathrm{~mol}^{-1}$. If energy change $\Delta \mathrm{E}$ during the...

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Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the...

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If a curve passes through the origin and the slope of the tangent to it at any point $(x, y)$...

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The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a measurement it...

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The number of significant figures in $50000.020 \times 10^{-3}$ is

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The integer ' $k$ ' for which the inequality $x^2-2(3 k-1) x+8 k^2-7>0$ is valid for every $x$ in $R$,...

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Two identical metal wires of thermal conductivities K1 and K2 respectively are connected in series. The effective thermal conductivity of...

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Which pair of oxides is acidic in nature?

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For a chemical reaction $\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}\left(\Delta_{\mathrm{r}} \mathrm{H}^0=\right. 80 \mathrm{~kJ} \mathrm{~mol}^{-1}$ ) the entropy change $\Delta_{\mathrm{r}} \mathrm{S}^0$ depends on the...

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The total number of positive integral solutions (x, y, z) such that xyz = 24 is :

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A current of 6 A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 2Ω...

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The coefficients $a, b$ and $c$ of the quadratic equation, $a x^2+b x+c=0$ are obtained by throwing a dice three...

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An amine on reaction with benzenesulphonyl chloride produces a compound insoluble in alkaline solution. This amine can be prepared by...

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An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that...

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$\lim _{n \rightarrow \infty}\left(1+\frac{1+\frac{1}{2}+\ldots \ldots+\frac{1}{n}}{n^2}\right)^n$ is equal to :

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Ceric ammonium nitrate and $\mathrm{CHCl}_3$ / alc. KOH are used for the identification of functional groups present in $\_\_\_\_$ and...

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If the curves, $\frac{x^2}{a}+\frac{y^2}{b}=1$ and $\frac{x^2}{c}+\frac{y^2}{d}=1$ intersect each other at an angle of $90^{\circ}$, then which of the following relations...

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If an electron is moving in the $n^{\text {th }}$ orbit of the hydrogen atom, then its velocity $\left(\mathrm{v}_n\right)$ for...

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2,4-DNP test can be used to identify :

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A group 15 element, which is a metal and forms a hydride with strongest reducing power among group 15 hydrides....

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Given below are two statements : Statement I: o-Nitrophenol is steam volatile due to intramolecular hydrogen bonding. Statement II: o-Nitrophenol...

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Seliwanoff test and Xanthoproteic test are used for the identification of _____and _____ respectively

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Two identical conducting spheres with negligible volume have 2.1 nC and -0.1 nC charges, respectively. They are brought into contact...

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In chromotography technique, the purification of compound is independent of :

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The image of the point (3, 5) in the line x – y + 1 = 0, lies on :

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Which one of the following lanthanoids does not form $\mathrm{MO}_2$ ? [ M is lanthanoid metal]

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In $\stackrel{1}{\mathrm{C}} \mathrm{H}_2=\stackrel{2}{\mathrm{C}}=\stackrel{3}{\mathrm{C}} \mathrm{H}-\stackrel{4}{\mathrm{C}} \mathrm{H}_3$ molecule, the hybridization of carbon $1,2,3$ and 4 respectively are:

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R...

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Let the lines $(2-i) z=(2+i) \bar{z}$ and $(2+i) z+(i-2) \bar{z}-4 i=0$, (here $i^2=-1$ ) be normal to a circle $C$....

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Compound A used as a strong oxidizing agent is amphoteric in nature. It is the part of lead storage batteries....

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The reaction of sulphur in alkaline medium is the below: $...

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All possible values of $\theta \in[0,2 \pi]$ for which $\sin 2 \theta+\tan 2 \theta>0$ lie in :

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A polyatomic ideal gas has 24 vibrational modes. What is the value of $\_\_\_\_$ y ?

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Match List-I with List-II :

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The correct order of electron gain enthalpy is

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Number of amphoteric compound among the following is __________

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A tangent is drawn to the parabola $y^2=6 x$ which is perpendicular to the line $2 x+y=1$. Which of the...

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Which of the following vitamin is helpful in delaying the blood clotting -

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The process that involves the removal of sulphur from the ores is :

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The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by...

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Which of the following is 'a' FALSE statement?

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At 1990 K and 1 atm pressure, there are equal number of $\mathrm{Cl}_2$ molecules and Cl atoms in the reaction...

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Which of the following reaction DOES NOT involve Hoffmann Bromamide degradation ?

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4.5 g of compound $\mathrm{A}(\mathrm{MW}=90)$ was used to make 250 mL of its aqueous solution. The molarity of the solution...

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On treating a compound with warm dil. $\mathrm{H}_2 \mathrm{SO}_4$, gas X is evolved which turns $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ paper acidified...

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When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface...

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Assertion A : Enol form of acetone $\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]$ exists in $

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The value of $\int_{-1}^1 x^2 e^{\left[x^3\right]} d x$ where $[t]$ denotes the greatest integer $\leq t$, is:

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When 9.45 g of $\mathrm{ClCH}_2 \mathrm{COOH}$ is added to 500 mL of water, its freezing point drops by $0.5^{\circ} \mathrm{C}$....

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The value of the integral $...

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The type of pollution that gets increased during the day time and in the presence of $\mathrm{O}_3$ is :

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Which of the following compound gives pink colour on reaction with phthalic anhydride in conc. $\mathrm{H}_2 \mathrm{SO}_4$ followed by treatment...

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A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced...

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Given below are two statements : Statement I : A mixture of chloroform and aniline can be separated by simple...

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Let $\alpha$ be the angle between the lines whose direction cosines satisfy the equations $l+\mathrm{m}-\mathrm{n}=0$ and $l^2+\mathrm{m}^2-\mathrm{n}^2 =0$. Then then...

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Given below are two statements : Statement I: $\mathrm{H}_2 \mathrm{O}_2$ can act as both oxidising and reducing agent in basic...

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Given below are two statements :one is labelled as Assertion A and the other is labelled as Reason R Assertion...

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A triangular plate is shown. A force $=\vec{F}=4 \hat{i}-3 \hat{j}$ is applied at point P . The torque at point...

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The product "A" and "B" formed in this reactions are :

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The equation of the line through the point $(0,1,2)$ and perpendicular to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{-2}$ is:

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Identify products A and B :

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The wavelength of an X-ray beam is $10 \A$. The mass of a fictitious particle having the same energy as...

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Which of the following is Lindlar catalyst ?

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The electrode potential of $\mathrm{M}^{2+} / \mathrm{M}$ of 3d-series elements shows positive value of :

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Let $f, g: N \rightarrow N$ such that $f(n+1)=f(n)+f(1) \forall n \in N$ and $g$ be any arbitrary function. Which...

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The functions of antihistamine are :

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Which of the following forms of hydrogen emits low energy $\beta^{-}$particles?

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The major components in "Gun Metal" are :

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Given below are two statements : Statement I: The $\mathrm{E}^{\circ}$ value of $\mathrm{Ce}^{4+} / \mathrm{Ce}^{3+}$ is +1.74 V . Statement...

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Q JEE MAIN 2021

If $0

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The initial velocity $v_i$ required to project a body vertically upward from the surface of the earth to reach a...

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The gas released during anaerobic degradation of vegetation may lead to :

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In the below chemical reaction, intermediate "X" and reagent/condition "A" are :

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When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that...

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Match List I with List II.

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The zener diode has a $V_z=30 \mathrm{~V}$. The current passing through the diode for the following circuit is $\_\_\_\_$ mA.

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The orbital having two radial as well as two angular nodes is -

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Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are...

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A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity $...

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Out of the following, which type of interaction is responsible for the stabilisation of $\alpha$-helix structure of proteins ?

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Statements about heavy water are given below. A. Heavy water is used in exchange reactions for the study of reaction...

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Given below are two statements : Statement I : Colourless cupric metaborate is reduced to cuprous metaborate in a luminous...

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Among the following, the aromatic compounds are :

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The peak electric field produced by the radiation coming from the 8 W bulb at a distance of 10 m...

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The ionization enthalpy of $\mathrm{Na}^{+}$formation from $\mathrm{Na}_{(\mathrm{g})}$ is $495.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$, while the electron gain enthalpy of Br is $...

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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Which of the following reagent is used for the following reaction ?

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Match List-I with List-II :

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What is the major product formed by HI on reaction with

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Consider the following chemical reaction. $...

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Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter 0.1μm. If the diameter of the...

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0.4 g mixture of $\mathrm{NaOH}, \mathrm{Na}_2 \mathrm{CO}_3$ and some inert impurities was first titrated with $\frac{\mathrm{N}}{10} \mathrm{HCl}$ using phenolphthalein as...

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The product 'P' in the below reaction is :

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The presence of ozone in troposphere

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1 mole of rigid diatomic gas performs a work of $Q / 5$ when heat $Q$ is supplied to it....

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(A) $\mathrm{HOCl}+\mathrm{H}_2 \mathrm{O}_2 \rightarrow \mathrm{H}_3 \mathrm{O}^{+}+\mathrm{Cl}^{-}+\mathrm{O}_2$ (B) $\mathrm{I}_2+\mathrm{H}_2 \mathrm{O}_2+2 \mathrm{OH}^{-} \rightarrow 2 \mathrm{I}^{-}+2 \mathrm{H}_2 \mathrm{O}+\mathrm{O}_2$ Choose the correct option.

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For the reaction, $\mathrm{aA}+\mathrm{bB} \rightarrow \mathrm{cC}+\mathrm{dD}$, the plot of $\log \mathrm{k}$ vs $\frac{1}{\mathrm{~T}}$ is given below : The temperature at...

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Find $\mathrm{A}, \mathrm{B}$ and C in the following reactions : $$ \begin{aligned} & \mathrm{NH}_3+\mathrm{A}+\mathrm{CO}_2 \rightarrow\left(\mathrm{NH}_4\right)_2 \mathrm{CO}_3 \\ & \left(\mathrm{NH}_4\right)_2 \mathrm{CO}_3+\mathrm{H}_2...

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Given below are two statements : Statement I: Both $\mathrm{CaCl}_2 .6 \mathrm{H}_2 \mathrm{O}$ and $\mathrm{MgCl}_2 .8 \mathrm{H}_2 \mathrm{O}$ undergo dehydration...

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Match List I with List II.

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In the reported figure of earth, the value of acceleration due to gravity is same at point A and C...

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In Freundlich adsorption isotherm, slope of AB line is:

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Using the provided information in the following paper chromatogram : the calculate $\mathrm{R}_{\mathrm{f}}$ value of A $\_\_\_\_$ $\times 10^{-1}$.

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Which among the following pairs of Vitamins is stored in our body relatively for longer duration ?

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The structure of Neoprene is –

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In the following reaction the reason why meta-nitro product also formed is :

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Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R ;...

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Time period of a simple pendulum is $T$. The time taken to complete $5 / 8$ oscillations starting from mean...

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The maximum and minimum amplitude of an amplitude modulated wave is 16 V and 8 V respectively. The modulation index...

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What is the final product (major) 'A' in the given reaction ?

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A ball of mass 10 kg moving with a velocity $10 \sqrt{3} \mathrm{~ms}^{-1}$ along $X$-axis, hits another ball of mass...

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Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure....

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The resistance $R=\frac{V}{I}$, where $V=(50 \pm 2) V$ and $I=(20 \pm 0.2) A$. The percentage error in $R$ is '...

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In the logic circuit shown in the figure, if input A and B are 0 to 1 respectively, the output...

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A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which $...

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The value of power dissipated across the zener diode $\left(V_z=15 V\right)$ connected in the circuit as shown in the figure...

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The first three spectral lines of H -atom in the Balmer series are given $\lambda_1, \lambda_2, \lambda_3$ considering the Bohr...

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Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is...

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A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed...

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In the figure given, the electric current flowing through the $5 \mathrm{k} \Omega$ resistor is ' x ' mA .

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A conducting bar of length L is free to slide on two parallel conducting rails as shown in the figure

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27 similar drops of mercury are maintained at 10 V each. All these spherical drops combine into a single big...

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The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V....

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Which of the following are isostructural pairs ? $\mathrm{SO}_4^{2-}$ and $\mathrm{CrO}_4^{2-}$ $\mathrm{SiCl}_4$ and $\mathrm{TiCl}_4$ $\mathrm{NH}_3$ and $\mathrm{NO}_3^{-}$ $\mathrm{BCl}_3$ and $\mathrm{BrCl}_3$

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A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls...

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A particle executes S.H.M. with amplitude ' $a$ ' and time period $V$. The displacement of the particle when its...

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The truth table for the followng logic circuit is :

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$\mathrm{Al}_2 \mathrm{O}_3$ was leached with alkali to get $X$. The solution of $X$ on passing of gas $Y$, forms $...

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The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation :

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In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two...

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The reaction of cyanamide, $\mathrm{NH}_2 \mathrm{CN}_{(\mathrm{s})}$ with oxygen was run in a bomb calorimeter and $\Delta \mathrm{U}$ was found to...

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An RC circuit as shown in the figure is driven by a AC source generating a square wave. The output...

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A point source of light S , placed at a distance 60 cm infront of the centre of a plane...

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The mass per unit length of a uniform wire is 0.135 $g / \mathrm{cm}$. A transverse wave of the form...

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Which of the following ore is concentrated using group 1 cyanide salt ?

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A car tyre is filled with nitrogen gas at 35 psi at $27^{\circ} \mathrm{C}$. It will burst if pressure exceeds...

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For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric $\left(U_e\right)$ and magnetic...

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A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second...

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The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers...

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Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on...

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'A' and 'B' in the following reactions are :

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In basic medium $\mathrm{CrO}_4^{2-}$ oxidises $\mathrm{S}_2 \mathrm{O}_3^{2-}$ to form $\mathrm{SO}_4^{2-}$ and itself changes into $\mathrm{Cr}(\mathrm{OH})_4^{-}$. The volume of 0.154 M...

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A 25 m long antenna is mounted on an antenna tower. The height of the antenna tower is 75 m....

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As shown in the figure, a block of mass $\sqrt{3} \mathrm{~kg}$ is kept on a horizontal rough surface of coefficient...

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1 molal aqueous solution of an electrolyte $A_2 B_3$ is $60 \%$ ionised. The boiling point of the solution at...

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Consider the elements Mg. Al, S, P and Si, the correct increasing order of their first ionization enthalpy is :

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The velocity-displacement graph describing the motion of a bicycle is shown in the figure.

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Among the following, the number of halide(s) which is/are inert to hydrolysis is _______.

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If the highest frequency modulating a carrier is 5 kHz , then the number of AM broadcast stations accommodated in...

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The product formed in the first step of the reaction of with excess $\mathrm{Mg} / \mathrm{Et}_2 \mathrm{O}\left(\mathrm{Et}=\mathrm{C}_2 \mathrm{H}_5\right)$ is :

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A boy pushes a box of mass 2 kg with a force $\vec{F}=(20 \hat{i}+10 \hat{j}) \mathrm{N}$ on a frictionless surface....

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An electron with kinetic energy $K_1$ enters between parallel plates of a capacitor at an angle ' $\alpha$ ' with...

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The major product of the following chemical reaction is :

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Time period of a simple pendulum is $T$ inside a lift when the lift is stationary. If the lift moves...

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A radiation is emitted by 1000 W bulb and it generates an electric field and magnetic field at $P$, placed...

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The volume V of a given mass of monoatomic gas changes with temperature T according to the relation $...

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An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging...

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Which statement is correct ?

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If e is the electronic charge, $c$ is the speed of light in free space and $h$ is Planck's constant,...

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The circuit contains two diodes each with a forward resistance of $50 \Omega$ and with infinite reverse resistance. If the...

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A conducting wire of length 'l', area of cross-section A and electric resistivity $\rho$ is connected between the terminals of...

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A common transistor radio set requires 12V (D.C.) for its operation. The D.C. source is constructed by using a transformer...

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Identify A and B in the chemical reaction.

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The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $\vec{a}, \vec{b}$ and $\vec{c}$...

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A ball will a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction...

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Four equal masses, m each are placed at the corners of a square of length (l) as shown in the...

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In an electrical circuit, a battery is connected to pass 20 C of charge through it in a certain given...

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An audio signal $v_m=20 \sin 2 \pi(1500 \mathrm{t})$ amplitude modulates a carrier $v_c=80 \sin 2 \pi(100,000 \mathrm{t})$. The value of...

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In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption $\left(\frac{x}{m}\right)$ is directly proportional to $P^x$. The value of...

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A wire of 1 W has a length of 1 m . It is stitched till its length increases by...

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In connection with the circuit drawn below, the value of current flowing through $2 \mathrm{k} \Omega$ resistor is $\_\_\_\_$ $...

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A person standing on a spring balance inside a stationary lift measures 60 kg. The weight of that person if...

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In thermodynamics, heat and work are :

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An electromagnetic wave of frequency 5 GHz , is travelling in a medium whose relative electric permittivity and relative magnetic...

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The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen...

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Five equal resistances are connected in a network as shown in figure. The net resistance between the points A and...

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Given below are two statements Statement I : A second's pendulum has a time period of 1 second. Statement II...

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An inclined plane is bent in such a way that the vertical cross-section is given by $y=\frac{x^2}{4}$ where $y$ is...

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A bar magnet of length 14 cm is placed in the magnetic meridian with its north pole pointing towards the...

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A large number of water drops, each of radius r, combine to have a drop of radius R. If the...

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A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift...

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Ellingham diagram is a graphical representation of:

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The maximum and minimum distances of a comet from the Sun are $1.6 \times 10^{12} \mathrm{~m}$ and $...

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A resonance circuit having inductance and resistance $2 \times 10^{-4} \mathrm{H}$ and $6.28 \Omega$ respectively oscillates at 10 MHz frequency....

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A scooter accelerates from rest for time $t_1$ at constant rate $a_1$ and then retards at constant rate $a_2$ for...

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LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is 1.9 eV. Calculate the wavelength of...

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The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2...

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plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and...

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The hybridization and magnetic nature of $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{4-}$ and $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$, respectively are:

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$\mathrm{Y}=\mathrm{A} \sin \left(\omega \mathrm{t}+\varphi_0\right)$ is the time-displacement equation of a SHM. At $t=0$ the displacement of the particle is $Y=\frac{A}{2}$...

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A radioactive sample is undergoing $\alpha$ decay. At any time $t_1$, its activity is A and another time $t_2$, the...

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The workdone by a gas molecule in an isolated system is given by, $\mathrm{W}=\alpha \beta^2 \mathrm{e}^{-\frac{x}{\alpha \mathrm{kT}}}$, where x is...

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Consider two satellites $S_1$ and $S_2$ with periods of revolution 1 hr . and 8 hr . respectively revolving around...

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Draw the output signal Y in the given combination of gates

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The angle of deviation through a prism is minimum when

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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A cube of side ' $a$ ' has point charges $+Q$ located at each of its vertices except at the...

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Compound(s) which will liberate carbon dioxide with sodium bicarbonate solution is/are:

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The pressure acting on a submarine is $3 \times 10^5 \mathrm{~Pa}$ at a certain depth. If the depth is doubled,...

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The temperature $\theta$ at the junction of two insulating sheets, having thermal resistances $\mathrm{R}_1$ and $\mathrm{R}_2$ as well as top...

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Which of the glycosidic linkage between galactose and glucose is present in lactose?

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A cell $E_1$ of emf 6 V and internal resistance $2 \Omega$ is connected with another cell E2 of emf...

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Two masses A and B, each of mass $M$ are fixed together by a massless spring. $A$ force acts on...

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In which of the following pairs, the outer most electronic configuration will be the same?

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A block of mass $m$ slides along a floor while a force of magnitude $F$ is applied to it at...

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Each side of a box made of metal sheet in cubic shape is ' $a$ ' at room temperature '...

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If two similar springs each of spring constant $\mathrm{K}_1$ are joined in series, the new spring constant and time period...

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An inclined plane making an angle of $30^{\circ}$ with the horizontal is placed in a uniform horizontal electric field $...

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Given below are two statements: Statement I : An allotrope of oxygen is an important intermediate in the formation of...

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Match List-I with List-II :

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Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin...

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The plots of radial distribution functions for various orbitals of hydrogen atom against 'r' are given below:

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An LCR circuit contains resistance of $110 \Omega$ and a supply of 220 V at $300 \mathrm{rad} / \mathrm{s}$ angular...

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One main scale division of a vernier callipers is ' $a$ ' cm and $n$th division of the vernier scale...

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Find the peak current and resonant frequency of the following circuit

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If an emitter current is changed by 4 mA , the collector current changes by 3.5 mA . The value...

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The correct statement about $\mathrm{B}_2 \mathrm{H}_6$ is:

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In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed one meter...

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Which one of the following reactions will not form acetaldehyde ?

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The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2...

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Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the...

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Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners...

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Complete combustion of 1.80 g of an oxygen containing compound $\left(\mathrm{C}_x \mathrm{H}_y \mathrm{O}_z\right)$ gave 2.64 g of $\mathrm{CO}_2$ and 1.08...

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The recoil speed of a hydrogen atom after it emits a photon in going from $n=5$ state to $n=1$ state...

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If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph ?

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Identify A in the given chemical reaction.

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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A charge q is placed at one corner of a cube as shown in figure. The flux of electrostatic field...

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Which of the following equation depicts the oxidizing nature of $\mathrm{H}_2 \mathrm{O}_2$ ?

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Four identical particles of equal masses 1kg made to move along the circumference of a circle of radius 1 m...

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A planet revolving in elliptical orbit has : (A)a constant velocity of revolution. (B) has the least velocity when it...

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Given below are two statements : Statement I : An electric dipole is placed at the centre of a hollow...

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Which of the following reaction/s will not give p-aminoazobenzene ?

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In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B,...

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A particle is moving with uniform speed along the circumference of a circle of radius R under the action of...

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According to molecular theory, the species among the following that does not exist is:

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The normal density of a material is $\rho$ and its bulk modulus of elasticity is K. The magnitude of increase...

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Given below are two statements: Statement I: $\mathrm{CeO}_2$ can be used for oxidation of aldehydes and ketones. Statement 11 :...

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The potential energy $(\mathrm{U})$ of a diatomic molecule is a function dependent on r (interatomic distance) as $\mathrm{U}=\frac{\alpha}{\mathrm{r}^{10}}-\frac{\beta}{\mathrm{r}^5}-3$ where, $\alpha$...

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An alternating current is given by the equation $\mathrm{i}=\mathrm{i}_1 \sin \omega \mathrm{t}+\mathrm{i}_2 \cos \omega \mathrm{t}$. The rms current will be

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If Y, K and  are the values of Young's modulus, bulk modulus and modulus of rigidity of any material...

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A coil of inductance 2H having negligible resistance is connected to a source of supply whose voltage is given by...

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Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see...

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512 identical drops of mercury are charged to a potential of 2V each. The drops are joined to form a...

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Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's...

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The same size images are formed by a convex lens when the object is placed at 20cm or at 10cm...

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A cord is wound round the circumference of wheel of radius $r$. The axis of the wheel is horizontal and...

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In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to...

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A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length...

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Given below are two statements : Statement-I : Two photons having equal linear momenta have equal wavelengths. Statement-II : If...

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If $\lambda_1$ and $\lambda_2$are the wavelengths of the third member of Lyman and first member of the Paschen series respectively,...

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An aeroplane, with its wings spread 10 m , is flying at a speed of $180 \mathrm{~km} / \mathrm{h}$ in...

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In a typical combustion engine the work done by a gas molecule is given $\mathrm{W}=\alpha^2 \beta e^{\frac{-\beta \mathrm{x}^2}{\mathrm{kT}}}$ where x...

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The length of metallic wire is $\ell_1$ when tension in it is $T_1$. It is $\ell_2$ when the tension is...

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A current through a wire depends on time as $\mathrm{i}=\alpha_0 t +\beta t^2$ where $\alpha_0=20 \mathrm{~A} / \mathrm{s}$ and $...

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Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free...

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Consider the combination of 2 capacitors $\mathrm{C}_1$ and $\mathrm{C}_2$,, with $C_2>C_1$,, when connected in parallel, the equivalent capacitance is $\frac{15}{4}$...

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In a Young's double slit experiment, the width of the one of the slit is three times the other slit....

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1. If $C$ and $V$ represent capacity and voltage respectively then what are the dimensions of $\lambda$, where $\frac{\mathrm{C}}{\mathrm{V}}=\lambda$ ?

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The focal length f is related to the radius of curvature r of the spherical convex mirror by:

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n mole a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.

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Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of...

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Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow...

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A series LCR circuit is designed to resonate at an angular frequency $\omega_0=10^5 \mathrm{rad} / \mathrm{s}$. The circuit draws 16...

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In the given circuit of potentiometer, the potential difference $E$ across $A B(10 m$ length $)$ is larger than $E_1$...

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A signal of 0.1 kW is transmitted in a cable. The attenuation of cable is -5 dB per km and...

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A small bob tied at one end of a thin string of length 1 m is describing a vertical circle...

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A point charge of $+12 \mu \mathrm{C}$ is at a distance 6 cm vertically above the centre of a square...

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In a certain thermodynamical process, the pressure of a gas depends on its volume as $\mathrm{kV}^3$. The work done when...

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The root mean square speed of molecules of a given mass of a gas at $27^{\circ} \mathrm{C}$ and 1 atmosphere...

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The electric field in a region is given $\vec{E}=\left(\frac{3}{5} E_0 \hat{i}+\frac{4}{5} E_0 \hat{j}\right) \frac{N}{C}$. The ratio of flux of reported...

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Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The...

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A transmitting station releases waves of wavelength 960 m . A capacitor of $2.56 \mu \mathrm{~F}$ is used in the...

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Two coherent light sources having intensity in the ratio 2x produce an interference pattern. The ratio $...

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A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The...

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The current (i) at time $t=0$ and $t=\infty$ respectively for the given circuit is

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A cylindrical wire of radius 0.5 mm and conductivity $5 \times 10^7 \mathrm{~S} / \mathrm{m}$ is subjected to an electric...

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A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its...

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on...

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Given below are two statements : Statement I : In a diatomic molecule, the rotational energy at a given temperature...

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In an octagon ABCDEFGH of equal side, what is the sum of $\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AD}}+\overrightarrow{\mathrm{AE}}+\overrightarrow{\mathrm{AF}}+\overrightarrow{\mathrm{AG}}+\overrightarrow{\mathrm{AH}}$ if, $\overrightarrow{A O}=2 \hat{i}+3 \hat{j}-4 \hat{k}$

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A particle is projected with velocity $v_0$ along $x$-axis. A damping force is acting on the particle which is proportional...

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Two radioactive substances $X$ and $Y$ originally have $N_1$ and $N_2$ nuclei respectively. Half life of $X$ is half of...

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Match List - I with List - II. Choose the correct answer from the options given below :

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A stone is dropped from the top of a building. When it crosses a point 5 m below the top,...

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A solid sphere of radius $R$ gravitationally attracts a particle placed at $3 R$ form its centre with a force...

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Zener breakdown occurs in a p-n junction having p and n both :

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Magnetic fields at two points on the axis of a circular coil at a distance of 0.05m and 0.2 m...

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A circular hole of radius $\left(\frac{a}{2}\right)$ is cut out of a circular disc of radius ' $a$ ' as shown...

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Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If $\mathrm{V}_2=2 \mathrm{~V}_1$ then...

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Match List – I with List – II List – I (a) h (Planck's constant) (b) E (kinetic energy) (c)...

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If the source of light used in a Young's double slit experiment is changed from red to violet :

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An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment with...

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According to Bohr atom model, in which of the following transitions will the frequency be maximum ?

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Which of the following equations represents a travelling wave ?

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A diatomic gas, having $C_p=\frac{7}{2} R$ and $C_v=\frac{5}{2} R$ is heated at constant pressure. The ratio dU : dQ :...

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An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be:

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The length of metallic wire is $\ell_1$ when tension in it is $T_1$. It is $\ell_2$ when the tension is...

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In a ferromagnetic material, below the curie temperature, a domain is defined as :

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An $\alpha$ particle and a proton are accelerated from rest by a potential difference of 200 V . After this,...

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If one mole of an ideal gas at $\left(P_1, V_1\right)$ is allowed to expand reversibly and isothermally (A to B)...

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A 5 V battery is connected across the points $X$ and $Y$. Assume $D_1$ and $D_2$ to be normal silicon...

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The de Broglie wavelength of a proton and a-particle are equal. The ratio of their velocities is :

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The pitch of the screw gauge is 1mm and there are 100 divisions on the circular scale. When nothing is...

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For extrinsic semiconductors; when doping level is increased;

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Figure shows a circuit that contains four identical resistors with resistance $\mathrm{R}=2.0 \Omega$, two identical inductors with inductance $\mathrm{L}=2.0 \mathrm{mH}$...

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If the time period of a two meter long simple pendulum is 2s, the acceleration due to gravity at the...

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Given below are two statement : Statement-I: A speech signal of 2 kHz is used to modulate a carrier signal...

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In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane....

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A proton, a deuteron and an  particle are moving with same momentum in a uniform magnetic field. The ratio...

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The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the...

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The period of oscillation of a simple pendulum is $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{~L}}{\mathrm{~g}}}$. Measured value of ' L ' is 1.0...

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Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of...

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The logic circuit shown above is equivalent to :

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A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains :

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A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency...

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On the basis of kinetic theory of gases, the gas exerts pressure because its molecules :

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Given below are two statement : one is labelled as Assertion A and the other is labelled as Reason R....

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Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly...

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When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :

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