Q JEE MAIN 2025

In an electrical circuit drawn below the amount of charge stored in the capacitor is $\mu \mathrm{C}$.

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Q JEE MAIN 2025

Let the area of the triangle formed by the lines $x+2=y-1=z, \frac{x-3}{5}=\frac{y}{-1}=\frac{z-1}{1}$ and $\frac{x}{-3}=\frac{y-3}{3}=\frac{z-2}{1}$ be $A$. Then $A^2$ is equal...

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Q JEE MAIN 2025

Let $r$ be the radius of the circle, which touches $x$ - axis at point $(a, 0), a

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Let the area of the bounded region $\left\{(x, y): 0 \leq 9 x \leq y^2, y \geq 3 x-6\right\}$ be...

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Q JEE MAIN 2025

The product of the last two digits of $(1919)^{1919}$ is $\_\_\_\_$

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Q JEE MAIN 2025

The number of integral terms in the expansion of $\left(5^{\frac{1}{2}}+7^{\frac{1}{8}}\right)^{1016}$ is

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Q JEE MAIN 2025

Let $\alpha$ be a solution of $x^2+x+1=0$, and for some $a$ and $b$ in $...

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Q JEE MAIN 2025

Let $f(x)$ be a positive function and $I_1=\int_{-\frac{1}{2}}^1 2 x f(2 x(1-2 x)) d x$ and $I_2=\int_{-1}^2 f(x(1-x)) d x$....

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Q JEE MAIN 2025

The Value of $\cot ^{-1}\left(\frac{\sqrt{1+\tan ^2(2)}-1}{\tan (2)}\right)-\cot ^{-1}\left(\frac{\sqrt{1+\tan ^2\left(\frac{1}{2}\right)}+1}{\tan \left(\frac{1}{2}\right)}\right)$ is equal to

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Q JEE MAIN 2025

The sum of the squares of the roots of $|x-2|^2+|x-2|-2=0$ and the squares of the roots of $x^2-2|x-3|-5=0$, is

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Q JEE MAIN 2025

Let $A=\{0,1,2,3,4,5\}$. Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $...

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Q JEE MAIN_2025

If $\int\left(\frac{1}{x}+\frac{1}{x^3}\right)\left(\sqrt[7]{3 x^{-24}+x^{-26}}\right) \mathrm{d} x=-\frac{\alpha}{3(\alpha+1)}\left(3 x^\beta+x^7\right)^{\frac{\alpha+4}{\alpha}}+C, x>0,(\alpha, \beta, \gamma \in \mathbf{Z})$, where C is the constant of integration, then $\alpha+\beta+\gamma$...

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Q JEE MAIN 2025

There are 12 points in a plane, no three of which are in the same straight line, except 5 points...

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Q JEE MAIN_2025

The sum of the series $...

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Q JEE MAIN_2025

If the function $f(x)=\frac{\tan (\tan x)-\sin (\sin x)}{\tan x-\sin x}$ is continuous at $x=0$, then $f(0)$ is equal to $\_\_\_\_$...

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Q JEE MAIN 2025

The integral $\int_{-1}^{\frac{3}{2}}\left(\left|\pi^2 x \sin (\pi x)\right|\right) d x$ is equal to :

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Q JEE MAIN_2025

Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2 a and 2...

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Q JEE MAIN 2025

Given below are two statements: Statement I : $\lim _{x \rightarrow 0}\left(\frac{\tan ^{-1} x+\log _e \sqrt{\frac{1+x}{1-x}}-2 x}{x^5}\right)=\frac{2}{5}$ Statement II: $...

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Q JEE MAIN_2025

For $\mathrm{t}>-1$, let $\alpha_{\mathrm{t}}$ and $\beta$, be the roots of the equation $$ \left((t+2)^{1 / 7}-1\right) x^2+\left((t+2)^{1 / 0}-1\right) x+\left((t+2)^{2...

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Q JEE MAIN_2025

Let $c_1$ and $c_2$ be the eccentricities of the ellipse $\frac{x^2}{b^2}+\frac{y^2}{25}=1$ and the hyperbola $\frac{x^2}{16}-\frac{y^2}{b^2}=1$. respectively. If $\mathrm{b}

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Q JEE MAIN 2025

Let $A=\left\{\theta \in[0,2 \pi]: 1+10 \operatorname{Re}\left(\frac{2 \cos \theta+i \sin \theta}{\cos \theta-3 i \sin \theta}\right)=0\right\}$. Then $\sum_{\theta \in \mathrm{A}} \theta^2$ is...

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Q JEE MAIN 2025

A line passing through the point $P(a, 0)$ makes an acute angle $\alpha$ with the positive $x$-axis. Let this line...

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Q JEE MAIN_2025

A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is...

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Q JEE MAIN 2025

Let the values of $\lambda$ for which the shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-\lambda}{3}=\frac{y-4}{4}=\frac{z-5}{5}$ is $\frac{1}{\sqrt{6}}$ be $\lambda_1$...

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Q JEE MAIN_2025

Let a random variable $X$ take values $0,1,2,3$ with $P(X=0)=P(X=1)=p, P(X=2)=P(X=3)$ and $E\left(X^2\right)=2 E(X)$. Then the value of $8 p-1$...

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Q JEE MAIN_2025

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a polynomial function of degree four having extreme values at $x=4$ and $x=5$. If...

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Q JEE MAIN 2025

Let $f(x)=x-1$ and $g(x)=e^x$ for $x \in \mathbb{R}$. If $\frac{d y}{d x}=\left(e^{-2 \sqrt{x}} g(f(f(x)))-\frac{y}{\sqrt{x}}\right), y(0)=0$, then $y(1)$ is

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Q JEE MAIN 2025

If the sum of the first 10 terms of the series $...

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Q JEE MAIN_2025

Let $p$ be the number of all triangles that can be formed by joining the vertices of a regular polygon...

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Q JEE MAIN 2025

If the set of all $a \in R-\{1\}$, for which the roots of the equation $(1-a) x^2+2(a-3) x+9=0$ are positive...

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Q JEE MAIN 2025

Let $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}-\hat{k}$. Let $\hat{c}$ be a unit vector in the plane of the vectors $\vec{a}$ and...

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Q JEE MAIN 2023

The coefficient of $x^5$ in the expansion of $\left(2 x^3-\frac{1}{3 x^2}\right)^5$

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Q JEE MAIN 2025

20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The...

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If $y=\cos \left(\frac{\pi}{3}+\cos ^{-1} \frac{x}{2}\right)$, then $(x-y)^2+3 y^2$ is equal to

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Q JEE MAIN 2025

Let $A(4,-2), B(1,1)$ and $C(9,-3)$ be the vertices of a triangle ABC . Then the maximum area of the parallelogram...

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Q JEE MAIN 2025

The equilibrium constant for decomposition of $\mathrm{H}_2 \mathrm{O}$ (g) $\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g})\left(\Delta \mathrm{G}^{\circ}=92.34 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)$ is $...

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Q JEE MAIN 2025

$ \begin{aligned} & \text { If } \frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}+\ldots \infty=\frac{\pi^4}{90} \\ & \frac{1}{1^4}+\frac{1}{3^4}+\frac{1}{5^4}+\ldots \infty=\alpha, \\ & \frac{1}{2^4}+\frac{1}{4^4}+\frac{1}{6^4}+\ldots \infty=\beta \end{aligned} $ then...

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Q JEE MAIN 2025

Let $\left(1+x+x^2\right)^{10}=a_0+a_1 x+a_2 x^2+\ldots+a_{20} x^{20}$. If $\left(a_1+a_3+a_5+\ldots+a_{19}\right)-11 a_2=121 k$, then $k$ is equal to $\_\_\_\_$

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Q JEE MAIN 2025

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

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Q JEE MAIN 2025

If the equation of the hyperbola with foci $(4,2)$ and $(8,2)$ is $3 x^2-y^2-\alpha x+\beta y+\gamma=0$, then $\alpha+\beta+\gamma$ is equal...

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Q JEE MAIN 2025

Let $a$ be the length of a side of a square OABC with O being the origin. Its side OA...

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$x \mathrm{mg}$ of $\mathrm{Mg}(\mathrm{OH})_2($ molar mass $=58)$ is required to be dissolved in 1.0 L of water to produce a...

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Q JEE MAIN 2025

Let $\vec{a}=2 \hat{i}-3 \hat{j}+\hat{k}, \vec{b}=3 \hat{i}+2 \hat{j}+5 \hat{k}$ and a vector $\vec{c}$ be such that $...

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Q JEE MAIN 2025

Let m and $\left.\mathrm{n}_{( } \mathrm{m}

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A metal complex with a formula $\mathrm{MCl}_4 \cdot 3 \mathrm{NH}_3$ is involved in $\mathrm{sp}^3 \mathrm{~d}^2$ hybridisation. It upon reaction with...

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Q JEE MAIN 2025

Let $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=3 \hat{i}-3 \hat{j}+3 \hat{k}, \vec{c}=2 \hat{i}-\hat{j}+2 \hat{k}$ and $\vec{d}$ be a vector such that $...

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Q JEE MAIN 2025

Let the ellipse $3 x^2+p y^2=4$ pass through the centre $C$ of the circle $x^2+y^2-2 x-4 y-11=0$ of radius $r$....

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Q JEE MAIN 2025

Sea water, which can be considered as a 6 molar $(6 \mathrm{M})$ solution of NaCl , has a density of...

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Let $I$ be the identity matrix of order $3 \times 3$ and for the matrix $...

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Q JEE MAIN 2025

Let $...

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Q JEE MAIN 2025

The molar conductance of an infinitely dilute solution of ammonium chloride was found to be $185 \mathrm{Scm}^2 \mathrm{~mol}^{-1}$ and the...

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Q JEE MAIN 2025

The energy of an electron in first Bohr orbit of H -atom is -13.6 eV. The magnitude of energy value...

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Q JEE MAIN 2025

If $\lim _{x \rightarrow 0}\left(\frac{\tan x}{x}\right)^{\frac{1}{x^2}}=p$, then $96 \log _e p$ is equal to $\_\_\_\_$

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Q JEE MAIN 2025

The amount of calcium oxide produced on heating 150 kg limestone ( pure) is _________ kg. (Nearest integer) Given: Molar...

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Q JEE MAIN 2025

The IUPAC name of the following compound is

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Given below are two statements. Statement (I): Molal depression constant $K_f$ is given by $\frac{M_1 R T_f}{\Delta S_{\text {fus }}}$,...

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Q JEE MAIN 2025

One litre buffer solution was prepared by adding 0.10 mol each of and in deionised water. The change in pH...

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The number of species from the following that are involved in $\mathrm{sp}^3 \mathrm{~d}^2$ hybridization is $$ \left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}, \mathrm{SF}_6,\left[\mathrm{CrF}_6\right]^{3-},\left[\mathrm{CoF}_6\right]^{3-},\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-} \text {...

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Q JEE MAIN 2025

In which pairs, the first ion is more stable than the second?

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Q JEE MAIN 2025

Identify the structure of the final product (D) in the following sequence of the reactions : Total number of hybridised...

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Q JEE MAIN 2025

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

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Consider the ground state of chromium atom $(Z=24)$ . How many electrons are with Azimuthal quantum number $l=1$ and $l=2$...

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Consider the following molecule (X). The structure of X is The major product formed when the given molecule (X) is...

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Q JEE MAIN_2025

Let $y=y(x)$ be the solution of the differential equation $\left(x^2+1\right) y^2-2 x y=\left(x^4+2 x^2+1\right) \cos x$. $y(0)=1$. Then $...

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Q JEE MAIN_2025

The number of real roots of the equation $x|x-2|+3|x-3|+1=0$ is i

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Let the function $f(x)=\frac{x}{3}+\frac{3}{x}+3, x \neq 0$ be strictly increasing in $\left(-\infty, \alpha_1\right) \cup\left(\alpha_2, \infty\right)$ and strictly decreasing in $...

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Q JEE MAIN 2025

In Dumas' method 292 mg of an organic compound released 50 mL of nitrogen gas at 300 K temperature and...

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If the orthocenter of the triangle formed by the lines $y=x+1, y=4 x-8$ and $y=m x+c$ is at $(3,-1)$ ,...

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Q JEE MAIN 2025

If $\int \frac{\left(\sqrt{1+x^2}+x\right)^{10}}{\left(\sqrt{1+x^2}-x\right)^9} \mathrm{~d} x=\frac{1}{\mathrm{~m}}\left(\left(\sqrt{1+x^2}+x\right)^0\left(\pi \sqrt{1+x^2}-x\right)\right)+\mathrm{C}$ where C is the constant of integration and $m, n \in \mathbf{N}$, then $m+n$...

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Q JEE MAIN 2025

Let the area of the triangle formed by a straight line $L: x+b y+c=0$ with co-ordinate axes be 48 square...

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Q JEE MAIN 2025

Butane reacts with oxygen to produce carbon dioxide and water following the equation given below. If 174.0 kg of butane...

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If $A$ and $B$ are two events such that $P(A)=0.7, P(B)=0.4$ and $P(A \cap \bar{B})=0.5$, where $\bar{B}$ denotes the complement...

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A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and...

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' $X$ ' is the number of electrons in $t_{2 g}$ orbitals of the most stable complex ion among $...

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Q JEE MAIN 2025

If $\alpha$ is a root of the equation $x^2+x+1=0$ and $\sum_{k=1}^n\left(\alpha^k+\frac{1}{\alpha^k}\right)^2=20$, then n is equal to $\_\_\_\_$ .

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Q JEE MAIN 2025

The number of paramagnetic metal complex species among $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+},\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$, $\left[\mathrm{MnCl}_6\right]^{3-},\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-},\left[\mathrm{CoF}_6\right]^{3-},\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$ and $\left[\mathrm{FeF}_6\right]^{3-}$ with same number of unpaired electrons is...

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Q JEE MAIN 2025

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$4 \int_0^1\left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right) d x-3 \log _e(\sqrt{3})$ is equal to :

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Q JEE MAIN 2025

Let the three sides of a triangle ABC be given by the vectors $2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}$ and $...

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Q JEE MAIN 2025

Which among the following compounds give yellow solid when reacted with ? Choose the correct answer from the options given...

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The number of solutions of the equation $(4-\sqrt{3}) \sin x-2 \sqrt{3} \cos ^2 x=-\frac{4}{1+\sqrt{3}}, x \in\left[-2 \pi, \frac{5 \pi}{2}\right]$ is

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Q JEE MAIN_2025

The number of solutions of the equation $\cos 2 \theta \cos \frac{\theta}{2}+\cos \frac{5 \theta}{2}=2 \cos ^2 \frac{5 \theta}{2}$ in $...

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Q JEE MAIN 2025

Given below are two statements : Statement (I) : On hydrolysis, oligo peptides give rise to fewer number of -amino...

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Q JEE MAIN 2025

A toxic compound "A" when reacted with NaCN in aqueous acidic medium yields an edible cooking component and food preservative...

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Q JEE MAIN 2025

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

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Q JEE MAIN_2025

If the locus of $z \in \mathrm{C}$, such that $\operatorname{Re}\left(\frac{z-1}{2 z+i}\right)+\operatorname{Re}\left(\frac{\bar{z}-1}{2 \bar{z}-i}\right)=2$, is a circle of radius r and center...

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Q JEE MAIN 2025

Each of the angles $\beta$ and $\gamma$ that a given line makes with the positive $y$ - and $z$-axes, respectively,...

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Half life of zero order reaction $\mathrm{A} \rightarrow$ product is 1 hour, when initial concentration of reactant is $2.0 \mathrm{molL}^{-1}$....

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Let $\mathrm{a}>0$. If the function $f(x)=6 x^3-45 a x^2+108 a^2 x+1$ attains its local maximum and minimum values at the...

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Q JEE MAIN_2025

If the area of the region $\left\{(x, y): 1+x^2 \leqslant y \leqslant \min \{x+7.11-3 x\}\right\}$ is A , then 3...

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Q JEE MAIN 2025

If the four distinct points $(4,6),(-1,5),(0,0)$ and $(k, 3 k)$ lie on a circle of radius $r$, then $10 k+r^2$...

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The sum of the infinite series $\cot ^{-1}\left(\frac{7}{4}\right)+\cot ^{-1}\left(\frac{19}{4}\right)+\cot ^{-1}\left(\frac{39}{4}\right)+\cot ^{-1}\left(\frac{67}{4}\right)+\ldots$. is :

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Q JEE MAIN 2025

Consider the following plots of log of rate constant $k(\log k)$ vs $\frac{1}{T}$ for three different reactions. The correct order...

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The extra stability of half-filled subshell is due to : (A) Symmetrical distribution of electrons (B) Smaller coulombic repulsion energy...

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If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the...

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Let the sum of the focal distances of the point $\mathrm{P}(4,3)$ on the hyperbola $\mathrm{H}: \frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{~b}^2}=1$ be $8 \sqrt{\frac{5}{3}}$. If...

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Let the Mean and Variance of five observations $x_1=1, x_2=3, x_3=a, x_4=7$ and $x_5=b, a>b$, be 5 and 10 respectively....

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Given below are two statements : Statement (I) : Alcohols are formed when alkyl chlorides are treated with aqueous potassium...

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Mixture of 1 g each of chlorobenzene, aniline and benzoic acid is dissolved in 50 mL ethyl acetate and placed...

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The correct decreasing order of spin only magnetic moment values (BM) of $\mathrm{Cu}^{+}, \mathrm{Cu}^{2+}, \mathrm{Cr}^{2+}$ and $\mathrm{Cr}^{3+}$ ions is :

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If the range of the function $f(x)=\frac{5-x}{x^2-3 x+2}, x \neq 1,2$, is $(-\infty, \alpha] \cup[\beta, \infty)$, then $\alpha^2+\beta^2$ is equal...

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Let the domains of the functions $f(x)=\log _4 \log _3 \log _7\left(8-\log _2\left(x^2+4 x+5\right)\right)$ and $\mathrm{g}(x)=\sin ^{-1}\left(\frac{7 x+10}{x-2}\right)$ be $...

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Q JEE MAIN 2025

The descending order of basicity of following amines is :

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The incorrect relationship in the following pairs in relation to ionisation enthalpies is :

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Let the product of $\omega_1=(8+i) \sin \theta+(7+4 i) \cos \theta$ and $\omega_2=(1+8 i) \sin \theta+(4+7 i) \cos \theta$ be $...

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Let $a_n$ be the $n^n$ term of an A.P. If $S_n=a_1+a_2+a_3+\ldots+a_n=700, a_0=7$ and $S_7=7$, then $a_n$ is equal to:

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The number of unpaired electrons responsible for the paramagnetic nature of the following complex species are respectively :

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Consider the given data : (a) $\mathrm{HCl}(\mathrm{g})+10 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{HCl} .10 \mathrm{H}_2 \mathrm{O} \quad \Delta \mathrm{H}=-69.01 \mathrm{~kJ} \mathrm{~mol}^{-1}$ (b)...

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If the system of equations $$ \begin{aligned} & 2 x+\lambda y+3 z=5 \\ & 3 x+2 y-z=7 \\ & 4...

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The centre of a circle $C$ is at the centre of the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$. Let $C$ pass through...

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Let $A=\{(\alpha, \beta) \in \mathbf{R} \times \mathbf{R}:|\alpha-1| \leqslant 4$ and $|\beta-5| \leqslant 6\}$ and $...

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Q JEE MAIN 2025

Choose the incorrect trend in the atomic radii (r) of the elements.

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If $\theta \in\left[-\frac{7 \pi}{6}, \frac{4 \pi}{3}\right]$, then the number of solutions of $\sqrt{3} \operatorname{cosec}^2 \theta-2(\sqrt{3}-1) \operatorname{cosec} \theta-4=0$, is equal tori

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Let $\quad f(x)+2 f\left(\frac{1}{x}\right)=x^2+5 \quad$ and $\quad 2 g(x)-3 g\left(\frac{1}{2}\right)=x, x>0$. If $\quad \alpha=\int_1^2 f(x) \mathrm{d} x, \quad$ and $...

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If the equation of the line passing through the point $\left(0,-\frac{1}{2}, 0\right)$ and perpendicular to the lines $...

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Liquid and form an ideal solution. The vapour pressures of pure liquids and are 350 and 750 mm Hg respectively...

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Let $\mathrm{A}=\{-3,-2,-1,0,1,2,3\}$ and R be a relation on A defined by $x \mathrm{Ry}$ if and only if $2 x-y \in\{0,1\}$....

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The atomic number of the element from the following with lowest $1^{\text {st }}$ ionisation enthalpy is :

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A dipeptide, " $x$ " on complete hydrolysis gives " $y$ " and " $z$ ". " $y$ " on...

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The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the...

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Let $\vec{a}$ and $\vec{b}$ be the vectors of the same magnitude such that $\frac{|\vec{a}+\vec{b}|+|\vec{a}-\vec{b}|}{|\vec{a}+\vec{b}|-|\vec{a}-\vec{b}|}=\sqrt{2}+1$. Then $\frac{|\vec{a}+\vec{b}|^2}{|\vec{a}|^2}$ is :

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If a curve $y=y(x)$ passes through the point $\left(1, \frac{\pi}{2}\right)$ and satisfies the differential equation $...

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Let A be a $3 \times 3$ real matrix such that $A^2(A-2 I)-4(A-I)=O$, where I and O are the identity...

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' X ' is the number of acidic oxides among $\mathrm{VO}_2, \mathrm{~V}_2 \mathrm{O}_3, \mathrm{CrO}_3, \mathrm{~V}_2 \mathrm{O}_5$ and $\mathrm{Mn}_2 \mathrm{O}_7$. The...

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The sum $1+\frac{1+3}{2!}+\frac{1+3+5}{3!}+\frac{1+3+5+7}{4!}+\ldots$ upto $\infty$ terms, 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 $\sum_{r=0}^{10}\left(\frac{10^{r+1}-1}{10^r}\right) \cdot{ }^{11} C_{r+1}=\frac{\alpha^{11}-11^{11}}{10^{10}}$, then $\alpha$ is equal to :

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A line passing through the point $\mathrm{A}(-2,0)$, touches the parabola $\mathrm{P}: y^2=x-2$ at the point $B$ in the first quadrant....

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If $z_1, z_2, z_3 \in \mathbb{C}$ are the vertices of an equilateral triangle, whose centroid is $z_0$, then $\sum_{k=1}^3\left(z_k-z_0\right)^2$ is...

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

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Let the length of a latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be 10 . If its eccentricity is the minimum...

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Which one of the following reactions will not lead to the desired ether formation in major proportion? (iso- $\mathrm{Bu} \Rightarrow$...

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If the length of the minor axis of an ellipse is equal to one fourth of the distance between the...

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If the sum of the first 20 terms of the series $$ \frac{4 \cdot 1}{4+3 \cdot 1^2+1^4}+\frac{4 \cdot 2}{4+3 \cdot...

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The correct order of basicity for the following molecules is :

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Let the system of equations $$ \begin{aligned} & x+5 y-z=1 \\ & 4 x+3 y-3 z=7 \\ & 24 x+y+\lambda...

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Let . Let R be a relation on defined by if and only if . Let be the number of...

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Let for two distinct values of p the lines $y=x+\mathrm{p}$ touch the ellipse $\mathrm{E}: \frac{x^2}{4^2}+\frac{y^2}{3^2}=1$ at the points A and...

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Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function. If $10 \int_1^x f(t) d t=5 x f(x)-x^5-9$ for all $...

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Given below are two statements : Statement (I) : For $\mathrm{ClF}_3$, all three possible structures may be drawn as follows....

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Let the equation $x(x+2)(12-k)=2$ have equal roots. Then the distance of the point $\left(k, \frac{k}{2}\right)$ from the line $...

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Given three identical bags each containing 10 balls, whose colours are as follows : A person chooses a bag at...

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Let $A$ be the point of intersection of the lines $L_1: \frac{x-7}{1}=\frac{y-5}{0}=\frac{z-3}{-1}$ and $L_2: \frac{x-1}{3}=\frac{y+3}{4}=\frac{z+7}{5}$. Let $B$ and $C$ be...

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The area of the region $\{(x, y):|x-y| \leq y \leq 4 \sqrt{x}\}$ is

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Consider the lines $\mathrm{L}_1: x-1=y-2=\mathrm{z}$ and $\mathrm{L}_2: x-2=y=\mathrm{z}-1$. Let the feet of the perpendiculars from the point $P(5,1,-3)$ on the...

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Choose the correct set of reagents for the following conversion.

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Let the mean and the standard deviation of the observation $2,3,3,4,5,7, a, b$ be 4 and $\sqrt{2}$ respectively. Then the...

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Let $A=\{1,2,3, \ldots, 100\}$ and $R$ be a relation on $A$ such that $R=\{(a, b): a=2 b+1\}$. Let $...

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The distance of the point $(7,10,11)$ from the line $\frac{x-4}{1}=\frac{y-4}{0}=\frac{z-2}{3}$ along the line $\frac{x-9}{2}=\frac{y-13}{3}=\frac{z-17}{6}$ is

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In $\mathrm{SO}_2, \mathrm{NO}_2^{-}$and $\mathrm{N}_3^{-}$the hybridizations at the central atom are respectively:

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Let $f$ be a differentiable function on $\mathbf{R}$ such that $f(2)=1, f^{\prime}(2)=4$. Let $\lim _{x \rightarrow 0}(f(2+x))^{3 / x}=\mathbf{e}^\alpha$. Then...

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Let $(a, b)$ be the point of intersection of the curve $x^2=2 y$ and the straight line $y-2 x-6=0$ in...

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Let $f: \mathrm{R} \rightarrow \mathrm{R}$ be a function defined by $f(x)=\|x+2|-2| x\|$. If $m$ is the number of points of...

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Given below are two statements : Statement (I): The first ionisation enthalpy of group 14 elements is higher than the...

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If $1^2 \cdot\left({ }^{15} C_1\right)+2^2 \cdot\left({ }^{15} C_2\right)+3^2 \cdot\left({ }^{15} C_3\right)+\ldots+15^2 \cdot\left({ }^{15} C_{15}\right)=2^m \cdot 3^n \cdot 5^k$, where $...

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Consider the lines $x(3 \lambda+1)+y(7 \lambda+2)=17 \lambda+5, \lambda$ being a parameter, all passing through a point P : One of...

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Let the point P of the focal chord PQ of the parabola $y^2=16 x$ be $(1,-4)$. If the focus of...

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Given below are two statements: Statement I : A homoleptic octahedral complex, formed using monodentate ligands, will not show stereoisomerism...

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Light from a point source in air falls on a spherical glass surface (refractive index, $\mu=1.5$ and radius of curvature...

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Line $L_1$ of slope 2 and line $L_2$ of slope $\frac{1}{2}$ intersect at the origin $O$. In the first quadrant,...

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A solid sphere with uniform density and radius R is rotating initially with constant angular velocity $\left(\omega_1\right)$ about its diameter....

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The correct statements from the following are. (A) $\mathrm{Tl}^{3+}$ is a powerful oxidising agent (B) $\mathrm{Al}^{3+}$ does not get reduced...

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If the domain of the function $f(x)=\log _7\left(1-\log _4\left(x^2-9 x+18\right)\right)$ is $(\alpha, \beta) \cup(\gamma, \delta)$, then $\alpha+\beta+\gamma+\delta$ is equal to

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The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes...

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Two cells of emf 1 V and 2 V and internal resistances $2 \Omega$ and $1 \Omega$, respectively, are connected...

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A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm ....

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Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the...

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Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}+3\left(\tan ^2 x\right) y+3 y=\sec ^2 x, y(0)=\frac{1}{3}+e^3$. Then...

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In a Young's double slit experiment, two slits are located 1.5 mm apart. The distance of screen from slits is...

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If $\lim _{x \rightarrow 0} \frac{\cos (2 x)+a \cos (4 x)-b}{x^4}$ is finite, then $(a+b)$ is equal to :

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Which of the following binary mixture does not show the behaviour of minimum boiling azeotropes?

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is connected in parallel with it. The effective capacitance of this combination is $\_\_\_\_$ $\mathrm{pF}_{\text {in }}$ (Given $...

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The integral $\int_0^\pi \frac{8 x d x}{4 \cos ^2 x+\sin ^2 x}$ is equal to

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An inductor of self inductance 1 H is connected in series with a resistor of $100 \pi \mathrm{ohm}$ and an...

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The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B...

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Let the matrix $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]$...

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The line $L_1$ is parallel to vector $\vec{a}=-3 \hat{i}+2 \hat{j}+4 \hat{k}$ and passes through the point $(7,6,2)$ and the line...

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A sample of a liquid is kept at 1 atm . It is compressed to 5 atm which leads to...

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If the probability that the random variable $X$ takes the value $x$ is given by $P(X=x)=k(x+1) 3^{-x}, x=0,1,2,3 \ldots$, where...

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A particle of charge $1.6 \mu \mathrm{C}$ and mass $16 \mu \mathrm{~g}$ is present in a strong magnetic field of...

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A physical quantity $C$ is related to four other quantities $p, q, r$ and $s$ as follows $$ C=\frac{p q^2}{r^3...

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A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends...

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What is the correct IUPAC name of

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If the mean and the variance of 6, 4, a, 8, b, 12,10,13 are 9 and 9.25 respectively, then a...

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Let the values of p , for which the shortest distance between the lines $\frac{x+1}{3}=\frac{y}{4}=\frac{z}{5}$ and $...

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Let $C$ be the circle of minimum area enclosing the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with eccentricity $\frac{1}{2}$ and foci $...

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If an optical medium possesses a relative permeability of $\frac{10}{\pi}$ and relative permittivity of $\frac{1}{0.0885}$, then the velocity of light...

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An electron in the hydrogen atom initially in the fourth excited state makes a transition to $n^{\text {th }}$ energy...

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An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' $-\sigma$. The rate of...

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The axis of a parabola is the line $y=x$ and its vertex and focus are in the first quadrant at...

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The correct statement amongst the following is :

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Let $f$ be a function such that $f(x)+3 f\left(\frac{24}{x}\right)=4 x, x \neq 0$. Then $f(3)+f(8)$ is equal to.

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Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A...

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The number of optically active products obtained from the complete ozonolysis of the given compound is

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The shortest distance between the curves $y^2=8 x$ and $x^2+y^2+12 y+35=0$ is:

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Choose the correct option for structures of A and B, respectively

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In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter...

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$\mathrm{A}(\mathrm{g}) \rightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ is a first order reaction. The reaction was started with reactant A only. Which of the following...

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The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $...

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A rod of linear mass density ' $\lambda$ ' and length ' $L$ ' is bent to form a ring...

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The hydration energies of $\mathrm{K}^{+}$and $\mathrm{Cl}^{-}$are $-x$ and $-y \mathrm{~kJ} / \mathrm{mol}$ respectively. If lattice energy of KCl is $...

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Electric charge is transferred to an irregular metallic disk as shown in figure. If $\sigma_1, \sigma_2, \sigma_3$ and $\sigma_4$ are...

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A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20...

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Match List - I with List - II. List - I (A) Solution of chloroform and acetone (B) Solution of...

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A body of mass 2 kg moving with velocity of $\vec{v}_{\mathrm{in}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}} \mathrm{ms}^{-1}$ enters into a constant force field...

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A quantity Q is formulated as $\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y}$ and Z are independent parameters which have fractional...

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Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming...

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Two metal spheres of radius $R$ and 3 R have same surface charge density $\sigma$. If they are brought in...

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

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For a nucleus of mass number and radius , the mass density of nucleus can be represented as 1.

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Figure shows a current carrying square loop $A B C D$ of edge length is ' a ' lying in...

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The output voltage in the following circuit is (Consider ideal diode case)

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An infinitely long wire has uniform linear charge density $\lambda=2 \mathrm{nC} / \mathrm{m}$. The net flux through a Gaussian cube...

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If the domain of the function $f(x)=\frac{1}{\sqrt{10+3 x-x^2}}+\frac{1}{\sqrt{x+|x|}}$ is $(a, b)$, then $(1+a)^2+b^2$ is equal to:

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If the image of the point $\mathrm{P}(1,0,3)$ in the line joining the points $\mathrm{A}(4,7,1)$ and $\mathrm{B}(3,5,3)$ is $Q(\alpha, \beta, \gamma)$,...

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

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On combustion 0.210 g of an organic compound containing $\mathrm{C}, \mathrm{H}$ and O gave $0.127 \mathrm{gH}_2 \mathrm{O}$ and $0.307 \mathrm{gCO}_2$...

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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 monoatomic gas having $\gamma=\frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to $...

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In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth...

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Width of one of the two slits in a Young's double slit interference experiment is half of the other slit....

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Two cylindrical rods $A$ and $B$ made of different materials, are joined in a straight line. The ratios of lengths,...

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Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height...

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The truth table corresponding to the circuit given below is :

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An inductor of reactance $100 \Omega$, a capacitor of reactance $50 \Omega$, and a resistor of resistance $50 \Omega$ are...

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Given below are two statements: Statement I : $\mathrm{H}_2 \mathrm{Se}$ is more acidic than $\mathrm{H}_2 \mathrm{Te}$ Statement II : $\mathrm{H}_2$...

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A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20...

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A block of mass 1 kg , moving along $x$ with speed $v_i=10 \mathrm{~m} / \mathrm{s}$ enters a rough region...

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A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a...

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The electric field in a region is given by $\overrightarrow{\mathrm{E}}=(2 \hat{i}+4 \hat{j}+6 \hat{k}) \times 10^3 \mathrm{~N} / \mathrm{C}$. The flux...

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A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed...

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$M$ and $R$ be the mass and radius of a disc. A small disc of radius $R / 3$ is...

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Xg of nitrobenzene on nitration gave 4.2 g of m -dinitrobenzene. $\mathrm{X}=$ $\_\_\_\_$ g. (nearest integer) [Given : molar mass...

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Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that,...

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A parallel plate capacitor has charge $5 \times 10^{-6} \mathrm{C}$. A dielectric slab is inserted between the plates and almost...

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A sample of $n$-octane $(1.14 \mathrm{~g})$ was completely burnt in excess of oxygen in a bomb calorimeter, whose heat capacity...

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

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Among, and Cu , identify the element with highest enthalpy of atomisation. The spin only magnetic moment value of that...

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A perfect gas ( 0.1 mol ) having $\overline{\mathrm{C}}_v=1.50 \mathrm{R}$ (independent of temperature) undergoes the above transformation from point 1...

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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 total number of structural isomers possible for the substituted benzene derivatives with the molecular formula $\mathrm{C}_9 \mathrm{H}_{12}$ is $\_\_\_\_$

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A dipole with two electric charges of $2 \mu \mathrm{C}$ magnitude each, with separation distance $0.5 \mu \mathrm{~m}$, is placed...

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In Dumas' method for estimation of nitrogen 0.4 g of an organic compound gave 60 mL of nitrogen collected at...

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Two cylindrical vessels of equal cross sectional area of $2 \mathrm{~m}^2$ contain water upto heights 10 m and 6 m...

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The major product in the following reaction is :

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A capillary tube of radius 0.1 mm is partly dipped in water (surface tension $70 \mathrm{dyn} / \mathrm{cm}$ and glass...

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A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is $...

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Given below are two statements: Statement I : Hyperconjugation is not a permanent effect. Statement II : In general, greater...

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Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio...

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What is the correct IUPAC name of

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

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Displacement of a wave is expressed as $x(t)=5 \cos \left(628 \mathrm{t}+\frac{\pi}{2}\right) \mathrm{m}$. The wavelength of the wave when its velocity...

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A mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between object and its image...

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Compounds that should not be used as primary standards in titrimetric analysis are : A. $\mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7$ B. Oxalic...

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The helium and argon are put in the flask at the same room temperature (300K). The ratio of average kinetic...

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

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There are 'n' number of identical electric bulbs, each is designed to draw a power p independently from the mains...

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Consider the following statements related to temperature dependence of rate constants. Identify the correct statements. A. The Arrhenius equation holds...

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A particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by...

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The dimension of $\sqrt{\frac{\mu_0}{\epsilon_0}}$ is equal to that of : ( $\mu_0=$ Vacuum permeability and $\varepsilon_0=$ Vacuum permittivity)

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Given below are two statements: Statement I : Wet cotton clothes made of cellulose based carbohydrate takes comparatively longer time...

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A particle moves along the $x$-axis and has its displacement $x$ varying with time t according to the equation: $$...

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The equation of a wave travelling on a string is $y=\sin [20 \pi x+10 \pi t]$, where $x$ and $t$...

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The correct orders among the following are Atomic radius: $\mathrm{B}

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An object with mass 500 g moves along x -axis with speed $v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}$. The force acting...

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Pressure of an ideal gas, contained in a closed vessel, is increased by $0.4 \%$ when heated by $1^{\circ} \mathrm{C}$....

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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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Fat soluble vitamins are: A. Vitamin $B_1$ B. Vitamin C C. Vitamin E D. Vitamin $\mathrm{B}_{12}$ E. Vitamin K Choose...

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Consider two blocks A and B of masses $m_1=10 \mathrm{~kg}$ and $m_2=5 \mathrm{~kg}$ that are placed on a frictionless table....

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Given below are two statements: Statement I : When a system containing ice in equilibrium with water (liquid) is heated,...

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

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Mass of magnesium required to produce 220 mL of hydrogen gas at STP on reaction with excess of dil. HCl...

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A block of mass 25 kg is pulled along a horizontal surface by a force at an angle with the...

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An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to 4 times of...

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he sequence from the following that would result in giving predominantly 3,4,5 Tribromoaniline is :

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In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension...

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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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In the following series of reactions identify the major products A & B respectively

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A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field...

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A monochromatic light of frequency $5 \times 10^{14} \mathrm{~Hz}$ travelling through air, is incident on a medium of refractive index...

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

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A magnetic dipole experiences a torque of $80 \sqrt{3} \mathrm{Nm}$ when placed in uniform magnetic field in such a way...

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Consider the following logic circuit. The output is Y = 0 when :

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The displacement x versus time graph is shown below. (A)The average velocity during 0 to 3 s is $...

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Which one of the following forces cannot be expressed in terms of potential energy?

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10 mL of 2 M NaOH solution is added to 20 mL of 1 M HCl solution kept in a...

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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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For electrons in '2s' and '2p' orbitals, the orbital angular momentum values, respectively are :

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A radioactive material first decays into Q and then Q decays to non-radioactive material . Which of the following figure...

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Given below are two statements: Statement I : $\mathrm{CrO}_3$ is a stronger oxidizing agent than $\mathrm{MoO}_3$ Statement II: $\mathrm{Cr}(\mathrm{VI})$ is...

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Given below are two statements : Statement (I): The dimensions of Planck's constant and angular momentum are same. Statement (II)...

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In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15...

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Three parallel plate capacitors $C_1, C_2$ and $C_3$ each of capacitance $5 \mu \mathrm{~F}$ are connected as shown in figure....

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Identify the diamagnetic octahedral complex ions from below ; A. $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$ B. $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ C. $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-}$ D. $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_3 \mathrm{~F}_3\right]$ Choose...

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A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex...

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40 mL of a mixture of $\mathrm{CH}_3 \mathrm{COOH}$ and HCl (aqueous solution) is titrated against 0.1 M NaOH solution conductometrically....

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Consider a rectangular sheet of solid material of length $l=9 \mathrm{~cm}$ and width $\mathrm{d}=4 \mathrm{~cm}$. The coefficient of linear expansion...

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A transparent block A having refractive index $\mu=1.25$ is surrounded by another medium of refractive index $\mu=1.0$ as shown in...

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An object is kept at rest at a distance of 3R above the earth's surface where is earth's radius. The...

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The standard cell potential ( $\mathrm{E}_{\text {cell }}^{\ominus}$ ) of a fuel cell based on the oxidation of methanol in...

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The unit of $\sqrt{\frac{2 \mathrm{I}}{\epsilon_0 \mathrm{C}}}$ is : $\mathrm{I}=$ intensity of an electromagnetic wave, C : speed of light)

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A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear...

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An electric bulb rated as 100W-220V is connected to an ac source of rms voltage 220 V. The peak value...

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A photo-emissive substance is illuminated with a radiation of wavelength $\lambda_i$ so that it releases electrons with de-Broglie wavelength $\lambda_e$....

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Consider a n-type semiconductor in which $n_e$ and $n_h$ are number of electrons and holes, respectively. (A) Holes are minority...

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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 wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim...

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A helicopter flying horizontally with a speed of at an altitude of 2 km , drops an object at an...

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For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal...

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The spin-only magnetic moment value of $M^{n+}$ ion formed among $\mathrm{Ni}, \mathrm{Zn}, \mathrm{Mn}$ and Cu that has the least enthalpy...

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For the reaction $A \rightarrow B$ the following graph was obtained. The time required (in seconds) for the concentration of...

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When 1 g each of compounds $A B$ and $A B_{2}$ are dissolved in 15 g of water separately, they...

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$0.2 \%(\mathrm{w} / \mathrm{v})$ solution of NaOH is measured to have resistivity $870.0 \mathrm{~m} \Omega \mathrm{~m}$. The molar conductivity of...

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Consider the above sequence of reactions. 151 g of 2-bromopentane is made to react. Yield of major product P is...

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

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Consider the following reactions. From these reactions which reaction will give carboxylic acid as a major product? (A) $...

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Reactant A converts to product D through the given mechanism (with the net evolution of heat) : $\mathrm{A} \rightarrow \mathrm{B}$...

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Which of the following statements are true? (A) The subsidiary quantum number $l$ describes the shape of the orbital occupied...

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When a concentrated solution of sulphanilic acid and 1-naphthylamine is treated with nitrous acid ( 273 K ) and acidified...

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Which of the following graphs correctly represents the variation of thermodynamic properties of Haber's process?

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The d-orbital electronic configuration of the complex among $\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+},\left[\mathrm{CoF}_{6}\right]^{3-},\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ and $\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ that has the highest CFSE is :

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

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In 3,3-dimethylhex-1-en-4-yne, there are $\_\_\_\_$ $s p^{3}$, $\_\_\_\_$ $s p^{2}$ and $\_\_\_\_$ sp hybridised carbon atoms respectively.

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Given below are two statements : Statement (I) : Neopentane forms only one monosubstituted derivative. Statement (II) : Melting point...

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The nature of oxide $\left(\mathrm{TeO}_{2}\right)$ and hydride $\left(\mathrm{TeH}_{2}\right)$ formed by Te, respectively are :

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Consider the following chemical equilibrium of the gas phase reaction at a constant temperature : $A(g) \rightleftharpoons B(g)+C(g)$ If $p$...

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Formation of $\mathrm{Na}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right]$, a purple coloured complex formed by addition of sodium nitroprusside in sodium carbonate extract of salt...

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Arrange the following in order of magnitude of work done by the system/on the system at constant temperature. (a) $...

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' x ' g of NaCl is added to water in a beaker with a lid. The temperature of the...

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In Dumas' method for estimation of nitrogen, 0.5 gram of an organic compound gave 60 mL of nitrogen collected at...

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Electronic configuration of four elements $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D are given below : (A) $...

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A tetrapeptide, " $x$ " on complete hydrolysis produced glycine (Gly), alanine (Ala), valine (Val), leucine (Leu) in equimolar proportion...

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Which among the following molecules is (a) involved in $s p^{3} d$ hybridization, (b) has different bond lengths and (c)...

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The type of hybridization and the magnetic property of $\left[\mathrm{MnCl}_{6}\right]^{3-}$ are

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A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of...

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The internal energy of air in $4 m \times 4 m \times 3 m$ sized room at 1 atmospheric pressure...

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The length of a light string is 1.4 m when the tension on it is 5 N . If the...

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A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim...

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A ray of light suffers minimum deviation when incident on a prism having angle of the ${ }_{6}^{4}$ prism equal...

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In the digital circuit shown in the figure, for the given inputs the $P$ and $Q$ values are :

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Two water drops each of radius ' $r$ ' coalesce to form a bigger drop. If ' $T$ ' is...

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Consider a circular loop that is uniformly charged and has a radius $a \sqrt{2}$. Find the position along the positive...

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Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in...

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A solenoid having area $A$ and length ' $l$ ' is filled with a material having relative permeability 2 ....

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A bi-convex lens has radius of curvature of both the surfaces same as $1 / 6 \mathrm{~cm}$. If this lens...

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An electron with mass ' m ' with an initial velocity $(t=0) \vec{v}=v_{0} \hat{i}\left(v_{0}>0\right)$ enters a magnetic field $\vec{B}=B_{0} \hat{j}$....

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A sportsman runs around a circular track of radius $r$ such that he traverses the path $A B A B$....

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In a moving coil galvanometer, two moving coils $M_{1}$ and $M_{2}$ have the following particulars : $...

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The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in...

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Energy released when two deuterons $\left({ }_{1} H^{2}\right)$ fuse to form a helium nucleus $\left({ }_{2} H e^{4}\right)$ is :...

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A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $X$-direction in 0.3 sec ....

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Match List - I with List - II.

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A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure....

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Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12...

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Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $\mathrm{Li}^{++}$ion in its ground state is...

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If $\mu_{0}$ and $\epsilon_{0}$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_{0} \epsilon_{0}}\right)$ is:

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Given a charge q , current I and permeability of vacuum $\mu_{o}$. Which of the following quantity has the dimension...

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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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Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them...

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If the domain of the function $\log _{5}\left(18 x-x^{2}-77\right)$ is ( $\alpha, \beta$ ) and the domain of the function...

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Element not showing variable oxidation state is :

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Which of the following is strongest Bronsted base

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A body of mass 1000 kg is moving horizontally with a velocity 6 m/s. If 200 kg extra mass is...

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If $24 \int_{0}^{\frac{\pi}{4}}\left(\sin \left|4 x-\frac{\pi}{12}\right|+[2 \sin x]\right) \mathrm{d} x=2 \pi+\alpha$, where $[\cdot]$ denotes the greatest integer function, then $\alpha$ is...

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If $\lim _{\mathrm{t} \rightarrow 0}\left(\int_{0}^{1}(3 x+5)^{\mathrm{t}} \mathrm{d} x\right)^{\frac{1}{\mathrm{t}}}=\frac{\alpha}{5 \mathrm{e}}\left(\frac{8}{5}\right)^{\frac{2}{3}}$, then $\alpha$ is equal to $\_\_\_\_$ .

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Let integers $a, b \in[-3,3]$ be such that $a+b \neq 0$. Then the number of all possible ordered pairs (a,...

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Let $y^{2}=12 x$ be the parabola and $S$ be its focus. Let PQ be a focal chord of the parabola...

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Let $a_{1}, a_{2}, \ldots, a_{2024}$ be an Arithmetic Progression such that $a_{1}+\left(a_{5}+a_{10}+a_{15}+\ldots+a_{2020}\right)+a_{2024}=2233$. Then $a_{1}+a_{2}+a_{3}+\ldots+a_{2024}$ is equal to $\_\_\_\_$ .

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If $\alpha x+\beta y=109$ is the equation of the chord of the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$, whose mid point is $\left(\frac{5}{2}, \frac{1}{2}\right)$,...

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If the set of all $a \in \mathbf{R}$, for which the equation $2 x^2+(a-5) x+15=3$ a has no real root,...

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If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as...

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Let $\hat{\mathrm{a}}$ be a unit vector perpendicular to the vectors $\overrightarrow{\mathrm{b}}=\hat{i}-2 \hat{j}+3 \hat{k}$ and $\overrightarrow{\mathrm{c}}=2 \hat{i}+3 \hat{j}-\hat{k}$, and makes an...

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Let $A=\left[a_{i j}\right]$ be a matrix of order $3 \times 3$, with $\mathrm{a}_{i j}=(\sqrt{2})^{i+j}$. If the sum of all the...

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If for the solution curve $y=f(x)$ of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}+(\tan x) y=\frac{2+\sec x}{(1+2 \sec x)^{2}}$, $...

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Let a circle $C$ pass through the points $(4,2)$ and $(0,2)$, and its centre lie on $3 x+2 y+2=0$. Then...

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Let the area enclosed between the curves $|y|=1-x^{2}$ and $x^{2}+y^{2}=1$ be $\alpha$. If $9 \alpha=\beta \pi+\gamma ; \beta, \gamma$ are...

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If $\sin x+\sin ^{2} x=1, x \in\left(0, \frac{\pi}{2}\right)$, then $...

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Let $\alpha, \beta(\alpha \neq \beta)$ be the values of $m$, for which the equations $x+y+z=1 ; x+2 y+4 z=m$ and...

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The remainder, when $7^{103}$ is divided by 23 , is equal to :

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Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains $n$ white balls and 3 black...

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Let $S=\mathbf{N} \cup\{0\}$. Define a relation $R$ from $S$ to $\mathbf{R}$ by: $...

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Let P be the foot of the perpendicular from the point $(1,2,2)$ on the line $\mathrm{L}: \frac{x-1}{1}=\frac{y+1}{-1}=\frac{z-2}{2}$. Let the line...

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Let a straight line $L$ pass through the point $P(2,-1,3)$ and be perpendicular to the lines $\frac{x-1}{2}=\frac{y+1}{1}=\frac{z-3}{-2}$ and $\frac{x-3}{1}=\frac{y-2}{3}=\frac{z+2}{4}$. If...

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Let $\mathrm{A}=\left[\mathrm{a}_{i j}\right]$ be a $2 \times 2$ matrix such that $\mathrm{a}_{i j} \in\{0,1\}$ for all $i$ and $j$. Let...

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Let $f(x)=\int_{0}^{x} \mathrm{t}\left(\mathrm{t}^{2}-9 \mathrm{t}+20\right) \mathrm{dt}, 1 \leq x \leq 5$. If the range of $f$ is $[\alpha, \beta]$, then $4(\alpha+\beta)$...

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Let the function $f(x)=\left(x^{2}-1\right)\left|x^{2}-\mathrm{a} x+2\right|+\cos |x|$ be not differentiable at the two points $x=\alpha=2$ and $x=\beta$. Then the distance of...

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Let the line $x+y=1$ meet the axes of $x$ and $y$ at $A$ and $B$, respectively. A right angled triangle...

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Isomeric hydrocarbons → negative Baeyer's test (Molecular formula $\mathrm{C}_{9} \mathrm{H}_{12}$ ) The total number of isomers from above with four...

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In the Claisen-Schmidt reaction to prepare, dibenzalacetone from 5.3 g of benzaldehyde, a total of 3.51 $g$ of product was...

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Total number of non bonded electrons present in $\mathrm{NO}_{2}{ }^{-}$ ion based on Lewis theory is $\_\_\_\_$ .

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Consider the following low-spin complexes $\mathrm{K}_{3}\left[\mathrm{Co}\left(\mathrm{NO}_{2}\right)_{6}\right], \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right], \mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right], \mathrm{Cu}_{2}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]$ and $\mathrm{Zn}_{2}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]$. The sum of the spin-only magnetic moment values of...

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In the sulphur estimation, 0.20 g of a pure organic compound gave 0.40 g of barium sulphate. The percentage of...

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Given below are two statements : Statement $(\mathrm{I}): \mathrm{NaCl}$ is added to the ice at $0^{\circ} \mathrm{C}$, present in the...

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Given below are two statements : Statement (I): In partition chromatography, stationary phase is thin film of liquid present in...

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For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for...

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If $C$ (diamond) $\rightarrow C$ (graphite ) $+X \mathrm{~kJ} \mathrm{~mol}^{-1}$ $\mathrm{C}($ diamond $)+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{YkJmol}^{-1}$ C (graphite) $+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{ZkJmol}^{-1}$...

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First ionisation enthalpy values of first four group 15 elements are given below. Choose the correct value for the element...

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

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$\mathrm{O}_{2}$ gas will be evolved as a product of electrolysis of :[0pt] (A) an aqueous solution of $\mathrm{AgNO}_{3}$ using silver...

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Which one of the following reaction sequences will give an azo dye?

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0.1 M solution of KI reacts with excess of $\mathrm{H}_{2} \mathrm{SO}_{4}$ and $\mathrm{KIO}_{3}$ solutions. According to equation $...

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The calculated spin-only magnetic moments of $\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{OH})_{6}\right]$ and $\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{OH})_{6}\right]$ respectively are :

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Given below are two statements :[0pt] Statement (I): It is impossible to specify simultaneously with arbitrary precision, both the linear...

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Identify the essential amino acids from below :[0pt] (A) Valine (B) Proline (C) Lysine (D) Threonine (E) Tyrosine Choose the...

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Consider the equilibrium[0pt] $\mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ If the pressure applied over the system increases by two fold at...

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Total number of sigma ( $\sigma$ ) $\_\_\_\_$ and $\operatorname{pi}(\pi)$ $\_\_\_\_$ bonds respectively present in hex-1-en-4-yne are :

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Identify the homoleptic complexes with odd number of d electrons in the central metal :[0pt] [JEE MAIN\_290125\_S2] [Coordination] [T-5] [Ea\$...

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Which one of the following, with HBr will give a phenol?

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Drug $X$ becomes ineffective after $50 \%$ decomposition. The original concentration of drug in a bottle was $...

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The type of oxide formed by the element among $\mathrm{Li}, \mathrm{Na}, \mathrm{Be}, \mathrm{Mg}, \mathrm{B}$ and Al that has the least...

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Which among the following halides will generate the most stable carbocation in the nucleophilic substitution reaction?

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Given below are two statements : Statement (I) : On nitration of m-xylene with $\mathrm{HNO}_{3}, \mathrm{H}_{2} \mathrm{SO}_{4}$ followed by oxidation,...

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The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9 \times 10^{-4} \mathrm{Tesla}$. If the solenoid...

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Two planets, A and B are orbiting a common star in circular orbits of radii $R_{A}$ and $R_{B}$, respectively, with...

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Two cars $P$ and $Q$ are moving on a road in the same direction. Acceleration of car $P$ increases linearly...

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A physical quantity $Q$ is related to four observables $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}$ as follows : $\mathrm{Q}=\frac{\mathrm{ab}}{} \mathrm{a}^{4}$ where, $...

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A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current...

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A poly-atomic molecule ( $C_{V}=3 R, C_{P}=4 R$, where $R$ is gas constant) goes from phase space point $...

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A point charge causes an electric flux of $-2 \times 10^{4} \mathrm{Nm}^{2} \mathrm{C}^{-1}$ to pass through a spherical Gaussian surface...

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The truth table for the circuit given below is :

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A plane electromagnetic wave propagates along the $+x$ direction in free space. The components of the electric field, $\vec{E}$ and...

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Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown...

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Two bodies A and B of equal mass are suspended from two massless springs of spring constant $k_{1}$ and $\mathrm{k}_{2}$,...

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

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A cup of coffee cools from $90^{\circ} \mathrm{C}$ to $80^{\circ} \mathrm{C}$ in $t$ minutes when the room temperature is $...

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In an experiment with photoelectric effect, the stopping potential

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A sand dropper drops sand of mass $m(t)$ on a conveyer belt at a rate proportional to the square root...

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Three equal masses $m$ are kept at vertices ( $\mathrm{A}, \mathrm{B}, \mathrm{C}$ ) of an equilateral triangle of side $a$...

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

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Two identical symmetric double convex lenses of focal length $f$ are cut into two equal parts $\mathrm{L}_{1}, \mathrm{~L}_{2}$ by $...

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A convex lens made of glass (refractive index $=1.5$ ) has focal length 24 cm in air. When it is...

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The number of spectral lines emitted by atomic hydrogen that is in the $4^{\text {th }}$ energy level, is

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An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density...

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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 capacitor, $\mathrm{C}_{1}=6 \mu \mathrm{~F}$ is charged to a potential difference of $\mathrm{V}_{0}=5 \mathrm{~V}$ using a 5 V battery. The...

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The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the...

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The number of natural numbers, between 212 and 999 , such that the sum of their digits is 15 ,...

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If $y=y(x)$ is the solution of the differential equation, $...

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The interior angles of a polygon with $n$ sides, are in an A.P. with common difference $6^{\circ}$. If the largest...

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Let $A$ and $B$ be the two points of intersection of the line $y+5=0$ and the mirror image of the...

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Let $f(x)=\lim _{\mathrm{n} \rightarrow \infty} \sum_{\mathrm{r}=0}^{\mathrm{n}}\left(\frac{\tan \left(x / 2^{r+1}\right)+\tan ^{3}\left(x / 2^{r+1}\right)}{1-\tan ^{2}\left(x / 2^{r+1}\right)}\right)$. Then $...

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Let $[x]$ denote the greatest integer less than or equal to $x$. Then the domain of $f(x)=\sec ^{-1}(2[x]+1)$ is :

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Bag $B_{1}$ contains 6 white and 4 blue balls, Bag $B_{2}$ contains 4 white and 6 blue balls, and Bag...

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If the midpoint of a chord of the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$ is $(\sqrt{2}, 4 / 3)$, and the length of the...

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If $f(x)=\int \frac{1}{x^{1 / 4}\left(1+x^{1 / 4}\right)} \mathrm{d} x, f(0)=-6$, then $f(1)$ is equal to :

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Let $f: \mathbf{R}-\{0\} \rightarrow(-\infty, 1)$ be a polynomial of degree 2 , satisfying $f(x) f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)$. If $f(\mathrm{~K})=-2 \mathrm{~K}$, then the...

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The area of the region bounded by the curves $x\left(1+y^{2}\right)=1$ and $y^{2}=2 x$ is:

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If $\sum_{r=1}^{13}\left\{\frac{1}{\sin \left(\frac{\pi}{4}+(r-1) \frac{\pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{r \pi}{6}\right)}\right\}=a \sqrt{3}+b, a, b \in Z$, then $a^{2}+b^{2}$ is equal to :

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If $\alpha+i \beta$ and $\gamma+i \delta$ are the roots of $x^{2}-(3-2 i) x-(2 i-2)=0, i=\sqrt{-1}$, then $\alpha \gamma+\beta \delta$ is...

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For $n \ge 2$, let ${S_n}$ denote the set of all subsets of $\{ 1,2, \ldots ,n\} $ with no...

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Let $A=\left[\begin{array}{cc}\frac{1}{\sqrt{2}} & -2 0 & 1\end{array}\right]$ and $\mathrm{P}=\left[\begin{array}{cc}\cos \theta & -\sin \theta \sin \theta & \cos \theta\end{array}\right], \theta>0$. If...

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If the components of $\overrightarrow{\mathbf{a}}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}$ along and perpendicular to $\overrightarrow{\mathbf{b}}=3 \hat{i}+\hat{j}-\hat{k}$ respectively, are $\frac{16}{11}(3 \hat{i}+\hat{j}-\hat{k})$ and $...

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The number of points of discontinuity of the function $f(x) = \left[ {\frac{{{x^2}}}{2}} \right] - [\sqrt x ],x \in [0,4]$,...

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Let the coefficients of three consecutive terms $T_{r}, T_{r+1}$ and $T_{r+2}$ in the binomial expansion of $(a+b)^{12}$ be in a...

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The number of singular matrices of order 2, whose elements are from the set {2,3,6,9}, is ______.

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Consider the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ having one of its focus at ${\rm{P}}( - 3,0)$. If the latus...

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The number of relations on the set ${\rm{A}} = \{ 1,2,3\} $, containing at most 6 elements including (1,2), which...

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If the shortest distance between the lines $\frac{{x - 1}}{2} = \frac{{y - 2}}{3} = \frac{{z - 3}}{4}$ and $...

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Let the system of equations: $2x + 3y + 5z = 9$ $7x + 3y - 2z = 8$ $...

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Let A be a $3 \times 3$ matrix such that $|{\mathop{\rm adj}\nolimits} ({\mathop{\rm adj}\nolimits} ({\mathop{\rm adj}\nolimits} {\rm{A}}))| = 81$. If...

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Let $\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that $f(2)=1$. If $\mathrm{F}(x)=x f(x)$ for all $...

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Let the angle $\theta ,0 < \theta < \frac{\pi }{2}$ between two-unit vectors $\hat a$ and $\hat b$ be $...

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Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ be three points in $\sqrt{3} \hat{i}+\hat{j}, \hat{i}+\sqrt{3} \hat{j}$ and $\mathrm{a} \hat{i}+(1-\mathrm{a}) \hat{j}$ respectively with respect to...

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$...

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Let $f$ be a real valued continuous function defined on the positive real axis such that $g(x)=\int_{0}^{x} t f(\mathrm{t}) \mathrm{dt}$....

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The integral $\int_0^\pi {\frac{{(x + 3)\sin x}}{{1 + 3{{\cos }^2}x}}} dx$ is equal to

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Let $f:[0,3] \rightarrow$ A be defined by $f(x)=2 x^{3}-15 x^{2}+36 x+7$ and $g:[0, \infty) \rightarrow B$ be defined by $\mathrm{g}(x)=\frac{x^{2025}}{x^{2025}+1}$....

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Let P be the parabola, whose focus is (-2, 1) and directrix is $2x + y + 2 = 0$....

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The square of the distance of the point $\left(\frac{15}{7}, \frac{32}{7}, 7\right)$ from the line $\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ in the direction of the...

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The remainder when ${\left( {{{(64)}^{(64)}}} \right)^{(64)}}$ is divided by 7 is equal to

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Two equal sides of an isosceles triangle are along $-x+2 y=4$ and $x+y=4$. If m is the slope of its...

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Let $x = - 1$ and $x = 2$ be the critical points of the function $...

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Let the line L pass through (1,1,1) and intersect the lines $...

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For positive integers $n$, if $4 a_{n}=\left(n^{2}+5 n+6\right)$ and $S_{n}=\sum_{k=1}^{n}\left(\frac{1}{a_{k}}\right)$, then the value of $507 S_{2025}$ is:

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If A and B are the points of intersection of the circle $x^{2}+y^{2}-8 x=0$ and the hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$ and a...

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Let ABC be the triangle such that the equations of lines AB and AC be $3y - x = 2$...

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Let $S$ be the set of all the words that can be formed by arranging all the letters of the...

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The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as...

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From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should...

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Let ${x_1},{x_2},{x_3},{x_4}$ be in a geometric progression. If 2,7,9,5 are subtracted respectively from ${x_1},{x_2},{x_3},{x_4}$, then the resulting numbers are in...

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Let ${C_1}$ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let ${C_2}$ be...

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

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Let the set of all values of $p \in $ $\mathbb{R}$, for which both the roots of the equation $...

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If for $\theta \in \left[ { - \frac{\pi }{3},0} \right]$, the points $...

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Among the statements (S1) : The set $\left\{ {z \in - \{ - i\} :|z| = 1} \right.$ and $...

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If the area of the region bounded by the curves $y = 4 - \frac{{{x^2}}}{4}$ and $...

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Thyroxine, the hormone has given below structure The percentage of iodine in thyroxine is ____%. (nearest integer) (Given molar mass...

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The percentage dissociation of a salt $\left( {{\rm{M}}{{\rm{X}}_3}} \right)$ solution at given temperature (van't Hoff factor ${\rm{i}} = 2$) is...

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The number of paramagnetic complexes among ${\left[ {{\rm{Fe}}{{\rm{F}}_6}} \right]^{3-}},{\left[ {{\rm{Fe}}{{({\rm{CN}})}_6}} \right]^{3-}},{\left[ {{\rm{Mn}}{{({\rm{CN}})}_6}} \right]^{3 - }}$, $...

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An organic compound weighing 500 mg, produced 220 mg of${\rm{C}}{{\rm{O}}_2}$, on complete combustion. The percentage composition of carbon in the...

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1 Faraday electricity was passed through ${\rm{C}}{{\rm{u}}^{2 + }}(1.5{\rm{M}},1\;{\rm{L}})/{\rm{Cu}}$ and 0.1 Faraday was passed through ${\rm{A}}{{\rm{g}}^ + }(0.2{\rm{M}},1\;{\rm{L}})/{\rm{Ag}}$ electrolytic cells....

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Given below are two statements: Statement I: D-(+)-glucose + D-(+) fructose $\xrightarrow{-\mathrm{H}_2 \mathrm{O}}$ Sucrose sucrose $\xrightarrow{\text { hydrolysis }} \mathrm{D}-(+)$...

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When a salt is treated with sodium hydroxide solution it gives gas X. On passing gas X through reagent Y...

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Which of the following is the correct IUPAC name of given organic compound (X) ?

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The reactions which cannot be applied to prepare an alkene by elimination, are. Choose the correct answer from the options...

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The first transition series metal 'M' has the highest enthalpy of atomisation in its series. One of its aquated ion...

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Given below are two statements: Statement I: Dimethyl ether is completely soluble in water. However, diethyl ether is soluble in...

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Reaction ${\rm{A}}({\rm{g}}) \to 2\;{\rm{B}}(\;{\rm{g}}) + {\rm{C}}({\rm{g}})$ is a first order reaction. It was started with pure A Which of the...

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Which of the following compounds is least likely to give effervescence of ${\rm{C}}{{\rm{O}}_2}$ in presence of aq. ${\rm{NaHC}}{{\rm{O}}_3}$ ?

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A person's wound was exposed to some bacteria and then bacterial growth started to happen at the same place. The...

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Total enthalpy change for freezing of 1 mol of water at ${10^\circ}{\rm{C}}$ to ice at $ - {10^\circ }{\rm{C}}$ is...

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Given below are two statements: Statement I: Mohr's salt is composed of only three types of ions-ferrous, ammonium and sulfate....

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The group 14 elements A and B have the first ionisation enthalpy values of 708 and $715\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}$ respectively....

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Which of the following statements are correct, if the threshold frequency of caesium is $5.16 \times {10^{14}}\;{\rm{Hz}}$ ? A. When...

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An octahedral complex having molecular composition ${\rm{Co}}.5{\rm{N}}{{\rm{H}}_3} \cdot {\rm{C}}{{\rm{l}}^2}.{\rm{S}}{{\rm{O}}_4}$ has two isomers A and B. The solution of A gives...

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Which of the following amine (s) show (s) positive carbylamine test? Choose the correct answer from the options given below:

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

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An aqueous solution of HCl with pH 1.0 is diluted by adding equal volume of water (ignoring dissociation of water)....

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The number of valence electrons present in the metal among ${\rm{Cr}},{\rm{Co}},{\rm{Fe}}$ and Ni which has the lowest enthalpy of atomisation...

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Given below are two statements: Statement I: Ozonolysis followed by treatment with ${\rm{Zn}},{{\rm{H}}_2}{\rm{O}}$ of cis-2-butene gives ethanal. Statement II: The...

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At the sea level, the dry air mass percentage composition is given as nitrogen gas: 70.0, oxygen gas: 27.0 and...

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Let C be the circle ${x^2} + {(y - 1)^2} = 2,{E_1}$ and ${E_2}$ be two ellipses whose centres lie...

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Let $...

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Let $A = \left[ {\begin{array}{*{20}{c}} {\cos \theta }&0&{ - \sin \theta }\\ 0&1&0\\ {\sin \theta }&0&{\cos \theta } \end{array}} \right]$....

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If the area of the region $\{ (x,y):|x - 5| \le y \le 4\sqrt x \} $ is A ,...

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Let $m$ and $n$ be the number of points at which the function $...

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The length of the latus-rectum of the ellipse, whose foci are (2,5) and (2, –3) and eccentricity is $\frac{4}{5}$ ,...

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In the expansion of ${\left( {\sqrt[3]{2} + \frac{1}{{\sqrt[3]{3}}}} \right)^n},n \in \;{\rm{N}}$ , if the ratio of ${15^{{\rm{th }}}}$ term from...

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A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and...

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Let the three sides of a triangle are on the lines $...

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The value of $...

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Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function satisfying $f(0) = 1$ and $f(2x) - f(x) = x$ for...

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If $...

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Considering the principal values of the inverse trigonometric functions, $...

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Consider the sets $A=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x^2+y^2=25\right\}, B=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x^2+9 y^2=144\right\}$, $...

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Consider the equation ${x^2} + 4x - n = 0$, where $n \in [20,100]$ is a natural number. Then the...

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Let $A = \{ 1,\,\,6,\,\,11,\,\,16, \ldots \} $ and $B = \{ 9,16,23,30, \ldots \} $ be the sets consisting...

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For an integer $n \ge 2$, if the arithmetic mean of all coefficients in the binomial expansion of $...

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Let the shortest distance between the lines $...

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Let A and B be two distinct points on the line $...

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Let $f,g:(1,\infty ) \to $ $\mathbb{R}$ be defined as $f(x) = \frac{{2x + 3}}{{5x + 2}}$ and $...

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If $10{\sin ^4}\theta + 15{\cos ^4}\theta = 6$, then the value of $...

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Consider two vectors $\vec u = 3\hat i - \hat j$ and $...

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The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3...

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Let $f:[0,\infty)\to$ $\mathbb{R}$ be a differentiable function such that $...

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$1 + 3 + {5^2} + 7 + {9^2} + .....$ upto 40 terms is equal to

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${\rm{KMn}}{{\rm{O}}_4}$ acts as an oxidising agent in acidic medium. 'X' is the difference between the oxidation states of Mn in...

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Fortification of food with iron is done using ${\rm{FeS}}{{\rm{O}}_4} \cdot 7{{\rm{H}}_2}{\rm{O}}$ . The mass in grams of the ${\rm{FeS}}{{\rm{O}}_4}$. $7{{\rm{H}}_2}{\rm{O}}$...

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The pH of a 0.01 M weak acid ${\rm{HX}}\left( {{{\rm{K}}_a} = 4 \times {{10}^{ - 10}}} \right)$ is found to...

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The total number of hydrogen bonds of a DNA-double Helix strand whose one strand has the following sequence of bases...

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In Dumas' method for estimation of nitrogen 1 g of an organic compound gave 150 mL of nitrogen collected at...

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Given below are two statements: Statement I: Nitrogen forms oxides with +1 to +5 oxidation states due to the formation...

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One mole of an ideal gas expands isothermally and reversibly from $10{\rm{d}}{{\rm{m}}^3}$ to $20{\rm{d}}{{\rm{m}}^3}$ at 300 K. $\Delta {\rm{U}},{\rm{q}}$ and...

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Which of the following molecule(s) show/s paramagnetic behavior? A. ${{\rm{O}}_2}$ B. ${{\rm{N}}_2}$ C. ${{\rm{F}}_2}$ D. ${{\rm{S}}_2}$ E. ${\rm{C}}{{\rm{l}}_2}$ Choose the...

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Given below are two statements. Statement I: The dipole moment of $...

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Benzene is treated with oleum to produce compound (X) which when further heated with molten sodium hydroxide followed by acidification...

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Given below are the pairs of group 13 elements showing their relation in terms of atomic radius. $...

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Which one of the following about an electron occupying the 1 s orbital in a hydrogen atom is incorrect? (Bohr's...

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XY is the membrane/partition between two chambers 1 and 2 containing sugar solutions of concentration ${{\rm{c}}_1}$ and $...

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Aldol condensation is a popular and classical method to prepare $\alpha ,\beta $ -unsaturated carbonyl compounds. This reaction can be...

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Pair of transition metal ions having the same number of unpaired electrons is

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Which one of the following complexes will have ${\Delta _0} = 0$ and $\mu = 5.96$ B.M?

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Let us consider a reversible reaction at temperature, T. In this reaction, both $\Delta {\rm{H}}$ and $\Delta {\rm{S}}$ were observed...

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An organic compound (X) with molecular formula ${{\rm{C}}_3}{{\rm{H}}_6}{\rm{O}}$ is not readily oxidised. On reduction it gives ${{\rm{C}}_3}{{\rm{H}}_8}{\rm{O}}({\rm{Y}})$ which reacts with...

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On charging the lead storage battery, the oxidation state of lead changes from ${x_1}$ to ${y_1}$ at the anode and...

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The major product (A) formed in the following reaction sequence is

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For $\mathrm{A}_2+\mathrm{B}_2 \rightleftharpoons 2 \mathrm{AB}$ ${{\rm{E}}_{\rm{a}}}$ for forward and backward reaction are 180 and $200\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}$ respectively If catalyst...

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Number of stereoisomers possible for the complexes, $\left[ {{\rm{CrC}}{{\rm{l}}_3}{{({\rm{py}})}_3}} \right]$ and ${\left[ {{\rm{CrC}}{{\rm{l}}_2}{{({\rm{ox}})}_2}} \right]^{3 - }}$ are respectively (py =...

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Rate law for a reaction between A and B is given by ${\rm{r}} = {\rm{k}}{[\;{\rm{A}}]^{\rm{n}}}{[\;{\rm{B}}]^{\rm{m}}}$ If concentration of A is...

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Predict the major product of the following reaction sequence:-

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Identify the pair of reactants that upon reaction, with elimination of HCl will give rise to the dipeptide Gly-Ala.

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Four capacitors each of capacitance 16$mu$F are connected as shown in the figure. The capacitance between points A and B...

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Two slabs with square cross section of different materials (1,2) with equal sides $(l)$ and thickness ${d_1}$ and ${d_2}$ such...

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Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of $\frac{1}{{\sqrt 2 }}$ Tesla,...

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Distance between object and its image (magnified by $ - \frac{1}{3}$) is 30 cm . The focal length of the...

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A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping....

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A small mirror of mass m is suspended by a massless thread of length $l$ . Then the small angle...

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A body of mass m is suspended by two strings making angles ${\theta _1}$ and ${\theta _2}$ with the horizontal...

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Two small spherical balls of mass 10 g each with charges $ - 2\mu {\rm{C}}$ and $2\mu {\rm{C}}$ , are...

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In an experiment with a closed organ pipe, it is filled with water by $\left( {\frac{1}{5}} \right)$ th of its...

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Two liquids A and B have ${\theta _A}$ and ${\theta _B}$ as contact angles in a capillary tube. If $...

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Current passing through a wire as function of time is given as ${\rm{I}}({\rm{t}}) = 0.02{\rm{t}} + 0.01\;{\rm{A}}$. The charge that...

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Considering the Bohr model of hydrogen like atoms, the ratio of the radius of 5th orbit of the electron in...

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Two infinite identical charged sheets and a charged spherical body of charge density '$\rho$' are arranged as shown in figure....

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Which of the following are correct expression for torque acting on a body? A. $...

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Two simple pendulums having lengths ${l_1}$ and ${l_2}$ with negligible string mass undergo angular displacements ${\theta _1}$ and ${\theta _2}$,...

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When an object is placed 40 cm away from a spherical mirror an image of magnification $\frac{1}{2}$ is produced. To...

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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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An alternating current is represented by the equation, $i = 100\sqrt 2 \sin (100\pi t)$ ampere. The RMS value of...

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In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of ${M^P}{L^Q}{T^R}{A^S}$, where...

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The Boolean expression ${\rm{Y}} = A\bar BC + \bar A\bar C$ can be realised with which of the following gate...

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Total number of molecules/species from following which will be paramagnetic is $\mathrm{O}_{2}, \mathrm{O}_{2}^{+}, \mathrm{O}_{2}^{-}, \mathrm{NO}, \mathrm{NO}_{2}, \mathrm{CO}, \mathrm{K}_{2}\left[\mathrm{NiCl}_{4}\right],\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}, \mathrm{~K}_{2}\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]$

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If $\vec L$ and $\vec P$ represent the angular momentum and linear momentum respectively of a particle of mass '$m$'...

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The spin only magnetic moment $(\mu)$ value (B.M.) of the compound with strongest oxidising power among $\mathrm{Mn}_{2} \mathrm{O}_{3}$, TiO and...

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Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12 ....

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Consider the following data : Heat of formation of $\mathrm{CO}_{2}(\mathrm{~g})=-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$ Heat of formation of $\mathrm{H}_{2} \mathrm{O}(\mathrm{l})=-286.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$...

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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 group 15 element forms $\mathrm{d} \pi-\mathrm{d} \pi$ bond with transition metals. It also forms hydride, which is a strongest...

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For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of...

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The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $...

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An ideal gas undergoes a cyclic transformation starting from the point $A$ and coming back to the same point by...

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The product B formed in the following reaction sequence is :

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The major product of the following reaction is :

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In a Young's double slit experiment, the slits are separated by 0.2 mm. If the slits separation is increased to...

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The total number of compounds from below when treated with hot $\mathrm{KMnO}_{4}$ giving benzoic acid is :

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Consider the sound wave travelling in ideal gases of ${\rm{He}},{\rm{C}}{{\rm{H}}_4}$, and ${\rm{C}}{{\rm{O}}_2}$. All the gases have the same ratio $...

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Assume a living cell with $0.9 \%(\omega / \omega)$ of glucose solution (aqueous). This cell is immersed in another solution...

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Identify correct conversion during acidic hydrolysis from the following : (A) starch gives galactose. (B) cane sugar gives equal amount...

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Consider an elementary reaction $\mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g}) \rightarrow \mathrm{C}(\mathrm{g})+\mathrm{D}(\mathrm{g})$ If the volume of reaction mixture is suddenly reduced to $\frac{1}{3}$ of its...

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Concentrated nitric acid is labelled as $75 \%$ by mass. The volume in mL of the solution which contains 30...

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Match List - I with List - II.[0pt] Choose the correct answer from the options given below :

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The area of the region bounded by the curve $y = \max \{ |x|,x|x - 2|\} $, the x-axis and...

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Let $...

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If the number of seven-digit numbers, such that the sum of their digits is even, is $...

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Let the product of the focal distances of the point $P(4,2\sqrt 3)$ on the hyperbola ${\rm{H}}:\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$...

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All five letter words are made using all the letters A, B, C, D, E and arranged as in an...

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Let \[f(x) = \left\{ {\begin{array}{*{20}{l}} {{{(1 + ax)}^{1/x}}}&{,x < 0}\\ {1 + b}&{,x = 0}\\ {\frac{{{{(x + 4)}^{1/2}} - 2}}{{{{(x...

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A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $...

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The sum 1 + 3 + 11 + 25 + 45 + 71 + ……… upto 20 terms, is equal...

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Let the domain of the function $f(x) = {\log _2}{\log _4}{\log _6}\left( {3 + 4x - {x^2}} \right)$ be (a,...

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The sum of all rational terms in the expansion of ${(2 + \sqrt 3 )^8}$ is

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Let $f(x) = \int {{x^3}} \sqrt {3 - {x^2}} dx$. If $5f(\sqrt 2 ) = - 4$, then $f(1)$ is...

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The number of solutions of the equation $...

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Let $z \in \mathbb{C}$ be such that $\frac{{{z^2} + 3i}}{{z - 2 + i}} = 2 + 3i$. Then the...

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If $y(x) = \left| {\begin{array}{*{20}{c}} {\sin x}&{\cos x}&{\sin x + \cos x + 1}\\ {27}&{28}&{27}\\ 1&1&1 \end{array}} \right|$, $...

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Let A be a matrix of order $3 \times 3$ and $|A| = 5$. If $...

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If the domain of the function $...

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Let g be a differentiable function such that $\int_0^x g (t)dt = x - \int_0^x t g(t)dt,x \ge 0$ and...

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Line ${L_1}$ passes through the point (1,2,3) and is parallel to z-axis. Line ${L_2}$ passes through the point $(\lambda ,5,6)$...

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A line passing through the point $P(\sqrt 5 ,\sqrt 5 )$ intersects the ellipse $\frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{{25}} = 1$ at...

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

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Arrange the following in increasing order of solubility product : $\mathrm{Ca}(\mathrm{OH})_{2}, \mathrm{AgBr}, \mathrm{PbS}, \mathrm{HgS}$

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The purification method based on the following physical transformation is :

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Given below are two statements : Statement (I): According to the Law of Octaves, the elements were arranged in the...

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Let ${\rm{A}} = \{ - 3, - 2, - 1,0,1,2,3\} $. Let R be a relation on A defined by...

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The amphoteric oxide among $\mathrm{V}_{2} \mathrm{O}_{3}, \mathrm{~V}_{2} \mathrm{O}_{4}$ and $\mathrm{V}_{2} \mathrm{O}_{5}$, upon reaction with alkali leads to formation of an...

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Let a line passing through the point (4, 1, 0) intersect the line $...

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If $...

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Given below are two statements : In the light of the above statements, choose the correct answer from the options...

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Let ${a_1},{a_2},{a_3}, \ldots $ be a G.P. of increasing positive numbers. If ${a_3}{a_5} = 729$ and $...

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Which of the following is/are not correct with respect to energy of atomic orbitals of hydrogen atom?[0pt] (A) $1 \mathrm{~s}

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The radius of the smallest circle which touches the parabolas $...

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Identify correct statements :[0pt] (A) Primary amines do not give diazonium salts when treated with $\mathrm{NaNO}_{2}$ in acidic condition. (B)...

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Let $\alpha$ and $\beta $ be the roots of ${x^2} + \sqrt 3 x - 16 = 0$, and $...

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Identify the inorganic sulphides that are yellow in colour :[0pt] [JEE MAIN\_280125\_S2][Chemical bonding] [T-16][M0derate] (A) $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{~S}$ (B) PbS (C)...

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Identify product $[A],[B]$ and $[C]$ in the following reaction sequence. $$ \mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{CH} \xrightarrow[\mathrm{H}_{2}]{\mathrm{Pd} / \mathrm{C}}[\mathrm{~A}] \xrightarrow[\text { (ii)...

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A thin transparent film with refractive index 1.4 , is held on circular ring of radius 1.8 cm . The...

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A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field $B$ exists into...

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Consider the following reactions $...

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The number of optical isomers exhibited by the iron complex (A) obtained from the following reaction is _____ $...

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During estimation of nitrogen by Dumas' method of compound ${\rm{X}}(0.42\;{\rm{g}})$ _______ mL of ${{\rm{N}}_2}$ gas will be liberated at STP....

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The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure...

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An electric dipole of dipole moment $6 \times 10^{-6} \mathrm{Cm}$ is placed in uniform electric field of magnitude $...

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Given : $\Delta {{\rm{H}}^ \ominus }{\rm{ sub }}$ $[{\rm{C }}({\rm{graphite}})] = 710\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}$ $...

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0.5 g of an organic compound on combustion gave 1.46 g of ${\rm{C}}{{\rm{O}}_2}$ and 0.9 g of ${{\rm{H}}_2}{\rm{O}}$. The percentage...

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Which compound would give 3-methyl-6-oxoheptanal upon ozonolysis?

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Identify [A] ,[B] and [C] , respectively in the following reaction sequence:

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Given below are two statements: Statement I : A catalyst cannot alter the equilibrium constant of the reaction, temperature remaining...

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In the following system, $\mathrm{PCl}_5(\mathrm{~g}) \leftrightharpoons \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g})$ at equilibrium, upon addition of xenon gas at constant T & p, the...

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The value of current $I$ in the electrical circuit as given below, when potential at $A$ is equal to the...

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A balloon and its content having mass $M$ is moving up with an acceleration ' $a$ '. The mass that...

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A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc...

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Number of molecules from below which cannot give iodoform reaction is: Ethanol, Isopropyl alcohol, Bromoacetone, 2-Butanol, 2-Butanone, Butanal, 2-Pentanone, 3-Pentanone,...

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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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In the following reactions, which one is NOT correct?

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The kinetic energy of translation of the molecules in 50 g of $\mathrm{CO}_{2}$ gas at $17^{\circ} \mathrm{C}$ is

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The metal ions that have the calculated spin-only magnetic moment value of 4.9 B.M. are : A. ${\rm{C}}{{\rm{r}}^{2 + }}$...

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A concave mirror produces an image of an object such that the distance between the object and image is 20...

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The least acidic compound, among the following is:

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A parallel plate capacitor of capacitance $1 \mu \mathrm{~F}$ is charged to a potential difference of 20 V . The...

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Which of the following is the correct structure of L- Fructose?

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In a long glass tube, mixture of two liquids $A$ and $B$ with refractive indices 1.3 and 1.4 respectively, forms...

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Correct order of limiting molar conductivity for cations in water at 298 K is :

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The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered...

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Match the LIST-I with LIST-II

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The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$, then the ratio of r.m.s. velocities...

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A body of mass 4 kg is placed on a plane at a point $P$ having coordinate $(3,4) m$. Under...

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Identify the correct statements from the following.

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A bar magnet has total length $2 l=20$ units and the field point $P$ is at a distance $d=10$ units...

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Given below are two statements: Statement I : The N - N single bond is weaker and longer than that...

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Which of the following properties will change when system containing solution 1 will become solution 2?

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In a reaction $A + B \to C$, initial concentrations of A and B are related as ${[A]_0} = 8{[B]_0}$....

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Which of the following phenomena can not be explained by wave theory of light ?

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The correct order of the complexes $...

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Among ${10^{ - 9}}\;{\rm{g}}$ (each) of the following elements, which one will have the highest number of atoms? Element: ${\rm{Pb}},{\rm{Po}},{\rm{Pr}}$...

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Which of the following postulate of Bohr's model of hydrogen atom is not in agreement with quantum mechanical model of...

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2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the...

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The frequency of revolution of the electron in Bohr's orbit varies with $n$, the principal quantum number as

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Which of the following statements are correct? A. The process of adding an electron to a neutral gaseous atom is...

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In the circuit shown here, assuming threshold voltage of diode is negligibly small, then voltage $V_{A B}$ is correctly represented...

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Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities...

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A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to a uniform magnetic field...

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A loop ABCDA, carrying current I = 12 A, is placed in a plane, consists of two semi-circular segments of...

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In the figure shown below, a resistance of $150.4\Omega $ is connected in series to an ammeter A of resistance...

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Three identical spheres of mass m, are placed at the vertices of an equilateral triangle of length a. When released,...

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Which of the following curves possibly represent one-dimensional motion of a particle? Choose the correct answer from the options given...

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A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg ,...

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The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V....

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A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of...

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

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The work function of a metal is 3 eV. The color of the visible light that is required to cause...

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The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of...

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The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2 m away...

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A particle is released from height S above the surface of the earth. At certain height its kinetic energy is...

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A person measures mass of 3 different particles as 435.42 g, 226.3g and 0.125 g. According to the rules for...

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Consider following statements for refraction of light through prism, when angle of deviation is minimum. A. The refracted ray inside...

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The angle of projection of a particle is measured from the vertical axis as $\phi $ and the maximum height...

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

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A wire of length 25 m and cross-sectional area $5\;{\rm{m}}{{\rm{m}}^2}$ having resistivity of $2 \times {10^{ - 6}}\Omega \;{\rm{m}}$ is...

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Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area $0.5\;{{\rm{m}}^2}$. It has a small...

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A piston of mass M is hung from a massless spring whose restoring force law goes as $...

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A parallel plate capacitor is filled equally(half) with two dielectrics of dielectric constants ${\varepsilon _1}$ and ${\varepsilon _2}$ , as...

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Choose the correct logic circuit for the given truth table having inputs A and B.

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During the melting of a slab of ice at 273 K at atmospheric pressure:

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Two blocks of masses m and $M,(M > m)$, are placed on a frictionless table as shown in figure. A...

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A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the...

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A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm...

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An infinite wire has a circular bend of radius a , and carrying a current I as shown in figure....

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Young's double slit interference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5...

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An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of...

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Three distinct numbers are selected randomly from the set $\{ 1,2,3, \ldots ,40\}$. If the probability, that the selected numbers...

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Let [.] denote the greatest integer function. If $\int_0^{{e^3}} {\left[ {\frac{1}{{{e^{x - 1}}}}} \right]} dx = \alpha - {\log _e}2$,...

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Let $f:R \to R$ be a thrice differentiable odd function satisfying $...

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The absolute difference between the squares of the radii of the two circles passing through the point (-9, 4) and...

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If the area of the region $...

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Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth...

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The magnetic field of an E.M. wave is given by $\overrightarrow{\mathrm{B}}=\left(\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j}\right) 30 \sin \left[\omega\left(\mathrm{t}-\frac{Z}{\mathrm{c}}\right)\right]$ (S.I. Units). The corresponding...

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

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

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Let $\mathrm{H}_{1}: \frac{x^{2}}{\mathrm{a}^{2}}-\frac{y^{2}}{\mathrm{~b}^{2}}=1$ and $\mathrm{H}_{2}:-\frac{x^{2}}{\mathrm{~A}^{2}}+\frac{y^{2}}{\mathrm{~B}^{2}}=1$ be two hyperbolas having length of latus rectums $15 \sqrt{2}$ and $12 \sqrt{5}$ respectively. Let...

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Number of functions $f:\{1,2, \ldots, 100\} \rightarrow\{0,1\}$, that assign 1 to exactly one of the positive integers less than or...

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If $\int \frac{2 x^{2}+5 x+9}{\sqrt{x^{2}+x+1}} \mathrm{~d} x=x \sqrt{x^{2}+x+1}+\alpha \sqrt{x^{2}+x+1}+\beta \log _{\mathrm{e}}\left|x+\frac{1}{2}+\sqrt{x^{2}+x+1}\right|+\mathrm{C}$, where $C$ is the constant of integration, then $...

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Let $P$ be the image of the point $Q(7,-2,5)$ in the line $L: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4}$ and $R(5, p, q)$ be a...

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Let $f:(0, \infty) \rightarrow \mathbf{R}$ be a function which is differentiable at all points of its domain and satisfies the...

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Let the points $\left(\frac{11}{2}, \alpha\right)$ lie on or inside the triangle with sides $x+y=11, x+2 y=16$ and $2 x+3 y=29$....

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In an arithmetic progression, if $S_{40}=1030$ and $S_{12}=57$, then $S_{30}-S_{10}$ is equal to:

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If $\alpha>\beta>\gamma>0$, then the expression $\cot ^{-1}\left\{\beta+\frac{\left(1+\beta^{2}\right)}{(\alpha-\beta)}\right\}+\cot ^{-1}\left\{\gamma+\frac{\left(1+\gamma^{2}\right)}{(\beta-\gamma)}\right\}+\cot ^{-1}\left\{\alpha+\frac{\left(1+\alpha^{2}\right)}{(\gamma-\alpha)}\right\}$ is equal to :

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Let $(2,3)$ be the largest open interval in which the function $f(x)=2 \log _{\mathrm{e}}(x-2)-x^{2}+a x+1$ is strictly increasing and $...

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Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The...

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Let the position vectors of three vertices of a triangle be $4 \vec{p}+\vec{q}-3 \vec{r},-5 \vec{p}+\vec{q}+2 \vec{r}$ and $2 \vec{p}-\vec{q}+2 \vec{r}$....

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If the equation of the parabola with vertex $\mathrm{V}\left(\frac{3}{2}, 3\right)$ and the directrix $x+2 y=0$ is $...

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The function $f:(-\infty, \infty) \rightarrow(-\infty, 1)$, defined by $f(x)=\frac{2^{x}-2^{-x}}{2^{x}+2^{-x}}$ is :

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Let $\overrightarrow{\mathrm{a}}=3 \hat{i}-\hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=\overrightarrow{\mathrm{a}} \times(\hat{i}-2 \hat{k})$ and $\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}} \times \hat{k}$. Then the projection of $\overrightarrow{\mathrm{c}}-2 \hat{j}$ on $\vec{a}$ is:

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Let $\mathrm{A}=\left\{x \in(0, \pi)-\left\{\frac{\pi}{2}\right\}: \log _{(2 / \pi)}|\sin x|+\log _{(2 / \pi)}|\cos x|=2\right\}$ and $B=\{x \geq 0: \sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0\}$. Then $...

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Let $\mathrm{A}=\left[a_{i j}\right]$ be a square matrix of order 2 with entries either 0 or 1 . Let E be...

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The number of real solution(s) of the equation $x^{2}+3 x+2=\min \{|x-3|,|x+2|\}$ is :

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For some a, b, let $$ f(x)=\left|\begin{array}{ccc} a+\frac{\sin x}{x} & 1 & \mathbf{b} \\ \mathbf{a} & 1+\frac{\sin x}{x} & \mathbf{b}...

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If $7=5+\frac{1}{7}(5+\alpha)+\frac{1}{7^{2}}(5+2 \alpha)+\frac{1}{7^{3}}(5+3 \alpha)+\ldots \ldots \ldots$, then the value of $\alpha$ is :

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The area of the region enclosed by the curves $y=\mathbf{e}^{x}, y=\left|\mathbf{e}^{x}-1\right|$ and $y$-axis is :

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If the system of equations $x+2 y-3 z=2$ $2 x+\lambda y+5 z=5$ $14 x+3 y+\mu z=33$ has infinitely many solutions,...

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The equation of the chord, of the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{16}=1$, whose mid-point is $(3,1)$ is :

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Suppose $A$ and $B$ are the coefficients of $30^{\text {th }}$ and $12^{\text {th }}$ terms respectively in the binomial...

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Let $[\mathrm{x}]$ denote the greatest integer function, and let m and n respectively be the numbers of the points, where...

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In Carius method of estimation of halogen, 0.25 g of an organic compound gave 0.15 g of silver bromide $(\mathrm{AgBr})$....

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If the system of linear equations $...

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The observed and normal molar masses of compound $M X_{2}$ are 65.6 and 164 respectively. The percent degree of ionisation...

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Let one focus of the hyperbola $H:\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ be at $(\sqrt {10} ,0)$ and the corresponding directrix...

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Consider a complex reaction taking place in three steps with rate constants $\mathrm{k}_{1}, \mathrm{k}_{2}$ and $\mathrm{k}_{3}$ respectively. The overall rate...

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Let $a \in R$ and A be a matrix of order $3 \times 3$ such that $...

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The hydrocarbon $(\mathrm{X})$ with molar mass $80 \mathrm{~g} \mathrm{~mol}^{-1}$ and $90 \%$ carbon has $\_\_\_\_$ degree of unsaturation.

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For $\alpha ,\beta ,\gamma \in R$ , if $...

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The possible number of stereoisomers for 5-phenylpent-4-en-2-ol is $\_\_\_\_$ .

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Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of...

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Based on the data given below : / \mathrm{Cl}^{(-)}}^{\circ}=1.36 \mathrm{~V} \mathrm{E}_{\mathrm{MnO}_{4}^{-} / \mathrm{Mn}^{2+}}^{\circ}=1.51 \mathrm{~V} & \mathrm{E}_{\mathrm{Cr}^{3+} / \mathrm{Cr}}^{\circ}=-0.74 \mathrm{~V} \end{array}...

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The largest $n \in N$ such that ${3^n}$ divides 50 ! is :

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Let $A = \left[ {\begin{array}{*{20}{c}} \alpha &{ - 1}\\ 6&\beta \end{array}} \right],\alpha > 0$, such that $\det (A) = 0$...

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Find the compound ' A ' from the following reaction sequences. $...

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Match List - I with List - II.[0pt] Choose the correct answer from the options given below :

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The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly...

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For the reaction, $\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})$ Attainment of equilibrium is predicted correctly by :

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If S and S' are the foci of the ellipse $\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{9} = 1$ and P be a point...

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Identify correct statement/s:[0pt] (A) $-\mathrm{OCH}_{3}$ and $-\mathrm{NHCOCH}_{3}$ are activating group. (B) -CN and -OH are meta directing group. (C) -CN...

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If the function $f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1$, where $a > 0$ , attains its local...

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Given below are two statements : In the light of the above statements, choose the correct answer from the options...

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In the given structure, number of sp and $\mathrm{sp}^{2}$ hybridized carbon atoms present respectively are:

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Given below are two statements : Statement (I): The first ionization energy of Pb is greater than that of Sn...

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If $\theta \in [ - 2\pi ,2\pi ]$, then the number of solutions of $...

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The elemental composition of a compound is $54.2 \% \mathrm{C}, 9.2 \% \mathrm{H}$ and $36.6 \% \mathrm{O}$. If the molar...

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Given below are two statements :[0pt] tatement (I): Experimentally determined oxygen-oxygen bond lengths in the $\mathrm{O}_{3}$ are found to be...

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For hydrogen atom, the orbital/s with lowest energy is/are :[0pt] (A) 4 s (B) $3 p_{x}$ (C) $3 d_{x^{2}-y^{2}}$ (D)...

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

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The structure of the major product formed in the following reaction is:

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If $\vec a$ is a nonzero vector such that its projections on the vectors $...

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The term independent of x in the expansion of $...

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Let the vertices Q and R of the triangle PQR lie on the line $...

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

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Let the focal chord PQ of the parabola ${y^2} = 4x$ make an angle of ${60^\circ}$ with the positive axis,...

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The successive 5 ionisation energies of an element are $800,2427,3658,25024$ and $32824 \mathrm{~kJ} / \mathrm{mol}$, respectively. By using the above...

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Let ${a_1},{a_2},{a_3}, \ldots $. be in an A.P. such that $...

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Which of the following mixing of 1 M base and 1 M acid leads to the largest increase in temperature?

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Let ${P_n} = {\alpha ^n} + {\beta ^n},n \in N$ . If ${P_{10}} = 123,{P_9} = 76,{P_8} = 47$ and...

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When Ethane-1,2-diamine is added progressively to an aqueous solution of Nickel (II) chloride, the sequence of colour change observed will...

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Let $f:R \to R$ be a twice differentiable function such that $...

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For reaction The correct order of set of reagents for the above conversion is:

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The conditions and consequence that favours the $\mathrm{t}_{2_{\mathrm{g}}^{3}} \mathrm{e}_{\mathrm{g}}^{1}$ configuration in a metal complex are :

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Let z be a complex number such that $|z| = 1$. If $...

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$\mathrm{S}(\mathrm{g})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{SO}_{3}(\mathrm{~g})+2 x \mathrm{kcal}$ $\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{SO}_{3}(\mathrm{~g})+y \mathrm{kcal}$ The heat of formation of $\mathrm{SO}_{2}(\mathrm{~g})$ is given by...

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Let A be the set of all functions $f:Z \to Z$ and R be a relation on A such that...

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The increase in pressure required to decrease the volume of a water sample by $0.2 \%$ is $...

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A string of length $L$ is fixed at one end and carries a mass of $M$ at the other end....

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Acceleration due to gravity on the surface of earth is ' $g$ '. If the diameter of earth is reduced...

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The ratio of the power of a light source $S_{1}$ to that the light source $S_{2}$ is $2 S_{1}$ is...

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A tightly wound long solenoid carries a current of 15 A . An electron is executing uniform circular motion inside...

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A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the...

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The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in...

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Consider the following electrochemical cell at standard condition. $Au(s)\left| {Q{H_2},Q} \right|N{H_4}X(0.01M)||A{g^ + }(1M)\mid Ag(s){E_{{\rm{cell }}}} = + 0.4V$ The couple...

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The position vector of a moving body at any instant of time is given as $...

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The energy $E$ and momentum $p$ of a moving body of mass $m$ are related by some equation. Given that...

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For the reaction A $\rightarrow$ products The concentration of A at 10 minutes is _____$ \times {10^{-3}}mol{L^{-1}}$ (nearest integer). The...

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Arrange the following in the ascending order of wavelength $(\lambda)$ : (A) Microwaves $\left(\mathrm{A}_{1}\right)$ (B) Ultraviolet rays $\left(\lambda_{2}\right)$ (C) Infrared...

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0.1 mol of the following given antiviral compound (P) will weigh _____ $\times {10^{-1}}g$ (nearest integer).

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Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?

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Consider the following equilibrium, $\mathrm{CO}(\mathrm{~g})+2 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_3 \mathrm{OH}(\mathrm{~g})$ 0.1 mol of CO along with a catalyst is present in...

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In photoelectric effect, the stopping potential $\left(\mathrm{V}_{0}\right) \mathrm{v} / \mathrm{s}$ frequency $(v)$ curve is plotted. (h is the Planck's constant...

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A transition metal (M) among Mn, Cr, Co and Fe has the highest standard electrode potential $...

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Consider the following molecules :

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The correct order of basic nature in aqueous solution for the bases $N{H_3},{H_2}N - N{H_2},C{H_3}C{H_2}N{H_2},{\left( {C{H_3}C{H_2}} \right)_2}NH$ and $...

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The property/properties that show irregularity in first four elements of group-17 is/are : (A) Covalent radius (B) Electron affinity (C)...

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Choose the correct tests with respective observations. (A) $CuS{O_4}$ (acidified with acetic acid) $ + {K_4}\left[ {Fe{{(CN)}_6}} \right] \to $...

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Two vessels A and B are connected via stopcock. The vessel A is filled with a gas at a certain...

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If equal volumes of $A{B_2}$ and XY (both are salts) aqueous solutions are mixed, which of the following combination will...

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Designate whether each of the following compounds is aromatic or not aromatic.

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An optically active alkyl halide ${C_4}{H_9}Br[A]$ reacts with hot KOH dissolved in ethanol and forms alkene [B] as major product...

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The output of the circuit is low (zero) for : (A) $X=0, Y=0$ (B) $X=0, Y=1$ (C) $X=1, Y=0$ (D)...

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A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 \times 10^{-8} \mathrm{C}$ charge...

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A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined...

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The temperature of a body in air falls from $40^{\circ} \mathrm{C}$ to $24^{\circ} \mathrm{C}$ in 4 minutes. The temperature 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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In the first configuration ( 1 ) as shown in the figure, four identical charges ( $q_{0}$ ) are kept...

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A long straight wire of a circular cross-section with radius 'a' carries a steady current I. The current I 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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$N$ equally spaced charges each of value $q$, are placed on a circle of radius $R$. The circle rotates about...

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A photograph of a landscape is captured by a drone camera at a height of 18 km . The size...

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In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of $P_{1}$...

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A particle oscillates along the $x$-axis according to the law, $x(\mathrm{t})=x_{0} \sin ^{2}\left(\frac{\mathrm{t}}{2}\right)$ where $x_{0}=1 \mathrm{~m}$. The kinetic energy (...

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On complete combustion 1.0 g of an organic compound (X) gave 1.46 g of $C{O_2}$ and 0.567 g of ${H_2}O$....

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Given below are two statements : In the light of the above statements, choose the most appropriate answer from the...

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A solution is made by mixing one mole of volatile liquid A with 3 moles of volatile liquid B. The...

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Identify the correct statement among the following :

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Given below are two statements : Statement (I) : The metallic radius of Al is less than that of Ga...

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Among $S{O_2},N{F_3},N{H_3},Xe{F_2},Cl{F_3}$ and $S{F_4}$, the hybridization of the molecule with nonzero dipole moment and highest number of lone-pairs of electrons...

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A molecule with the formula $A{X_4}Y$ has all it's elements from p-block. Element A is rarest, monoatomic, non-radioactive from its...

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Given below are two statements : Statement (I): In octahedral complexes, when ${\Delta _o} < P$ high spin complexes are...

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$CaC{O_3}(s) + 2HCl(aq) \to CaC{l_2}(aq) + C{O_2}(g) + {H_2}O(l)$ Consider the above reaction, what mass of $CaC{l_2}$ will be formed...

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According to Bohr's model of hydrogen atom, which of the following statement is incorrect?

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Which of the following graph correctly represents the plots of ${K_H}$ at 1 bar for gases in water versus temperature?

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Consider the following compound (X) The most stable and least stable carbon radicals, respectively, produced by homolytic cleavage of corresponding...

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A, B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are...

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A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire...

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An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in...

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Let $\alpha, \beta$ be the roots of the equation $x^{2}-\mathrm{ax}-\mathrm{b}=0$ with $\operatorname{Im}(\alpha)

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The roots of the quadratic equation $3 x^{2}-p x+q=0$ are $10^{\text {th }}$ and $11^{\text {th }}$ terms of an...

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A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid...

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The variance of the numbers 8, 21, 34, 47, .............., 320 is._______.

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For ac circuit shown in figure, ${\rm{R}} = 100{\rm{k}}\Omega $ and ${\rm{C}} = 100{\rm{pF}}$ and the phase difference between $...

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The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys...

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The focus of the parabola $y^{2}=4 x+16$ is the centre of the circle $C$ of radius 5 . If the...

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If $\mathrm{I}=\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \mathrm{~d} x$, then $...

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Let $\int \mathrm{x}^{3} \sin x \mathrm{~d} x=\mathrm{g}(x)+\mathrm{C}$, where C is the constant of integration. If $...

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Two wires A and B are made of same material having ratio of lengths $\frac{{{L_A}}}{{{L_B}}} = \frac{1}{3}$ and their diameters...

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The distance of the line $\frac{x-2}{2}=\frac{y-6}{3}=\frac{z-3}{4}$ from the point $(1,4,0)$ along the line $\frac{x}{1}=\frac{y-2}{2}=\frac{z+3}{3}$ is :

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An ac current is represented as $i = 5\sqrt 2 + 10\cos \left( {650\pi t + \frac{\pi }{6}} \right)Amp$ The...

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$\lim _{x \rightarrow \infty} \frac{\left(2 x^{2}-3 x+5\right)(3 x-1)^{\frac{x}{2}}}{\left(3 x^{2}+5 x+4\right) \sqrt{(3 x+2)^{x}}}$ is equal to :

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Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power...

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If the area of the region $\left\{(x, y):-1 \leq x \leq 1,0 \leq y \leq \mathrm{a}+\mathrm{e}^{|x|}-\mathrm{e}^{-x}, \mathrm{a}>0\right\}$ is $\frac{\mathrm{e}^{2}+8 \mathrm{e}+1}{\mathrm{e}}$,...

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A cubic block of mass m is sliding down on an inclined plane at ${60^\circ}$ with an acceleration of $\frac{g}{2}$,...

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A rod of length eight units moves such that its ends $A$ and $B$ always lie on the lines $x-y+2=0$...

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Two projectiles are fired from ground with same initial speeds from same point at angles $\left( {{{45}^\circ}+\alpha}\right)$ and $\left({{{45}^\circ}-\alpha}\right)$ with...

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The number of complex numbers $z$, satisfying $|z|=1$ and $\left|\frac{z}{\bar{z}}+\frac{\bar{z}}{z}\right|=1$, is :

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Let the shortest distance from ( $\mathrm{a}, 0$ ), $\mathrm{a}>0$, to the parabola $y^{2}=4 x$ be 4 . Then the...

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If the square of the shortest distance between the lines $\frac{x-2}{1}=\frac{y-1}{2}=\frac{z+3}{-3}$ and $\frac{x+1}{2}=\frac{y+3}{4}=\frac{z+5}{-5}$ is $\frac{m}{n}$, where $m, n$ are coprime...

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Let $\mathrm{A}=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x+y| \geqslant 3\}$ and $\mathrm{B}=\{(x, y) \in \mathbf{R} \times \mathbf{R}:|x|+|y| \leq 3\}$. If $...

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In a hydrogen like ion, the energy difference between the ${2^{{\rm{nd }}}}$ excitation energy state and ground is 108.8 eV...

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Match the LIST-I with LIST-I

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If in the expansion of $(1+x)^{\mathrm{p}}(1-x)^{\mathrm{q}}$, the coefficients of x and $x^{2}$ are 1 and -2 , respectively, then $p^{2}+q^{2}$...

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Let the range of the function $...

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A lens having refractive index 1.6 has focal length of 12 cm, when it is in air. Find the focal...

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Let $X=\mathbf{R} \times \mathbf{R}$. Define a relation R on X as : $\left(a_{1}, b_{1}\right) R\left(a_{2}, b_{2}\right) \Leftrightarrow b_{1}=b_{2}$. Statement I:...

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If ${_0}$ denotes the permittivity of free space and ${\Phi _E}$ is the flux of the electric field through the...

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Let the point A divide the line segment joining the points $P(-1,-1,2)$ and $Q(5,5,10)$ internally in the ratio $r: 1(r>0)$....

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Uniform magnetic fields of different strengths $\left( {{B_1}} \right.$ and $\left. {{B_2}} \right)$, both normal to the plane of the...

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In the following circuit, the reading of the ammeter will be ( Take Zener breakdown voltage = 4V)

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The system of equations $x+y+z=6$, $x+2 y+5 z=9$, $x+5 y+\lambda z=\mu$, has no solution if

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Let $x=x(y)$ be the solution of the differential equation $y=\left(x-y \frac{d x}{d y}\right) \sin \left(\frac{x}{y}\right), y>0$ and $x(1)=\frac{\pi}{2}$ Then $...

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Two harmonic waves moving in the same direction superimpose to form a wave $x = {\rm{a}}\cos (1.5{\rm{t}})\cos (50.5{\rm{t}})$ where t...

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The length of the chord of the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$, whose mid-point is $\left(1, \frac{1}{2}\right)$, is :

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A board has 16 square as shown in the figures : Out of these 16 squares, two squares are chosen...

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A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream...

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A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and...

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Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]$ be a $3 \times 3$ matrix such that $\mathrm{A}\left[\begin{array}{l}0 1 0\end{array}\right]=\left[\begin{array}{l}0 0 1\end{array}\right], \mathrm{A}\left[\begin{array}{l}4 1 3\end{array}\right]=\left[\begin{array}{l}0 1 0\end{array}\right]$...

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Two charges ${q_1}$ and ${q_2}$ are separated by a distance of 30 cm. A third charge ${q_3}$ initially at 'C'...

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Two plane polarized light waves combine at a certain point whose electric field components are $...

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An object of mass 1000 g experiences a time dependent force $...

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A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same...

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For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is

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A rod of length 5 L is bent right angle keeping one side length as 2 L .

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The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility...

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A compound ' $X$ ' absorbs 2 moles of hydrogen and ' $X$ ' upon oxidation with $\mathrm{KMnO}_{4}{ }^{*} \mathrm{H}^{+}$gives...

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The bond dissociation enthalpy of $\mathrm{X}_{2} \Delta \mathrm{H}_{\text {bond }}^{\circ}$ calculated from the given data is $\_\_\_\_$ $\mathrm{kJmol}{ }^{-1}$. (Nearest...

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When 81.0 g of aluminium is allowed to react with 128.0 g of oxygen gas, the mass of aluminium oxideproduced...

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0.01 mole of an organic compound $(X)$ containing $10 \%$ hydrogen, on complete-combustion produced$0.9 \mathrm{gH}_{2} \mathrm{O}$. Molar mass of $(\mathrm{X})$...

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Consider the following sequence of reactions. Total number of $\mathrm{sp}^{3}$ hybridised carbon atoms in the major product C formed is...

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Standard electrode potentials for a few half cells are mentioned below : $\mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{\circ}=0.34 \mathrm{~V}, \mathrm{E}_{\mathrm{Zn}^{2+} / \mathrm{Zn}}^{\circ}=-0.76 \mathrm{~V}$...

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Identify $\mathrm{A}, \mathrm{B}$ and C in the given below reaction sequence

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The ascending order of relative rate of solvolysis of following compounds is :

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Identify the coordination complexes in which the central metal ion has $d^{4}$ configuration. Choose the correct answer from the options...

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The $\alpha$-Helix and $\beta$-Pleated sheet structures of protein are associated with its :

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A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of $100c{m^2}$ with hinged...

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A steel wire of length 2 m and Young's modulus $2.0 \times {10^{11}}N{m^{ - 2}}$ is stretched by a force....

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A person travelling on a straight line moves with a uniform velocity ${v_1}$ for a distance x and with a...

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${\gamma_A}$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. ${\gamma_B}$ is the specific...

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If the measured angular separation between the second minimum to the left of the central maximum and the third minimum...

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Given below are the atomic numbers of some group 14 elements. The atomic number of the element with lowest melting...

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Given below are two statements about X -ray spectra of elements : Statement (I): A plot of $\sqrt{v}$ ( $v=$...

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Identify the products [A] and [B], respectively in the following reaction:

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A river is flowing from west to east direction with speed of $9km{h^{-1}}$ . If a boat capable of moving...

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Given below are two statements: Statement (I): The boiling points of alcohols and phenols increase with increase in the number...

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Which of the following graphs most appropriately represents a zero order reaction?

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Consider a binary solution of two volatile liquid components 1 and $2 . x_{1}$ and $y_{1}$ are the mole fractions...

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When a non-volatile solute is added to the solvent, the vapour pressure of the solvent decreases by 10 mm of...

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The relationship between the magnetic susceptibility $(\chi )$ and the magnetic permeability $(\mu )$ is given by : (${\mu _0}$...

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Consider the reaction $\mathrm{X}_{2} \mathrm{Y}(\mathrm{g}) \rightleftharpoons \mathrm{X}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{Y}_{2}(\mathrm{~g})$. The equation representing correct relationship between the degree of dissociation $(x)$ of...

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Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge...

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

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Moment of inertia of a rod of mass 'M' and length 'L' about an axis passing through its center and...

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A slanted object AB is placed on one side of convex lens as shown in the diagram. The image is...

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A light wave is propagating with plane wave fronts of the type $x + y + z = $ constant....

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A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The...

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The effect of temperature on spontaneity of reactions are represented as : The incorrect combinations are:

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A point charge + q is placed at the origin. A second point charge +9 q is placed at (d,...

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A monochromatic light is incident on a metallic plate having work function $\phi$. An electron, emitted normally to the plate...

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Considering Bohr's atomic model for hydrogen atom: (A) the energy of H atom in ground state is same as energy...

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Match List - I with List - II. List - I $\hspace{5cm}$ List - II (A) Coefficient of viscosity $\hspace{2cm}$(I)...

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Given below are two statements : Consider the following reaction Statement (I) : In the case of formaldehyde K is...

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Match List - I with List - II. List - I List - II (A) Bronze (I) (B) Brass (II)...

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A particle is subjected to two simple harmonic motions as: ${x_1} = \sqrt 7 \sin 5tcm$ and $...

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Consider the following reactions $$ \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \xrightarrow[-\mathrm{H}_{2} \mathrm{O}]{\mathrm{KOH}}[\mathrm{~A}] \xrightarrow[-\mathrm{H}_{2} \mathrm{O}]{\mathrm{H}_{2} \mathrm{O}_{4}}[\mathrm{~B}]+\mathrm{K}_{2} \mathrm{SO}_{4} $$ The products $[\mathrm{A}]$ and $[\mathrm{B}]$,...

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The battery of a mobile phone is rated as 4.2 V, 5800 mAh. How much energy is stored in it...

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Given below are two statements : Statement (I): For a given shell, the total number of allowed orbitals is given...

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A small bob of mass 100 mg and charge $ + 10\mu C$ is connected to an insulating string of...

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pH of water is 7 at $25^{\circ} \mathrm{C}$. If water is heated to $80^{\circ} \mathrm{C}$., it's pH will :

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A zener diode with 5 V zener voltage is used to regulate an unregulated dc voltage input of 25 V...

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The equation for real gas is given by $\left( {P + \frac{a}{{{V^2}}}} \right)(V - b) = RT$, where P, V,...

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In an adiabatic process, which of the following statements is true?

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At steady state the charge on the capacitor, as shown in the circuit below, is $\_\_\_\_$ $\mu \mathrm{C}$.

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A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure....

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A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth...

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Let ${B_1}$ be the magnitude of magnetic field at center of a circular coil of radius R carrying current I....

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A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image...

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In a series LCR circuit, a resistor of $300 \Omega$, a capacitor of 25 nF and an inductor of 100...

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Let $S=\left\{m \in \mathbf{Z}: A^{m^2}+A^m=3 I-A^{-6}\right\}$, where $A=\left[\begin{array}{cc}2 & -1 \\ 1 & 0\end{array}\right]$. Then $n(S)$ is equal to ______.

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Let $\mathrm{S}=\left\{x: \cos ^{-1} x=\pi+\sin ^{-1} x+\sin ^{-1}(2 x+1)\right\}$. Then $\sum_{x \in \mathrm{~S}}(2 x-1)^2$ is equal to ______.

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A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance $2.5 \mu \mathrm{~F}$....

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Let $f:(0,\infty ) \to {\bf{R}}$ be a twice differentiable function. If for some $...

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The equation of a transverse wave travelling along a string is $y(x, t)=4.0 \sin \left[20 \times 10^{-3} x+600 t\right] \mathrm{mm}$,...

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The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS...

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Two point charges $-4 \mu \mathrm{c}$ and $4 \mu \mathrm{c}$, constituting an electric dipole, are placed at $(-9,0,0) \mathrm{cm}$ and...

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Let [t] be the greatest integer less than or equal to t. Then the least value of $p\in \mathbb{N}$ for...

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A massless spring gets elongated by amount $X_{1}$ under a tension of 5 N . Its elongation is $X_{2}$ under...

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Let ${{\rm{L}}_1}:\frac{{x - 1}}{1} = \frac{{y - 2}}{{ - 1}} = \frac{{z - 1}}{2}$ and $...

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Let $\overrightarrow {\rm{a}} = \hat i + 2\hat j + \hat k$ and $...

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Let $...

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Let $A = \left[ {{a_{ij}}} \right] = \left[ {\begin{array}{*{20}{c}} {{{\log }_5}128}&{{{\log }_4}5}\\ {{{\log }_5}8}&{{{\log }_4}25} \end{array}} \right]$. If ${A_{ij}}$ is...

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Let ${x_1},{x_2}, \ldots .,{x_{10}}$ be ten observations such that $...

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Let ABC be a triangle formed by the lines $...

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Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these...

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Let $\left| {{z_1} - 8 - 2i} \right| \le 1$ and $...

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Let M and N respectively be the maximum and the minimum values of $...

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The value of $...

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Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of...

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Let the line $x + y = 1$ meet the circle ${x^2} + {y^2} = 4$ at the points A...

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The integral $80\int_0^{\frac{\pi }{4}} {\left( {\frac{{\sin \theta + \cos \theta }}{{9 + 16\sin 2\theta }}} \right)} d\theta $ is equal...

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The number of solutions of the equation $...

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

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Let the ellipse ${{\rm{E}}_1}:\frac{{{x^2}}}{{{{\rm{a}}^2}}} + \frac{{{y^2}}}{{\;{{\rm{b}}^2}}} = 1,{\rm{a}} > {\rm{b}}$ and ${{\rm{E}}_2}:\frac{{{x^2}}}{{\;{{\rm{A}}^2}}} + \frac{{{y^2}}}{{\;{{\rm{B}}^2}}} = 1,\;{\rm{A}} < {\rm{B}}$ have same...

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Define a relation R on the interval $\left[ {0,\frac{\pi }{2}} \right)$ by if and only if $...

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The least value of n for which the number of integral terms in the Binomial expansion of ${(\sqrt[3]{7} + \sqrt[{12}]{{11}})^n}$...

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Let P be the set of seven digit numbers with sum of their digits equal to 11 . If the...

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Let the area of the region $...

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The molar mass of the water insoluble product formed from the fusion of chromite ore (${\rm{FeC}}{{\rm{r}}_2}{{\rm{O}}_4}$) with ${\rm{N}}{{\rm{a}}_2}{\rm{C}}{{\rm{O}}_3}$ in presence...

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0.1 mole of compound 'S' will weigh ______ g. (Given molar mass in ${\rm{gmo}}{{\rm{l}}^{ - 1}}{\rm{C}}:12,{\rm{H}}:1,{\rm{O}}:16$ )

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Given below are some nitrogen containing compounds

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The sum of sigma ($\sigma$) and pi ($\pi$) bonds in Hex-1,3-dien-5-yne is

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If ${{\rm{A}}_2}\;{\rm{B}}$ is 30% ionised in an aqueous solution, then the value of van't Hoff factor (i) is ____$...

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The standard reduction potential values of some of the p-block ions are given below. Predict the one with the strongest...

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Match List - I with List - II.

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The reaction ${A_2} + {B_2} \to 2{\rm{AB}}$ follows the mechanism

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An element 'E' has the ionisation enthalpy value of $374\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}$. 'E' reacts with elements A, B, C and...

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

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In the following substitution reaction :

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Match List - I with List - II.

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Given below are two statements : Statement (I) : The radii of isoelectronic species increases in the order. $...

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Total number of nucleophiles from the following is :

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Match List - I with List - II.

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The molar conductivity of a weak electrolyte when plotted against the square root of its concentration, which of the following...

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The correct increasing order of stability of the complexes based on ${\Delta _0}$ value is : I. $...

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If ${a_0}$ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength $(\lambda )$ of...

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At temperature T, compound ${\rm{A}}{{\rm{B}}_{2(\;{\rm{g}})}}$ dissociates as ${\rm{A}}{{\rm{B}}_{2(\;{\rm{g}})}}$ ⇌ ${\rm{AB}}({\rm{g}}) + \frac{1}{2}\;{{\rm{B}}_{2(\;{\rm{g}})}}$ having degree of dissociation x (small compared to...

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Choose the correct statements. (A) Weight of a substance is the amount of matter present in it. (B) Mass is...

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For a ${\rm{Mg}}\left| {{\rm{M}}{{\rm{g}}^{2 + }}({\rm{aq}})} \right|\left| {{\rm{A}}{{\rm{g}}^ + }({\rm{aq}})} \right|{\rm{Ag}}$ the correct Nernst Equation is :

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The correct option with order of melting points of the pairs $({\rm{Mn}},{\rm{Fe}}),({\rm{Tc}},{\rm{Ru}})$ and $({\rm{Re}},{\rm{Os}})$ is :

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The steam volatile compounds among the following are :

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1.24 g of ${\rm{A}}{{\rm{X}}_2}$ (molar mass $124\;{\rm{g}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}$) is dissolved in 1 kg of water to form a solution...

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500 J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm...

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Two light beams fall on a transparent material block at point 1 and 2 with angle ${\theta_1}$ and ${\theta_2}$, respectively,...

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The maximum speed of a boat in still water is 27km/h. Now this boat is moving downstream in a river...

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In a hydraulic lift, the surface area of the input piston is $6\;{\rm{c}}{{\rm{m}}^2}$ and that of the output piston is...

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A container of fixed volume contains a gas at ${27^\circ}{\rm{C}}$ . To double the pressure of the gas, the temperature...

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The coordinates of a particle with respect to origin in a given reference frame is (1,1,1) meters. If a force...

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The pair of physical quantities not having same dimensions is :

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Match List - I with List - II. List - I (A) Electric field inside (distance ${\rm{r}} > 0$ from...

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Consider ${{\rm{I}}_1}$ and ${{\rm{I}}_2}$ are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If $...

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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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At the interface between two materials having refractive indices ${n_1}$ and ${n_2}$ , the critical angle for reflection of an...

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An electric dipole of mass m, charge q, and length $l$ is placed in a uniform electric field $...

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The expression given below shows the variation of velocity $(v)$ with time $({\rm{t}})$, $v = A{t^2} + \frac{{Bt}}{{C + t}}$....

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As shown below, bob A of a pendulum having massless string of length 'R' is released from ${60^\circ}$ to the...

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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 workdone in an adiabatic change in an ideal gas depends upon only :

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Let $u$ and $v$ be the distances of the object and the image from a lens of focal length $f$....

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The fractional compression $\left( {\frac{{\Delta V}}{V}} \right)$ of water at the depth of 2.5 km below the sea level 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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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion...

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Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly...

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A coil of area A and N turns is rotating with angular velocity $\omega$ in a uniform magnetic field $...

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Two projectiles are fired with same initial speed from same point on ground at angles of $\left(45^{\circ}-\alpha\right)$ and $\left(45^{\circ}+\alpha\right)$, respectively,...

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A body of mass 'm' connected to a massless and unstretchable string goes in verticle circle of radius 'R' under...

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For the circuit shown above, equivalent GATE is :

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If $\lambda $ and K are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The...

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If $\alpha = 1 + \sum\limits_{r = 1}^6 {{{( - 3)}^{r - 1}}} {\quad ^{12}}{{\rm{C}}_{2r - 1}}$, then the distance...

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Let $...

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Let M denote the set of all real matrices of order $3 \times 3$ and let $...

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Let ${{\rm{E}}_1}:\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ be an ellipse. Ellipses ${{\rm{E}}_1}$'s are constructed such that their centres and eccentricities are...

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Let $...

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If $...

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Let ${{\rm{T}}_{\rm{r}}}$ be the ${{\rm{r}}^{{\rm{th }}}}$ term of an A.P. If for some ${\rm{m}},{{\rm{T}}_{\rm{m}}} = \frac{1}{{25}},\;{{\rm{T}}_{25}} = \frac{1}{{20}}$ , and...

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The sum, of the squares of all the roots of the equation $...

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Let ABCD be a trapezium whose vertices lie on the parabola ${{\rm{y}}^2} = 4{\rm{x}}$. Let the sides AD and BC...

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If $f(x) = \frac{{{2^x}}}{{{2^x} + \sqrt 2 }},{\rm{x}} \in $, then $\sum\limits_{{\rm{k}} = 1}^{81} f \left( {\frac{{\rm{k}}}{{82}}} \right)$ is equal...

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Let O be the origin, the point A be ${z_1} = \sqrt 3 + 2\sqrt 2 i$, the point $...

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Let the equation of the circle, which touches x-axis at the point $(a,0),a > 0$ and cuts off an intercept...

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The area (in sq. units) of the region $...

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Let $^{\rm{n}}{{\rm{C}}_{{\rm{r}} - 1}} = 28{,^{\rm{n}}}{{\rm{C}}_{\rm{r}}} = 56$ and $^{\rm{n}}{{\rm{C}}_{{\rm{r}} + 1}} = 70$. Let $...

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Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by $...

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$\cos \left( {{{\sin }^{ - 1}}\frac{3}{5} + {{\sin }^{ - 1}}\frac{5}{{13}} + {{\sin }^{ - 1}}\frac{{33}}{{65}}} \right)$ is equal to:

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The relation $R = \{ (x,y):x,y \in $ and $x + y$ is even is:

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Let ${\rm{A}}(x,y,z)$ be a point in xy-plane, which is equidistant from three points (0,3,2),(2,0,3) and (0,0,1). Let $...

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Let $\left\langle {{a_{\rm{n}}}} \right\rangle $ be a sequence such that ${a_0} = 0,{a_1} = \frac{1}{2}$ and $...

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The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0 , 1,2,3,4,5,6,7,...

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The sum of all local minimum values of the function $...

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Let for some function ${\rm{y}} = f(x),\int_0^x t f(t)dt = {x^2}f(x),x > 0$ and $f(2) = 3$. Then $f(6)$ is...

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Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to...

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If the image of the point (4,4,3) in the line $...

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Two number ${k_1}$ and ${k_2}$ are randomly chosen from the set of natural numbers. Then, the probability that the value...

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Consider the following sequence of reactions:

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Given below is the plot of the molar conductivity vs $\sqrt {{\rm{ concentration }}}$ for KCl in aqueous solution.

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Quantitative analysis of an organic compound (X) shows following % composition. C : 14.5% Cl : 64.46% H: 1.8% (Empirical...

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The formation enthalpies, $\Delta {{\rm{H}}_{\rm{f}}}^ \ominus $ for ${{\rm{H}}_{({\rm{g}})}}$ and ${{\rm{O}}_{({\rm{g}})}}$ are 220.0 and $250.0\;{\rm{kJ}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}$ , respectively, at...

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The molarity of a 70% (mass/mass) aqueous solution of a monobasic acid (X) is _____ $ \times {10^{ - 1}}$...

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Consider ' n ' is the number of lone pair of electrons present in the equatorial position of the most...

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Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K ....

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The molecules having square pyramidal geometry are

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The correct order of stability of following carbocations is :

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What is the freezing point depression constant of a solvent, 50 g of which contain 1 g non volatile solute...

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For a given reaction $R \to P,{t_{1/2}}$ is related to ${[A]_0}$ as given in table. Given: $\log 2 = 0.30$...

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Which of the following oxidation reactions are carried out by both ${{\rm{K}}_2}{\rm{C}}{{\rm{r}}_2}{{\rm{O}}_7}$ and ${\rm{KMn}}{{\rm{O}}_4}$ in acidic medium? A. $...

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Given below are two statements: Statement I : D-glucose pentaacetate reacts with 2, 4-dinitrophenylhydrazine Statement II : Starch, on heating...

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A weak acid HA has degree of dissociation x . Which option gives the correct expression of ${\rm{(pH}} - {\rm{p}}{{\rm{K}}_{\rm{a}}})$...

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The incorrect decreasing order of atomic radii is

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A molecule ("P") on treatment with acid undergoes rearrangement and gives ("Q"). ("Q") on ozonolysis followed by reflux under alkaline...

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Both acetaldehyde and acetone (individually) undergo which of the following reactions? A. Iodoform Reaction B. Cannizaro Reaction C. Aldol Condensation...

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Given below are two statements: Statement I: In the oxalic acid vs ${\rm{KMn}}{{\rm{O}}_4}$ (in the presence of dil ${{\rm{H}}_2}{\rm{S}}{{\rm{O}}_4}$) titration...

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Consider the following elements ${\rm{In}},{\rm{Tl}},{\rm{Al}},{\rm{Pb}},{\rm{Sn}}$ and Ge. The most stable oxidation states of elements with highest and lowest first ionisation...

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The compounds that produce ${\rm{C}}{{\rm{O}}_2}$ with aqueous ${\rm{NaHC}}{{\rm{O}}_3}$ solution are:

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The products A and B in the following reactions, respectively are

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In a multielectron atom, which of the following orbitals described by three quantum numbers will have same energy in absence...

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

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The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet...

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Given below are two statements:

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Two iron solid discs of negligible thickness have radii ${R_1}$ and ${R_2}$ and moment of intertia ${I_1}$ and ${I_2}$, respectively....

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A double slit interference experiment performed with a light of wavelength 600 nm forms an interference fringe pattern on a...

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The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of...

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A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed...

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In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured...

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Choose the correct nuclear process from the below options [p : proton, n : neutron, ${{\rm{e}}^-}$ : electron, ${{\rm{e}}^+}$ :...

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The centre of mass of a thin rectangular plate (fig - x) with sides of length a and b, whose...

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A particle of mass 'm' and charge 'q' is fastened to one end 'A' of a massless string having equilibrium...

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Consider following statements: A. Surface tension arises due to extra energy of the molecules at the interior as compared to...

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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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Two capacitors ${C_1}$ and ${C_2}$ are connected in parallel to a battery. Charge-time graph is shown below for the two...

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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 Carnot engine (E) is working between two temperatures 473 K and 273 K. In a new system two engines...

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Which of the following circuits has the same output as that of the given circuit?

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A proton of mass '${m_P}$' has same energy as that of a photon of wavelength '$\lambda $'. If the proton...

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A bead of mass 'm' slides without friction on the wall of a vertical circular hoop of radius 'R' as...

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A hemispherical vessel is completely filled with a liquid of refractive index $\mu$. A small coin is kept at the...

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Due to presence of an em-wave whose electric component is given by $...

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A thin prism ${P_1}$ with angle ${4^0}$ made of glass having refractive index 1.54, is combined with another thin prism...

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In the experiment for measurement of viscosity '$\eta$' of given liquid with a ball having radius R, consider following statements....

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A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square....

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Consider a long thin conducting wire carrying a uniform current I. A particle having mass "M" and charge "q" is...

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Find the equivalent resistance between two ends of the following circuit

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Three infinitely long wires with linear charge density $\lambda $ are placed along the x -axis, y -axis and z-...

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For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas...

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Let f be a differentiable function such that $...

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Let $S = \left\{ {{p_1},{p_2} \ldots ,{p_{10}}} \right\}$ be the set of first ten prime numbers. Let $...

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If for some $\alpha ,\beta ;\alpha \le \beta ,\alpha + \beta = 8$ and $...

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The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is

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Let A be a $3 \times 3$ matrix such that ${X^T}AX = O$ for all nonzero $3 \times 1$ matrices...

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If $I(m,n) = \int_0^1 {{x^{m - 1}}} {(1 - x)^{n - 1}}dx,m,n > 0$, then $I(9,14) + I(10,13)$ is

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A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B...

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$...

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For some ${\rm{n}} \ne 10$, let the coefficients of the 5th, 6th and 7th terms in the binomial expansion of...

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The product of all the rational roots of the equation $...

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Let in a $\Delta ABC$, the length of the side AC be 6, the vertex B be (1, 2, 3)...

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Let the lines $3x - 4y - \alpha = 0,8x - 11y - 33 = 0$, and $...

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Let $f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}$ be a function such that $f(x) - 6f\left( {\frac{1}{x}} \right) = \frac{{35}}{{3x}} - \frac{5}{2}$ ....

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Let the product of the focal distances of the point $\left( {\sqrt 3 ,\frac{1}{2}} \right)$ on the ellipse $...

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For a statistical data ${{\rm{x}}_1},{{\rm{x}}_2}, \ldots ,{{\rm{x}}_{10}}$ of 10 values, a student obtained the mean as 5.5 and $...

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Let $f(x) = \frac{{{2^{x + 2}} + 16}}{{{2^{2x + 1}} + {2^{x + 4}} + 32}}$. Then the value of...

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

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If $\alpha $ and $\beta $ are the roots of the equation $2{z^2} - 3z - 2i = 0$, where...

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If the system of equations $2x - y + z = 4$ $5x + \lambda y + 3z = 12$...

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Let $...

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Let the line passing through the points (-1, 2, 1) and parallel to the line $...

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Let ${S_n} = \frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \ldots $ upto $n$ terms. If the sum of...

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Consider the region $R = \left\{ {(x,y):x \le y \le 9 - \frac{{11}}{3}{x^2},x \ge 0} \right\}$. The area, of the...

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The area of the region $\left\{ {(x,y):{x^2} + 4x + 2 \le y \le |x + 2|} \right\}$ is equal...

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Let circle C be the image of ${x^2} + {y^2} - 2x + 4y - 4 - 0$ in the...

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$37.8\;{\rm{g}}\;{{\rm{N}}_2}{{\rm{O}}_5}$ was taken in a 1 L reaction vessel and allowed to undergo the following reaction at 500 K $2\;{{\rm{N}}_2}{{\rm{O}}_{5(\:{\rm{g}})}}$...

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Xg of benzoic acid on reaction with aq ${\rm{NaHC}}{{\rm{O}}_3}$ released ${\rm{C}}{{\rm{O}}_2}$ that occupied 11.2 L volume at STP. X is...

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Among the following cations, the number of cations which will give characteristic precipitate in their identification tests with $...

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Consider the following reaction occurring in the blast furnace: ${\rm{F}}{{\rm{e}}_3}{{\rm{O}}_{4(\;{\rm{s}})}} + 4{\rm{C}}{{\rm{O}}_{({\rm{g}})}} \to 3{\rm{F}}{{\rm{e}}_{({\rm{l}})}} + 4{\rm{C}}{{\rm{O}}_{2(\;{\rm{g}})}}$ 'x' kg of iron...

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Standard entropies of ${{\rm{X}}_2},{{\rm{Y}}_2}$ and ${\rm{X}}{{\rm{Y}}_5}$ are 70, 50 and $110{\mkern 1mu} {\rm{J}}{{\rm{K}}^{-1}}{\rm{mo}}{{\rm{l}}^{-1}}$ respectively. The temperature in Kelvin at which...

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Preparation of potassium permanganate from ${\rm{Mn}}{{\rm{O}}_2}$ involves two step process in which the 1st step is a reaction with KOH...

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$\;{{\rm{K}}_{{\rm{sp }}}}$ for ${\rm{Cr}}{({\rm{OH}})_3}$ is $1.6 \times {10^{ - 30}}$. What is the molar solubility of this salt in water?

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Following are the four molecules "P", "Q", "R" and "S". Which one among the four molecules will react with $...

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The large difference between the melting and boiling points of oxygen and sulphur may be explained on the basis of

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Given below are two statements I and II. Statement-I : Dumas method is used for estimation of "Nitrogen" in an...

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Which of the following arrangements with respect to their reactivity in nucleophilic addition reaction is correct?

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Given below are two statements: Statement-I : The conversion proceeds well in the less polar medium. $...

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One mole of the octahedral complex compound ${\rm{Co}}{\left( {{\rm{N}}{{\rm{H}}_3}} \right)_5}{\rm{C}}{{\rm{l}}_3}$ gives 3 moles of ions on dissolution in water. One...

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The carbohydrate "Ribose" present in DNA, is A. A pentose sugar B. present in pyranose from C. in "D" configuration...

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Which of the following ions is the strongest oxidizing agent? (Atomic Number of Ce = 58, Eu = 63, Tb...

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For the given cell $...

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The product (1) formed in the following reaction sequence is

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Let us consider an endothermic reaction which is non-spontaneous at the freezing point of water. However, the reaction is spontaneous...

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Which one of the carbocations from the following is most stable?

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Consider the given plots of vapour pressure (VP) vs temperature (T/K). Which amongst the following options is correct graphical representation...

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Which of the following linear combination of atomic orbitals will lead to formation of molecular orbitals in homonuclear diatomic molecules...

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Which of the following statement is true with respect to ${{\rm{H}}_2}{\rm{O}},{\rm{N}}{{\rm{H}}_3}$ and ${\rm{C}}{{\rm{H}}_4}$ ? A. The central atoms of all...

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Which of the following statements are NOT true about the periodic table? A. The properties of elements are function of...

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For a reaction, ${{\rm{N}}_2}{{\rm{O}}_{5(\;{\rm{g}})}} \to 2{\rm{N}}{{\rm{O}}_{2(\;{\rm{g}})}} + \frac{1}{2}{{\rm{O}}_{2(\;{\rm{g}})}}$ in a constant volume container, no products were present initially. The final...

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Aman has been asked to synthesise the molecule . He thought of preparing the molecule using an aldol condensation reaction....

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The temperature of 1 mole of an ideal monoatomic gas is increased by ${50^0{C}}$ at constant pressure. The total heat...

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A current of 5A exists in a square loop of side $\frac{1}{{\sqrt 2 }}\;{\rm{m}}$ . Then the magnitude of the...

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The least count of a screw gauge is 0.01 mm. If the pitch is increased by 75% and number of...

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A square loop of sides $a = 1\;{\rm{m}}$ is held normally in front of a point charge ${\rm{q}} = 1{\rm{C}}$....

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A wire of resistance $9\Omega$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices...

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A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index...

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An electron of mass 'm' with an initial velocity $\overrightarrow {\rm{v}} = {{\rm{v}}_0}\hat i\left( {{{\rm{v}}_0} > 0} \right)$ enters an...

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Consider the following statements: A. The junction area of solar cell is made very narrow compared to a photo diode....

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A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of ${f_1}$ in air. Another...

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An object of mass 'm' is projected from origin in a vertical xy plane at an angle ${45^0}$ with the...

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A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm. If D and d...

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What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D...

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The amount of work done to break a big water drop of radius 'R' into 27 small drops of equal...

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Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is...

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An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a...

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An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly...

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A car of mass 'm' moves on a banked road having radius 'r' and banking angle $\theta $. To avoid...

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The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form...

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A force ${\rm{F}} - \alpha + \beta {{\rm{x}}^2}$ acts on an object in the x -direction. The work done by...

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A uniform solid cylinder of mass 'm' and radius 'r' rolls along an inclined rough plane of inclination $45º$. If...

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A parallel plate capacitor was made with two rectangular plates, each with a length of $l = 3\;{\rm{cm}}$ and breath...

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A satellite is launched into a circular orbit of radius 'R' around the earth. A second satellite is launched into...

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During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation...

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For an experimental expression $y = \frac{{32.3 \times 1125}}{{27.4}}$, where all the digits are significant. Then to report the value...

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An alternating current is given by $I = {I_A}\sin \omega t + {I_B}\cos \omega t$ . The r.m.s current will...

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If the set of all values of a, for which the equation $5{x^3} - 15x - a = 0$ has...

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If the area of the larger portion bounded between the curves ${x^2} + {y^2} = 25$ and $...

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Let the circle C touch the line $x - y + 1 = 0$ , have the centre on the...

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The sum of all rational terms in the expansion of ${\left( {1 + {2^{1/3}} + {3^{1/2}}} \right)^6}$ is equal to...

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If the equation $a(b - c){x^2} + b(c - a)x + c(a - b) = 0$ has equal roots, where...

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One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4....

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If A,B, and $\left( {{\mathop{\rm adj}\nolimits} \left( {{{\rm{A}}^{ - 1}}} \right) + {\mathop{\rm adj}\nolimits} \left( {{{\rm{B}}^{ - 1}}} \right)} \right)$...

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Let $\left| {\frac{{\bar z - i}}{{2\bar z + i}}} \right| = \frac{1}{3},z \in C$ , be the equation of a...

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Let ${\rm{I}}(x) = \int {\frac{{dx}}{{{{(x - 11)}^{\frac{{11}}{{13}}}}{{(x + 15)}^{\frac{{15}}{{13}}}}}}} \cdot $. If $...

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Let P be the foot of the perpendicular from the point $Q(10, - 3, - 1)$ on the line $...

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Let the area of a $\Delta PQR$ with vertices $P(5,4),Q( - 2,4)$ and $R(a,b)$ be 35 square units. If its...

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Let the position vectors of the vertices A, B and C of a tetrahedron A, B, C, D be $...

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Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width....

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Let a curve $y = f(x)$ pass through the points (0,5) and $\left( {{{\log }_e}2,k} \right)$. If the curve satisfies...

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The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the...

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If the first term of an A.P. is 3 and the sum of its first four terms is equal to...

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If the function $...

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Let the arc AC of a circle subtend a right angle at the centre O . If the point B...

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The value of $...

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If the line $3x-2y+12=0$ intersects the parabola $4y=3{{x}^{2}}$ at the points A and B, then at the vertex of the...

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The value of $\left( {\sin {{{70}}^{{}^\circ }}} \right)\left( {\cot {{{10}}^{{}^\circ }}\cot {{{70}}^{{}^\circ }}-1} \right)$ is

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If the system of equations $(\lambda -1)\text{x}+(\lambda -4)\text{y}+\lambda \text{z}=5$ $\lambda \text{x}+(\lambda -1)\text{y}+(\lambda -4)\text{z}=7$ $(\lambda +1)\text{x}+(\lambda +2)\text{y}-(\lambda +2)\text{z}=9$ has infinitely many...

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Let $R=\{(1,2),(2,3),(3,3)\}$ be a relation defined on the set $\{1,2,3,4\}$. Then the minimum number of elements, needed to be added...

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If $\frac{\pi }{2}\le x\le \frac{{3\pi }}{4}$ , then ${{\cos }^{{-1}}}\left( {\frac{{12}}{{13}}\cos x+\frac{5}{{13}}\sin x} \right)$ is equal to

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Let $f(x)={{\log }_{e}}x$ and $ g(x)=\frac{{{{x}^{4}}-2{{x}^{3}}+3{{x}^{2}}-2x+2}}{{2{{x}^{2}}-2x+1}}$ . Then the domain of $fog$ is

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For the thermal decomposition of ${{\text{N}}_{2}}{{\text{O}}_{5}}(~\text{g})$ at constant volume, the following table can be formed, for the reaction mentioned below....

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Consider the following sequence of reactions to produce major product (A)

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If 1 mM solution of ethylamine produces $\text{pH}=9$ , then the ionization constant $\left( {{{\text{K}}_{\text{b}}}} \right)$ of ethylamine is ${{10}^{{-x}}}$....

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During "S" estimation, 160 mg of an organic compound gives 466 mg of barium sulphate. The percentage of Sulphur in...

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The standard enthalpy and standard entropy of decomposition of ${{\text{N}}_{2}}{{\text{O}}_{4}}$ to $\text{N}{{\text{O}}_{2}}$ are $55.0~\text{kJ}~\text{mo}{{\text{l}}^{{-1}}}$ and $175.0~\text{J}/\text{K}/\text{mol}$ respectively. The standard free...

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The major product of the following reaction is:

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Which of the following happens when $\text{N}{{\text{H}}_{4}}\text{OH}$ is added gradually to the solution containing 1 M ${{\text{A}}^{{2+}}}$ and ions? Given...

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$\text{CrC}{{\text{l}}_{3}}\cdot \text{xN}{{\text{H}}_{3}}$ can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point...

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Propane molecule on chlorination under photochemical condition gives two di-chloro products, "x" and "y". Amongst "x" and "y", "x" is...

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The d-electronic configuration of an octahedral Co (II) complex having magnetic moment of 3.95 BM is:

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Match the LIST-I with LIST-II

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The incorrect statement among the following is:

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$2.8\times {{10}^{{-3}}}~\text{mol}$ of $\text{C}{{\text{O}}_{2}}$ is left after removing ${{10}^{{21}}}$ molecules from its 'X' mg sample. The mass of $\text{C}{{\text{O}}_{2}}$ taken...

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$\text{FeO}_{4}^{{2-}}\xrightarrow{{+2.0~\text{V}}}\text{F}{{\text{e}}^{{3+}}}\xrightarrow{{0.8~\text{V}}}\text{F}{{\text{e}}^{{2+}}}\xrightarrow{{-0.5~\text{V}}}\text{F}{{\text{e}}^{0}}$ In the above diagram, the standard electrode potentials are given in volts (over the arrow). The value of ${{\text{E}}_{{\text{FeO}_{4}^{{2-}}/\text{F}{{\text{e}}^{{2+}}}}}}$...

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Which among the following react with Hinsberg's reagent?

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

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The correct set of ions (aqueous solution) with same colour from the following is:

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Given below are two statements: Statement I: In Lassaigne's test, the covalent organic molecules are transformed into ionic compounds. Statement...

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What amount of bromine will be required to convert 2 g of phenol into 2,4,6-tribromophenol? (Given molar mass in $\text{gmo}{{\text{l}}^{{-1}}}$...

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The complex that shows Facial - Meridional isomerism is:

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Ice at $-{{5}^{{}^\circ }}\text{C}$ is heated to become vapor with temperature of ${{110}^{{}^\circ }}\text{C}$ at atmospheric pressure. The entropy change...

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Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is...

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The correct stability order of the following species/molecules is:

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Given below are two statements: Statement I: Fructose does not contain an aldehydic group but still reduces Tollen's reagent Statement...

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The element that does not belong to the same period of the remaining elements (modern periodic table) is:

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A positive ion A and a negative ion B has charges $6.67\times {{10}^{{-19}}}\text{C}$ and $9.6\times {{10}^{{-10}}}\text{C}$, and masses $19.2\times {{10}^{{-27}}}~\text{kg}$...

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A force $\text{f}={{\text{x}}^{2}}\text{y}\widehat{\text{i}}+{{\text{y}}^{2}}\widehat{\text{j}}$ acts on a particle in a plane $\text{x}+\text{y}=10$ . The work done by this force during a...

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An ideal gas initially at ${{0}^{{}^\circ }}\text{C}$ temperature, is compressed suddenly to one fourth c the ratio of specific heat...

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Two particles are located at equal distance from origin. The position vectors of those are represented by $\overrightarrow{\text{A}}=2\widehat{\text{i}}+3n\widehat{\text{j}}+2\widehat{\text{k}}$ and $\overrightarrow{\text{B}}=2\widehat{\text{i}}-2\widehat{\text{j}}+4\text{p}\widehat{\text{k}}$,...

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In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the...

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The electric flux is $\phi =\alpha \sigma +\beta \lambda $ where $\lambda $ and $\sigma$ are linear and surface charge...

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The position of a particle moving on x -axis is given by $\text{x}(\text{t})=\text{A}\sin \text{t}+\text{B}{{\cos }^{2}}\text{t}+\text{C}{{\text{t}}^{2}}+\text{D}$ , where t is time....

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Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5...

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http://competishun.com/wp-content/uploads/2025/12/1-18-300x184.jpg

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A sub-atomic particle of mass ${{10}^{{-30}}}~\text{kg}$ is moving with a velocity $2.21\times {{10}^{6}}~\text{m}/\text{s}$. Under the matter wave consideration, the particle...

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A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of...

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What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness 'h' in terms of...

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A point particle of charge Q is located at P along the axis of an electric dipole 1 at a...

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Given below are two statements: Statement I: The hot water flows faster than cold water Statement II: Soap water has...

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Given a thin convex lens (refractive index $\mu_2$ ), kept in a liquid (refractive index $\mu_1, \mu_1

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Consider a moving coil galvanometer (MCG): A. The torsional constant in moving coil galvanometer has dimentions $\left[ {\text{M}{{\text{L}}^{2}}~{{\text{T}}^{{-2}}}} \right]$ B....

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A spherical surface of radius of curvature R, separates air from glass (refractive index = 1.5). The centre of curvature...

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Refer to the circuit diagram given in the figure. which of the following observations are correct? A. Total resistance of...

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A solid sphere of mass ' $m$ ' and radius ' $r$ ' is allowed to roll without slipping from...

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The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the...

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Regarding self-inductance: A. The self-inductance of the coil depends on its geometry. B. Self-inductance does not depend on the permeability...

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Using the given P-V diagram, the work done by an ideal gas along the path ABCD is :

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A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is...

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Match List - I with List - II.

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A radioactive nucleus $n_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus...

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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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What is the current through the battery in the circuit shown below ?

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The electric field of an electromagnetic wave in free space is $...

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Identify the valid statements relevant to the given circuit at the instant when the key is closed. A. There will...

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The energy of a system is given as $E(t)=\alpha^{3} e^{-\beta t}$, where $t$ is the time and $\beta=0.3 \mathrm{~s}^{-1}$. The...

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Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge...

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The refractive index of the material of a glass prism is $\sqrt{3}$. The angle of minimum deviation is equal to...

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The width of one of the two slits in Young's double slit experiment is $d$ while that of the other...

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A ball having kinetic energy KE , is projected at an angle of $60^{\circ}$ from the horizontal. What will be...

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If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time...

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In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the...

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A concave mirror of focal length $f$ in air is dipped in a liquid of refractive index $\mu$. Its focal...

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A galvanometer having a coil of resistance $30 \Omega$ need 20 mA of current for full-scale deflection. If a maximum...

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A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk....

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Two charges $7 \mu \mathrm{c}$ and $-4 \mu \mathrm{c}$ are placed at $(-7 \mathrm{~cm}, 0,0)$ and $(7 \mathrm{~cm}, 0,0)$ respectively....

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A plane electromagnetic wave of frequency 20 MHz travels in free space along the +x direction. At a particular point...

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The maximum percentage error in the measurement of density of a wire is [Given, mass of wire $...

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Given are statements for certain thermodynamic variables, (A) Internal energy, volume (V) and mass (M) are extensive variables. (B) Pressure...

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The tube of length L is shown in the figure. The radius of cross section at the point (1) 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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A ball of mass 100 g is projected with velocity 20 m/s at 60° with horizontal. The decrease in kinetic...

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To obtain the given truth table, following logic gate should be placed at G :

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A light source of wavelength $\lambda$ illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2...

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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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For a diatomic gas, if $\gamma_1=\left(\frac{C p}{C v}\right)$ for rigid molecules and $\gamma_2=\left(\frac{C p}{C v}\right)$ for another diatomic molecules, but...

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For a short dipole placed at origin $O$, the dipole moment $P$ is along $x$-axis, as shown in the figure....

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A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a...

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A parallel plate capacitor of area $\mathrm{A}=16 \mathrm{~cm}^2$ and separation between the plates 10 cm is charged by a DC...

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A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $...

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A tube of length 1 m is filled completely with an ideal liquid of mass 2 M and closed at...

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The net current flowing in the given circuit is ______A.

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Two long parallel wires $X$ and $Y$, separated by a distance of 6 cm , carry currents of 5 A...

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A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the...

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Identify the number of structure/s from the following which can be correlated to D-glyceraldehyde.

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Given below are two statements : Statement (I) : Nitrogen, sulphur, halogen and phosphorus present in an organic compound are...

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Consider the given figure and choose the correct option :

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Identify the homoleptic complex(es) that is/are low spin. (A) $\left[\mathrm{Fe}(\mathrm{CN})_5 \mathrm{NO}\right]^{2-}$ (B) $\left[\mathrm{CoF}_6\right]^{3-}$ (C) $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-}$ (D) $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ (E) $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$...

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\begin{aligned} &\text { Arrange the following compounds in increasing order of their dipole moment . }\\ &\mathrm{HBr}, \mathrm{H}_2 \mathrm{~S}, \mathrm{NF}_3...

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The molar solubility(s) of zirconium phosphate with molecular formula $\left(\mathrm{Zr}^{4+}\right)_3\left(\mathrm{PO}_4^{3-}\right)_4$ is given by relation :

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Given below are two statements : Statement (I): A spectral line will be observed for a $...

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Density of 3 M NaCl solution is 1.25 g/mL. The molality of the solution is :

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The maximum covalency of a non-metallic group 15 element ‘E’ with weakest E – E bond is :

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Let $A(6,8), B(10 \cos \alpha,-10 \sin \alpha)$ and $C(-10 \sin \alpha, 10 \cos \alpha)$, be the vertices of a triangle....

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Let \( y = f(x) \) be the solution of the differential equation \[\frac{dy}{dx} = \frac{y - x^2 + 4x}{\sqrt{1...

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Let $A=\{1,2,3\}$. The number of relations on $A$, containing $(1,2)$ and $(2,3)$ which are reflexive and transitive but not symmetric,...

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The position vectors of two 1 kg particles, (A) and (B), are given by $\overrightarrow{\mathbf{r}}_{\mathrm{A}}=\left(\alpha_1 \mathrm{t}^2 \hat{i}+\alpha_2 \hat{j}+\alpha_3 \hat{t}\right) \mathrm{m}$...

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Which of the following statement is not true for radioactive decay?

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Given below are two statements : Statement I : One mole of propyne reacts with excess of sodium to liberate...

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A vessel at 1000 K contains ${\rm{C}}{{\rm{O}}_2}$ with a pressure of 0.5 atm . Some of ${\rm{C}}{{\rm{O}}_2}$ is converted into...

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If $\sum_{r=1}^{30} \frac{r^2\left({ }^{30} C_r\right)^2}{{ }^{30} C_{r-1}}=\alpha \times 2^{29}$, then $\alpha$ is equal to

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How many different stereoisomers are possible for the given molecule?

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Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius...

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The incorrect statements regarding geometrical isomerism are : (A) Propene shows geometrical isomerism. (B) Trans isomer has identical atoms/groups on...

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Match List-I with List-II.

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Lanthanoid ions with $4{f^7}$ configuration are : (A) $\mathrm{Eu}^{2+}$ (B) $\mathrm{Gd}^{3+}$ (C) $\mathrm{Eu}^{3+}$ (D) $\mathrm{Tb}^{3+}$ (E) $\mathrm{Sm}^{2+}$ Choose the correct...

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The products formed in the following reaction sequence are :

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Which of the following electrolyte can be used to obtain ${{\rm{H}}_2}\;{{\rm{S}}_2}{{\rm{O}}_8}$ by the process of electrolysis?

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Let the distance between two parallel lines be 5 units and a point $P$ lie between the lines at a...

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Given below are two statements :

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Arrange the following solutions in order of their increasing boiling points (i) $10^{-4} \mathrm{MNaCl}$ (ii) $10^{-4} \mathrm{M}$ Urea (iii) $...

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The compounds which give positive Fehling's test are :

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Which of the following electronegativity order is incorrect?

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A liquid when kept inside a thermally insulated closed vessel at 25°C was mechanically stirred from outside. What will be...

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Which of the following acids is a vitamin?

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The IUPAC name of the following compound is :

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From the magnetic behaviour of $\left[\mathrm{NiCl}_4\right]^{2-}$ (paramagnetic) and $\left[\mathrm{Ni}(\mathrm{CO})_4\right]$ (diamagnetic), choose the correct geometry and oxidation state.

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Radius of the first excited state of Helium ion is given as: ${{\rm{a}}_0} \to$ radius of first stationary state of...

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In which of the following complexes the CFSE, ${\Delta _{\rm{o}}}$ will be equal to zero ?

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The perpendicular distance, of the line $\frac{x-1}{2}=\frac{y+2}{-1}=\frac{z+3}{2}$ from the point $\mathrm{P}(2,-10,1)$, is :

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Some $\mathrm{CO}_2$ gas was kept in a sealed container at a pressure of 1 atm and at 273 K ....

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In Carius method for estimation of halogens, 180 mg of an organic compound produced 143.5 mg of AgCl. The percentage...

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${\rm{A}} \to \;{\rm{B}}$ The molecule A changes into its isomeric form B by following a first order kinetics at a...

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The number of molecules/ions that show linear geometry among the following is ${\rm{S}}{{\rm{O}}_2},{\rm{BeC}}{{\rm{l}}_2},{\rm{C}}{{\rm{O}}_2},\;{\rm{N}}_3^ - ,{\rm{N}}{{\rm{O}}_2},\;{{\rm{F}}_2}{\rm{O}},{\rm{Xe}}{{\rm{F}}_2},{\rm{NO}}_2^ + ,{\rm{I}}_3^ - ,{{\rm{O}}_3}$

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Let the curve $z(1+i)+\bar{z}(1-i)=4, z \in \mathbf{C}$, divide the region $|z-3| \leq 1$ into two parts of areas $\alpha$ and...

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Consider the following sequence of reactions : Molar mass of the product formed (A) is ______ $g^{-1}$.

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Let for $...

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Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black...

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The product of all solutions of the equation $\mathrm{e}^{5\left(\log _{\mathrm{c}} x\right)^2+3}=x^8, x>0$, is :

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Let $A=\{1,2,3,4\}$ and $B=\{1,4,9,16\}$. Then the number of many-one functions $f: A \rightarrow B$ such that $1 \in f(\mathrm{~A})$ is...

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A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2 A . The amount of...

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If $\sum_{r=1}^n T_r=\frac{(2 n-1)(2 n+1)(2 n+3)(2 n+5)}{64}, then {\lim _{n \rightarrow \infty} \sum_{r=1}^n\left(\frac{1}{T_r}\right)}$ is equal to :

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A circle $C$ of radius 2 lies in the second quadrant and touches both the coordinate axes. Let $r$ be...

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Let the foci of a hyperbola be (1,14) and (1,-12). If it passes through the point(1, 6), then the length...

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A coin is tossed three times. Let $X$ denote the number of times a tail follows a head. If $\mu$...

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Suppose that the number of terms in an A.P. is $2 k, k \in \mathbf{N}$. If the sum of all...

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Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that $f(x+y)=f(x) f(y)$ for all $x, y \in \mathbf{R}$....

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Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of $...

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Let $\alpha_\theta$ and $\beta_\theta$ be the distinct roots of $2 x^2+(\cos \theta) x-1=0, \theta \in(0,2 \pi)$. If m and M...

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Given below are two statements : Statement (I): Corrosion is an electrochemical phenomenon in which pure metal acts as an...

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Let $A=\{1,2,3, \ldots, 10\}$ and $B = \left\{ {\frac{m}{n}:m,n \in A,m < n} \right.$ and $\left. {gcd(m,n) = 1} \right\}$....

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The area of the region, inside the circle ${(x - 2\sqrt 3 )^2} + {y^2} = 12$ and outside the...

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Let $x=x(y)$ be the solution of the differential equation ${{y}^{2}}~\text{d}x+\left( {x-\frac{1}{y}} \right)\text{d}y=0$. If $x(1)=1$, then $x\left( {\frac{1}{2}} \right)$ is :

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If $x=f(y)$ is the solution of the differential equation $$ \left(1+y^2\right)+\left(x-2 \mathrm{e}^{\tan ^{-1} y}\right) \frac{\mathrm{d} y}{\mathrm{~d} x}=0, y \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)...

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Let ${{z}_{1}},{{z}_{2}}$ and ${{z}_{3}}$ be three complex numbers on the circle $|z|=1$ with $...

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Let $f(x)$ be a real differentiable function such that $f(0)=1$ and $f(x+y)=f(x){{f}^{\prime }}(y)+{{f}^{\prime }}(x)f(y)$ for all $x,y\in \mathbf{R}$. Then $...

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Let ${{a}_{1}},{{a}_{2}},{{a}_{3}},\ldots $ be a G.P. of increasing positive terms. If ${{a}_{1}}{{a}_{5}}=28$ and ${{a}_{2}}+{{a}_{4}}=29$, then ${{a}_{6}}$ is equal to :

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If the system of linear equations : $$ \begin{aligned} & x+y+2 z=6 \\ & 2 x+3 y+a z=a+1 \\ &...

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In a group of 3 girls and 4 boys, there are two boys $B_1$ and $B_2$. The number of ways,...

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Let $\mathrm{L}_1: \frac{x-1}{3}=\frac{y-1}{-1}=\frac{z+1}{0}$ and $\mathrm{L}_2: \frac{x-2}{2}=\frac{y}{0}=\frac{z+4}{\alpha}, \alpha \in \mathbf{R}$, be two lines, which intersect at the point $B$. If $P$...

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The area of the region enclosed by the curves $y=x^2-4 x+4$ and $y^2=16-8 x$ is:

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Let A be a square matrix of order 3 such that $\det (A)=-2$ and $\det (3\operatorname{adj}(-6\operatorname{adj}(3A)))={{2}^{{m+n}}}\cdot {{3}^{{mn}}},m>n$. Then $4m+2n$ is...

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Let a line pass through two distinct points $\mathrm{P}(-2,-1,3)$ and Q , and be parallel to the vector $...

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If $\sum_{r=0}^5 \frac{{ }^{11} C_{2 r+1}}{2 r+2}=\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}-\mathrm{n}$ is equal to ..........

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Let $\vec{c}$ be the projection vector of $\vec{b}=\lambda \hat{i}+4 \hat{k}, \lambda>0$, on the vector $\vec{a}=\hat{i}+2 \hat{j}+2 \hat{k}$. If $|\vec{a}+\vec{c}|=7$, then...

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Let the function, $f(x)= \begin{cases}-3 a^2-2, & x1, \mathbf{b} \in \mathbf{R}$. If the area of the region enclosed by $y=f(x)$...

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For a $3 \times 3$ matrix $M$, let trace $(M)$ denote the sum of all the diagonal elements of $M$....

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From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways,...

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If $\int \mathrm{e}^x\left(\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}}+\frac{x}{1-x^2}\right) \mathrm{d} x=\mathrm{g}(x)+\mathrm{C}$, where C is the constant of integration, then...

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Let the parabola $y={{x}^{2}}+\text{p}x-3$ , meet the coordinate axes at the points P,Q and R. If the circle C with...

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The sum of all values of $\theta \in[0,2 \pi]$ satisfying $2 \sin ^2 \theta=\cos 2 \theta$ and $...

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Let the triangle PQR be the image of the triangle with vertices (1,3)(3,1) and (2,4) in the line $x+2y=2$. If...

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Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that the angle between them is $\frac{\pi}{3}$. If $\lambda \vec{a}+2 \vec{b}$...

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Let $\mathrm{E}: \frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1, \mathrm{a}>\mathrm{b}$ and $\mathrm{H}: \frac{x^2}{\mathrm{~A}^2}-\frac{y^2}{\mathrm{~B}^2}=1$. Let the distance between the foci of E and the foci of $H$...

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Let ${{\text{L}}_{1}}:\frac{{x-1}}{2}=\frac{{y-2}}{3}=\frac{{z-3}}{4}$ and ${{\text{L}}_{2}}:\frac{{x-2}}{3}=\frac{{y-4}}{4}=\frac{{z-5}}{5}$ be two lines. Then which of the following points lies on the line of the shortest...

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Let $f(x)=\int_0^{x^2} \frac{\mathrm{t}^2-8 \mathrm{t}+15}{\mathrm{e}^{\mathrm{t}}} \mathrm{dt}, x \in \mathbf{R}$. Then the numbers of local maximum and local minimum points of $f$,...

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Let $\alpha, \beta, \gamma$ and $\delta$ be the coefficients of $x^7, x^5, x^3$ and $x$ respectively in the expansion of...

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Let $\mathrm{P}(4,4 \sqrt{3})$ be a point on the parabola $y^2=4 \mathrm{ax}$ and PQ be a focal chord of the parabola....

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The number of non-empty equivalence relations on the set {1,2,3} is :

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If $\lim _{x \rightarrow \infty}\left(\left(\frac{\mathrm{e}}{1-\mathrm{e}}\right)\left(\frac{1}{\mathrm{e}}-\frac{x}{1+x}\right)\right)^x=\alpha$, then the value of $\frac{\log _{\mathrm{e}} \alpha}{1+\log _{\mathrm{e}} \alpha}$ equals :

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If $A$ and $B$ are two events such that $P(A \cap B)=0.1$, and $P(A \mid B)$ and $P(B \mid A)$...

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The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view...

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20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration...

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The complex of $\mathrm{Ni}^{2+}$ ion and dimethyl glyoxime contains $\_\_\_\_$ number of Hydrogen $(\mathrm{H})$ atoms.

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Niobium (Nb) and ruthenium (Ru) have "x" and "y" number of electrons in their respective 4 d orbitals. The value...

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The compound with molecular formula $\mathrm{C}_6 \mathrm{H}_6$, which gives only one monobromo derivative and takes up four moles of hydrogen...

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Consider the following cases of standard enthalpy of reaction ( $\Delta \mathrm{H}_{\mathrm{r}}^{\circ}$ in $\mathrm{kJmol}^{-1}$ ) $$ \begin{aligned} & \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})+\frac{7}{2}...

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The species which does not undergo disproportionation reaction is :

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The maximum number of RBr producing 2-methylbutane by above sequence of reactions is _______ . (Consider the structural isomers only)

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When sec-butyl cyclohexane reacts with bromine in the presence of sunlight, the major product is :

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Given below are two statements : Statement (I) : An element in the extreme left of the periodic table forms...

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The correct order of the following complexes in terms of their crystal field stabilization energies is :

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The most stable carbocation from the following is :

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The alkane from below having two secondary hydrogens is :

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Residue (A) + HCl (dil) → Compound (B) Structure of residue (A) and compound (B) formed respectively is :

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Three conductors of same length having thermal conductivity $\mathrm{k}_1, \mathrm{k}_2$ and $\mathrm{k}_3$ are connected as shown in figure. Area of...

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Match the Compounds (List - I) with the appropriate Catalyst/Reagents (List - II) for their reduction into corresponding amines. Choose...

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A particle is projected at an angle of $30^{\circ}$ from horizontal at a speed of $60 \mathrm{~m} / \mathrm{s}$. The...

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In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to...

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A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of...

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Given is a thin convex lens of glass (refractive index $\mu$) and each side having radius of curvature R. One...

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A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is...

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A small point of mass $m$ is placed at a distance 2 R from the centre ' $O$ ' of...

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A bob of mass $m$ is suspended at a point $O$ by a light string of length $l$ and left...

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Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance $R_p=1 \Omega$ as shown in...

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A uniform circular disc of radius 'R' and mass 'M' is rotating about an axis perpendicular to its plane and...

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Which one of the following is the correct dimensional formula for the capacitance in F M, L, T and C...

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Given below are two statements : Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller...

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A force $\overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i}-2 \hat{j}-\hat{k}$. What will be...

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The torque due to the force $(2 \hat{i}+\hat{j}+2 \hat{k})$ about the origin, acting on a particle whose position vector 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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A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in...

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A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different...

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Given below are two statements : Statement I: In a vernier callipers, one vernier scale division is always smaller than...

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An amount of ice of mass $10^{-3} \mathrm{~kg}$ and temperature $-10^{\circ} \mathrm{C}$ is transformed to vapour of temperature $110^{\circ} \mathrm{C}$...

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An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10...

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Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature...

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An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then...

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A parallel-plate capacitor of capacitance 40 $\mu$ F is connected to a 100 V power supply. Now the intermediate space...

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A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown...

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Which of the following resistivity $(\rho )$ v/s temperature (T) curves is most suitable to be used in wire bound...

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A line charge of length $\frac{\mathrm{a}}{2}$ is kept at the center of an edge BC of a cube ABCDEFGH having...

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An electron in the ground state of the hydrogen atom has the orbital radius of $5.3 \times {10^{ - 11}}\;{\rm{m}}$...

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Match List - I with List - II.

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If B is magnetic field and $\mu_0$ is permeability of free space, then the dimensions of $\left(B / \mu_0\right)$ is

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The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we...

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Which of the following circuits represents a forward biased diode?

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