Q JEE MAIN 2019

A compound ' $X$ ' on treatment with $\mathrm{Br}_2 / \mathrm{NaOH}$, provided $\mathrm{C}_3 \mathrm{H}_9 \mathrm{~N}$, which gives positive carbylamine test....

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Q JEE MAIN 2019

The major product of the following reaction is

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Q JEE Main 2019

The major product formed in the reaction given below will be

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Q JEE MAIN 2019

Benzene diazonium chloride on reaction with aniline in the presence of dilute hydrochloric acid gives :

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Q JEE MAIN 2019

The major product of the following reaction is :

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Q JEE MAIN 2019

In an experiment, brass and steel wires of length 1 m each with areas of cross section $1 \mathrm{~mm}^2$ are...

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Q JEE Main 2019

Let $z_1$ and $z_2$ be any two non-zero complex numbers such that $3\left|z_1\right|=4\left|z_2\right|$. If $z=\frac{3 z_1}{2 z_2}+\frac{2 z_2}{3 z_1}$ then

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Q JEE MAIN 2026

Let A be the focus of the parabola $y^2=8 x$. Let the line $y=m x+c$ intersect the parabola at two...

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Q JEE MAIN_2019

$$ \text { If } \int \frac{d x}{\left(x^2-2 x+10\right)^2}=A\left(\tan ^{-1}\left(\frac{x-1}{3}\right)+\frac{f(x)}{x^2-2 x+10}\right)+C $$ where C is a constant of integration, then...

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Q JEE MAIN_2019_

ABC is a triangular park with $\mathrm{AB}=\mathrm{AC}=100$ metres. A vertical tower is situated at the mid-point of $B C$. If...

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Q JEE MAIN_2019_

Let $f \sim R \rightarrow R$ be differentiable at $c \in R$ and $f(c)=$ 0. If $g(x)=|f(x)|$, then at $...

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Q JEE MAIN_2019_

If $y=y(x)$ is the solution of the differential equation $\frac{\mathrm{dt}}{\mathrm{dx}}=(\tan \mathrm{x}-\mathrm{y}) \sec ^2 \mathrm{x}, \mathrm{x} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, such that $...

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Q JEE MAIN_2019_

If $\alpha$ and $\beta$ are the roots of the quadratic equation, $x^2+x \sin \theta-2 \sin \theta=0, \quad \theta \in\left(0, \frac{\pi}{2}\right)$,...

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Q JEE MAIN_2019

Let $f(x)=e^x-x$ and $g(x)=x^2-x, \forall x \in R$. Then the set of all $x \in R$, where the function $...

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Q _ JEE MAIN_2019_

The sum $$ \frac{3 \times 1}{1^2}+\frac{5 \times\left(1^3+2^3\right)}{1^2+2^2}+\frac{7 \times\left(1^3+2^3+3^3\right)}{1^2+2^2+3^2}+\ldots $$ upto $10^{\text {th }}$ term, is.

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Q JEE MAIN_2019

If the coefficients of $x^2$ and $x^3$ are both zero, in the expansion of the expression $...

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Q JEE MAIN_2019_

Let $f(x)=x^2, x \in R$. For any $A \subseteq R$, define $g(A)=\{x \in R: f(x) \in A\}$. If $S=[0,4]$, then...

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Q JEE MAIN_2019_

If $Q(0,-1,-3)$ is the image of the point $P$ in the plane $3 x-y+4 z=2$ and $R$ is the point...

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Q JEE MAIN_2019_

If $a_1, a_2, a_3, \ldots \ldots .$, an are in A.P. and $a_1+a_4+a_7+ a_{16}+a_{16}=114$, then $a_1+a_6+a_{11}+a_{16}$ is equal to:

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Q JEE MAIN_2019_

The region represented by $|x-y| \leq 2$ and $|x+y| \leq 2$ is bounded by a:

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Q JEE MAIN_2019_

If the circles $x^2+y^2+5 K x+2 y+K=0$ and $2\left(x^2+\right. \left.y^2\right)+2 K x+3 y-1=0,(K \in R)$, intersect at the points $P$...

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Q Statistics_ JEE MAIN_2019_

If for some $x \in R$, the frequency distribution of the marks obtained by 20 students in a test is:

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Q JEE MAIN_2019_

Assume that each born child is equally likely to be a boy or a girl. If two families have two...

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Q JEE MAIN_2019_

If the system of linear equations $$ \begin{aligned} & x+y+z=5 \\ & x+2 y+2 z=6 \\ & x+3 y+\lambda z=\mu,(\lambda,...

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Q JEE MAIN_2019_

Let $A(3,0-1), B(2,10,6)$ and $C(1,2,1)$ be the vertices of a triangle and $M$ be the mid point of $A C$....

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Q JEE MAIN_2019_

If the line $x-2 y=12$ is tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at the point $\left(3, \frac{-9}{2}\right)$, then the length of...

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Q JEE MAIN_2019_

If a directrix of a hyperbola centred at the origin and passing through the point $(4,-2 \sqrt{3})$ is $...

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Q JEE MAIN_2019

If $\lim _{x \rightarrow 1} \frac{x^4-1}{x-1}=\lim _{x \rightarrow *} \frac{x^3-k^3}{x^2-k^2}$, then $k$ is

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Q JEE MAIN_2019

Which one of the following Boolean expressions is a tautology ?

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Q JEE MAIN_2019_

The line x = y touches a circle at the point (1, 1). If the circle also passes through the...

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Q JEE MAIN_2019_

$\lim _{n \rightarrow \infty}\left(\frac{(n+1)^{1 / 3}}{n^{4 / 3}}+\frac{(n+2)^{1 / 3}}{n^{1 / 3}}+\ldots . .+\frac{(2 n)^{1 / 3}}{n^{4 / 3}}\right)$ is...

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Q JEE MAIN 2019

Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{8}$ respectively. If all hit at the...

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Q JEE MAIN 2019

If the function $f: R-\{1,-1\} \rightarrow A$ defined by $f(x)=\frac{x^2}{1-x^2}$, is surjective, then $A$ is equal to :

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Q JEE MAIN 2019

Let the sum of the first $n$ terms of a nonconstant A.P., $a_1, a_2, a_3, \ldots$. be $50 n+\frac{n(n-7)}{2} A$,...

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Q JEE MAIN 2019

The solution of the differential equation $x \frac{d y}{d x}+2 y=x^2(x \neq 0)$ with $y(1)=1$, is :

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Q JEE MAIN 2019

The value of $\int_0^{\pi / 2} \frac{\sin ^3 x}{\sin x+\cos x} d x$ is :

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Q JEE MAIN 2019

Slope of a line passing through P(2, 3) and intersecting the line, x + y = 7 at a distance...

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Q JEE MAIN 2019

A committee of 11 members is to be formed from 8 males and 5 females. If m is the number...

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Q JEE MAIN 2019

The value of $\cos ^2 10^{\circ}-\cos 10^{\circ} \cos 50^{\circ}+\cos ^2 50^{\circ}$ is:

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Q JEE MAIN 2019

Let $\alpha$ and $\beta$ be the roots of the equation $x^2+x+1=0$. Then for $y \neq 0$ in $...

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Q JEE MAIN 2019

If the line $y=m x+7 \sqrt{3}$ is normal to the hyperbola $\frac{x^2}{24}-\frac{y^2}{18}=1$, then a value of $m$ is :

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Q JEE MAIN_2019_

If the length of the perpendicular from the point ( $\beta$, $0, \beta)(\beta \neq 0)$ to the line, $\frac{x}{1}=\frac{y-1}{0}=\frac{z+1}{-1}$ is...

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Q _ JEE MAIN_2019_

$$ \text { If } f(x)=\left\{\begin{array}{cc} \frac{\sin (p+1) x+\sin x}{x} & , x0 \end{array}\right. $$ is continuous at $x=0$, then...

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Q JEE MAIN 2019

The area (in sq. units) of the region $A=\left\{(x, y): x^2 \leq y \leq x+2\right\}$ is :

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Q JEE MAIN_2019_

If $...

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Q JEE MAIN 2019

Let f(x) = 15 – |x – 10|; x $\in$ R. Then the set of all values of x, at...

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Q JEE MAIN 2019

Let $S=\left\{\theta \in[-2 \pi, 2 \pi] ; 2 \cos ^2 \theta+3 \sin \theta=0\right\}$ . Then the sum of the elements...

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Q JEE MAIN_2019_

The value of $\int_0^{2 \pi}[\sin 2 x(1+\cos 3 x)] d x$, where $[t]$ denotes the greatest integer function, is:

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Q JEE MAIN_2019_

The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9...

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Q JEE MAIN 2019

$...

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Q JEE MAIN_2019

If $a>0$ and $z=\frac{(1+i)^2}{a-i}$, has magnitude $\sqrt{\frac{2}{5}}$, then $\bar{z}$ is equal to:

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Q JEE MAIN 2019

Let $\sum_{k=1}^{10} f(a+k)=16\left(2^{10}-1\right)$ , where the function f satisfies f(x + y) = f(x) f(y) for all natural numbers x,...

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Q JEE MAIN_2019_

All the pairs ( $x, y$ ) that satisfy the inequality $...

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Q JEE MAIN 2019

Let $\vec{\alpha}=3 \hat{i}+\hat{j}$ and $\vec{\beta}=2 \hat{i}-\hat{j}+3 \hat{k}$. If $\vec{\beta}=\vec{\beta}_1-\vec{\beta}_2$ , where $\vec{\beta}_1$ is parallel to $\vec{\alpha}$ and $\vec{\beta}_2$ is perpendicular...

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Q JEE MAIN 2019

All the points in the set $\mathrm{S}=\left\{\frac{\alpha+\mathrm{i}}{\alpha-\mathrm{i}}: \alpha \in \mathrm{R}\right\}(\mathrm{i}=\sqrt{-1})$ lie on a :

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Q JEE MAIN 2019

If the function f defined on $\left(\frac{\pi}{6}, \frac{\pi}{3}\right)$ by $...

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Q JEE MAIN 2019

If one end of a focal chord of the parabola, $y^2$ = 16x is at (1, 4), then the length...

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Q JEE MAIN 2019

The integral $\int \sec ^{2 / 3} x \operatorname{cosec}^{4 / 3}$ is equal to : (Here C is a constant...

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Q JEE MAIN 2019

If the fourth term in the Binomial expansion of $\left(\frac{2}{x}+x^{\log _8 x}\right)^6$ (x > 0) is 20 $\times 8^7$ ,...

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Q JEE MAIN 2019

If the standard deviation of the numbers –1, 0, 1, k is $\sqrt{5}$ where k > 0, then k is...

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Q JEE MAIN 2019

If f(x) is a non-zero polynomial of degree four, having local extreme points at x = –1, 0, 1; then...

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Q JEE MAIN 2019

If a tangent to the circle $x^2+y^2=1$ intersects the coordinate axes at distinct points P and Q, then the locus...

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Q JEE MAIN 2019

If the line, $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{4}$ meets the plane, x + 2y + 3z = 15 at a point P, then the...

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Q JEE MAIN 2019

Let p, q$\in$ R. If $2-\sqrt{3}$ is a root of the quadratic equation, $x^2+p x+q=0$, then :

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Q JEE MAIN 2019

The organic compound that gives following qualitative analysis is

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Q JEE MAIN 2019

The correct sequence of amino acids present in the tripeptide given below is : The given tripeptide contains.

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Q JEE MAIN 2019

The major product of the following reaction is

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Q JEE MAIN 2019

Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?

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Q JEE MAIN 2019

For the following reaction, the mass of water produced from 445 g of $\mathrm{C}_{57} \mathrm{H}_{110} \mathrm{O}_6$ is: $$ 2 \mathrm{C}_{57}...

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Q JEE MAIN 2019

The degenerate orbitals of $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}$ are

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Q JEE MAIN 2019

The major product of the following reaction is:

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Q JEE MAIN 2019

The increasing basicity order of the following compounds is:

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Q JEE MAIN 2019

For the reaction, $2 \mathrm{~A}+\mathrm{B} \rightarrow$ products, when the concentration of A and B both were doubled, the rate of...

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Q JEE MAIN 2019

The aerosol is a kind of colloid in which

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Q JEE MAIN 2019

The major product formed in the following reaction is:

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Q JEE MAIN 2019

The complex that has highest crystal field splitting energy (Δ), is

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Q JEE MAIN 2019

Homoleptic octahedral complexes of a metal ion ' $\mathrm{M}^{3+1}$ with three monodentate ligands $\mathrm{L}_1, \mathrm{~L}_2$ and $\mathrm{L}_3$ absorb wavelengths in...

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Q JEE MAIN 2019

The correct statement regarding the given Ellingham diagram is

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Q JEE MAIN 2019

At $100^{\circ} \mathrm{C}$, copper $(\mathrm{Cu})$ has FCC unit cell structure with cell edge length of $\mathrm{x} \AA$. What is the...

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Q JEE MAIN 2019

Aniline dissolved in dilute HCl is reacted with sodium nitrite at 0ºC. This solution was added dropwise to a solution...

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Q JEE MAIN 2019

The temporary hardness of water is due to

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Q JEE MAIN 2019

The correct IUPAC name of the following compound is

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Q JEE MAIN 2019

Which of the following statements is not true about sucrose?

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Q JEE MAIN 2019

If the line $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}$ intersects the plane $2 x+3 y-z+13=0$ at a point $P$ and the plane $3 x+y+4 z=16$...

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Q JEE MAIN 2019

If $m$ is the minimum value of $k$ for which the function $f(x)=x \sqrt{k x-x^2}$ is increasing in the interval...

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Q JEE MAIN 2019

For $x \in R$, let $[x]$ denote the greatest integer $\leq x$, then the sum of the series $...

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Q JEE MAIN 2019

If $B=\left[\begin{array}{ccc}5 & 2 \alpha & 1 \\ 0 & 2 & 1\end{array}\right]$ is the inverse of a $...

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Q JEE MAIN 2019

If $\alpha$ and $\beta$ are the roots of the equation $375 x^2-25 x-2=0$, then $...

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Q JEE MAIN 2019

If $A$ is a symmetric matrix and $B$ is a skew-symmetric matrix such that $...

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Q JEE MAIN 2019

The correct statement among the following is

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Q JEE MAIN 2019

The major products of the following reaction are

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Enthalpy of sublimation of iodine is $24 \mathrm{cal} \mathrm{g}^{-1}$ at $200^{\circ} \mathrm{C}$. If specific heat of $\mathrm{I}_2(\mathrm{~s})$ and $\mathrm{I}_2(\mathrm{vap})$ are...

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Q JEE MAIN 2019

The correct set of species responsible for the photochemical smog is :

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Q JEE MAIN 2019

Peptization is a

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Which of the following is a thermosetting polymer?

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Q JEE MAIN 2019

The idea of froth floatation method came from a person X and this method is related to the process Y...

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Q JEE MAIN 2019

An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1...

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What is the molar solubility of $\mathrm{Al}(\mathrm{OH})_3$ in 0.2 M NaOH solution? Given that, solubility product of $\mathrm{Al}(\mathrm{OH})_3=2.4 \times 10^{-2}$

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Q JEE MAIN 2019

The group number, number of valence electrons, and valency of an element with atomic number 15, respectively, are

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Q JEE MAIN 2019

The mole fraction of a solvent in aqueous solution of a solute is 0.8 . The molality (in $\mathrm{mol} \mathrm{kg}-1$...

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Q JEE MAIN 2019

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Q JEE MAIN 2019

The basic structural unit of feldspar, zeolites, mica, and asbestos is

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Q JEE MAIN 2019

Let $z \in C$ with $\operatorname{lm}(z)=10$ and it satisfies $\frac{2 z-n}{2 z+n}=2 i-1$ for some natural number $n$. Then :

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Q JEE MAIN_2019_

Match the refining methods (Column I) with metals (Column II). Column I Column II (Refining methods) (Metals) (I) Liquation (a)...

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Q JEE MAIN 2019

An organic compound ' A ' is oxidized with $\mathrm{Na}_2 \mathrm{O}_2$ followed by boiling with $\mathrm{HNO}_3$. The resultant solution is...

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Q JEE MAIN 2019

A value of $\alpha$ such that $$ \int_\alpha^{\alpha+1} \frac{\mathrm{dx}}{(\mathrm{x}+\alpha)(\mathrm{x}+\alpha+1)}=\log _{\mathrm{e}}\left(\frac{9}{8}\right) \text { is: } $$

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Q JEE MAIN 2019

Let A, B and C be sets such that φ ≠ A ∩ B ⊆ C. Then which of the...

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Q JEE MAIN 2019

The major product of the following reaction is

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A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice),...

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A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through...

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The term independent of $x$ in the expansion of $\left(\frac{1}{60}-\frac{x^8}{81}\right) \cdot\left(2 x^2-\frac{3}{x^2}\right)^6$ is equal to :

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Q JEE MAIN 2019

$\lim _{x \rightarrow 0} \frac{x+2 \sin x}{\sqrt{x^2+2 \sin x+1}-\sqrt{\sin ^2 x-x+1}}$ is :

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Q JEE MAIN 2019

If $\alpha, \beta$ and $\gamma$ are three consecutive terms of a non-constant G.P. such that the equations $...

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Q JEE MAIN_2019_

Three complexes, $\quad\left[\mathrm{CaCl}\left(\mathrm{NH}_3\right)_5\right]^{2+}(\mathrm{I})$, $\left[\mathrm{Ca}\left(\mathrm{NH}_3\right)_5 \mathrm{H}_2 \mathrm{O}\right]^{3+}(\mathrm{II})$ and $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ (III) absorb light in the visible region. The correct order of the...

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At 300 K and 1 atmospheric pressure, 10 mL of a hydrocarbon required 55 mL of $\mathrm{O}_2$ for complete combustion,...

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Q JEE MAIN_2019_

The synonym for water gas when used in the production of methanol is :

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A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (–1,...

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A gas undergoes physical adsorption on a surface and follows the given Freundlich adsorption isotherm equation $\frac{\mathrm{x}}{\mathrm{m}}=\mathrm{kp}^{0.5}$ Adsorption of the...

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Q JEE MAIN 2019

If ${ }^{20} \mathrm{C}_1+\left(2^2\right)^{20} \mathrm{C}_2+\left(3^2\right)^{20} \mathrm{C}_3+\ldots \ldots . .+\left(20^2\right)^{20} \mathrm{C}_{20}=\mathrm{A}\left(2^\beta\right)$, then the ordered pair $(\mathrm{A}, \beta)$ is equal to:

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At room temperature, a dilute solution of urea is prepared by dissolving 0.60 g of urea in 360 g of...

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Q JEE MAIN 2019

Let $\alpha \in(0, \pi / 2)$ be fixed. If the integral $...

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Q JEE MAIN_2019_

The regions of the atmosphere, where clouds form and where we live, respectively, are :

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Q JEE MAIN 2019

The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines

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Let α ∈ R and the three vectors

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Let S be the set of all α ∈ R such that the equation, cos2x + αsinx = 2α –...

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Q JEE MAIN 2019

A plane which bisects the angle between the two given planes 2x – y + 2z – 4 = 0...

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Q JEE MAIN 2019

An example of a disproportionation reaction is

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The general solution of the differential equation $\left(y^2-x^3\right) d x-x y d y=0(x \neq 0)$ is : (where c is...

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Q JEE MAIN 2019

Complete removal of both the axial ligands (along the z-axis) from an octahedral complex leads to which of the following...

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Q JEE MAIN 2019

The electrons are more likely to be found

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Q JEE MAIN 2019

The Boolean expression ~ (p ⇒ (~ q)) is equivalent to

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Q JEE-MAIN 2019

The Boolean expression $((p \wedge q) \vee(p \vee \sim q)) \wedge(\sim p \wedge \sim q)$ is equivalent to

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Q JEE-MAIN 2019

Let $S_k=\frac{1+2+3+\ldots .+k}{k}$. If $\mathrm{S}_1^2+\mathrm{S}_2^2+\ldots \ldots+\mathrm{S}_{10}^2=\frac{5}{12} \mathrm{~A}$, then A is equal to

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Q JEE MAIN 2019

A value of θ ∈ (0, π/3), for which

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Q JEE-MAIN 2019

The integral $\int \cos \left(\log _e x\right) d x$ is equal to (where $C$ is a constant of integration)

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Q JEE MAIN 2019

If [x] denotes the greatest integer ≤ x, then the system of linear equations [sinθ]x + [– cosθ]y = 0...

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Q JEE-MAIN 2019

Let $S$ be the set of all points in $(-\pi, \pi)$ at which the function, $f(x)=\min \{\sin x, \cos x\}$...

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Q JEE MAIN 2019

The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be...

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Q JEE MAINN 2019

If $a_1, a_2, a_3, \ldots .$. are in A.P. such that $a_1+a_7+a_{16}=40$, then the sum of the first 15 terms...

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Q JEE MAIN 2019

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team...

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If the vertices of a hyperbola be at (–2, 0) and (2, 0) and one of its foci be at...

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Q JEE MAIN 2019

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Q JEE MAIN 2019

The maximum area (in sq. units) of a rectangle having its base on the $x$-axis and its other two vertices...

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Q JEE MAIN 2019

If $\frac{z-\alpha}{z+\alpha}(a \in R)$ is a purely imaginary number and $|z|=2$, then a value of $\alpha$ is

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Q JEE-MAIN 2019

If the straight line, $2 x-3 y+17=0$ is perpendicular to the line passing through the points $(7,17)$ and $(15, \beta)$,...

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Q JEE-MAIN 2019

Considering only the principal values of inverse functions, the set $A=\left\{x \geq 0 ; \tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\right\}$

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Q JEE-MAIN 2019

If $\lambda$ be the ratio of the roots of the quadratic equation in $x, 3 m^2 x^2+m(m-4) x+2=0$, then the...

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The sum of the distinct real values of $\mu$, for which the vectors, $\mu \hat{j}+\hat{j}+\hat{k}, \hat{i}+\mu \hat{j}+\hat{k}, \hat{i}+\hat{j}+\mu \hat{k}$ are...

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Q JEE-MAIN 2019

Let $C 1$ and $C 2$ be the centres of the circles $x^2+y^2-2 x-2 y-2=0$ and $x^2+y^2-6 x-6 y+14=0$ respectively....

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Q JEE-MAIN 2019

The area (in sq. units) of the region bounded by the parabola, $y=x^2+2$ and the lines, $y=x+1, x=0$ and $x=3$,...

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Q JEE MAIN 2019

Let $y=y(x)$ be the solution of the differential equation, $x \frac{d y}{d x}+y=x \log _e x x,(x>1)$. If $...

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Q JEE-MAIN 2019

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is

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A tetrahedron has vertices $P(1,2,1), Q(2,1,3), R(-1,1,2)$ and $O(0,0,0)$. The angle between the faces $O P Q$ and $...

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The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first...

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The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7,9...

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If a variable line, $3 x+4 y-\lambda=0$ is such that the two circles $x^2+y^2-2 x-2 y+1=0$ and $x^2+y^2-18 x-2 y+78=0$...

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During the change of $\mathrm{O}_2$ to $\mathrm{O}_2^{-}$, the incoming electron goes to the orbital:

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The increasing order of the $\mathrm{pK}_{\mathrm{b}}$ of the following compound is :

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In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the...

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Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x +...

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Consider three boxes, each containing 10 balls labelled 1, 2, ...,10. Suppose one ball is randomly drawn from each of...

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The increasing order of the reactivity of the following compounds towards electrophilic aromatic substitution reactions is :

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The metal that gives hydrogen gas upon treatment with both acid as well as base is

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The perpendicular distance from the origin to the plane containing the two lines, $\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5}{7}$ and $\frac{x-1}{1}=\frac{y-4}{4}=\frac{z+4}{7}$ is

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An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the...

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$$ \text { The derivative of } \tan ^{-1}\left(\frac{\sin x-\cos x}{\sin x+\cos x}\right) \text {, with respect to } \frac{x}{2}...

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Q JEE MAIN 2019

Glucose and Galactose are having identical configuration in all the positions except position

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Let $f$ and $g$ be continuous functions on $[0$, a $]$ such that $f(x)=f(a-x)$ and $g(x)+g(a-x)=4$, then $...

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The area of the region A = {(x, y) : 0 ≤ y ≤ x|x| + 1 and –1 ≤...

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The correct order of catenation is:

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An element has a face-centred cubic (fcc) structure with a cell edge of a. The distance between the centres of...

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For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that...

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A ratio of the 5 th term from the beginning to the $5^{\text {th }}$ term from the end in...

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A data consists of $n$ observations $x_1, x_2 \ldots, x_n$. If $\sum_{i=1}^n\left(x_i+1\right)^2=9 n$ and $\sum_{i=1}^n\left(x_i-1\right)^2=5 n$, then the standard deviation...

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Q JEE MAIN 2019

The complex ion that will lose its crystal field stabilization energy upon oxidation of its metal to +3 state is:

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An ellipse, with foci at (0, 2) and (0, –2) and minor axis of length 4, passes through which of...

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The equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane containing the straight lines $\frac{x}{3}=\frac{y}{4}=\frac{z}{2}$...

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Q JEE-MAIN 2019

The maximum value of $3 \cos \theta+5 \sin \left(\theta-\frac{\pi}{6}\right)$ for any real value of $\theta$ is

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Which of the following statements is not true about RNA

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50 mL of 0.5 M oxalic acid is needed to neutralize 25 mL of sodium hydroxide solution. The amount of...

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A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length...

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In the following skew conformation of ethane, H′ – C – C – H″ dihedral angle is

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Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of Y....

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The major product(s) obtained in the following reaction is/are

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The element with Z = 120 (not yet discovered) will be an/a

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If the circles $x^2+y^2-16 x-20 y+164=r^2$ and $(x-4)^2+(y-7)^2=36$ intersect at two distinct points, then

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$$ \text { Which one of the following is likely to give a precipitate with } \mathrm{AgNO}_3 \text { solution?...

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Iodine reacts with concentrated HNO3 to yield Y along with other products. The oxidation state of iodine in Y, is

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Let $\mathrm{a}, \mathrm{b}$ and c be the $7^{\text {th }}, 11^{\text {th }}$ and $13^{\text {th }}$ terms respectively of...

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The correct sequence of thermal stability of the following carbonates is :

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The coordination numbers of Co and Al in $\left[\mathrm{Co}(\mathrm{Cl})(\mathrm{en})_2\right] \mathrm{Cl}$ and $\mathrm{K}_3\left[\mathrm{Al}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]$, respectively, are (en $=$ ethane -1 ,...

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The number of all possible positive integral values of $\alpha$ for which the roots of the quadratic equation, $...

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The major product of the following reaction is

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If $x=3$ tan $t$ and $y=3$ sect, then the value of $\frac{d^2 y}{d x^2}$ at $t=\frac{\pi}{4}$, is

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Consider the following reactions :

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Among the following compounds most basic amino acid is

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$ \int_0^{\pi / 3} \frac{\tan \theta}{\sqrt{2 \mathrm{ksec} \theta}} \mathrm{~d} \theta=1-\frac{1}{\sqrt{2}},(\mathrm{k}>0) $ then the value of $k$ is

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For a diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation...

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Which of the given statements is INCORRECT about glycogen?

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Let $\mathrm{A}(4,-4)$ and $\mathrm{B}(9,6)$ be points on the parabola, $\mathrm{y}^2=4 \mathrm{x}$. Let C be chosen on the arc AOB of...

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The correct statement is

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The major product of the following reaction

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But-2-ene on reaction with alkaline $\mathrm{KMnO}_4$ at elevated temperature followed by acidification will give :

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In the following reactions, products A and B are

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For each $x \in R$, let $[x]$ be the greatest integer less than or equal to $x$. Then $...

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The major product of the following addition reaction is

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Thermal decomposition of a Mn compound $(\mathrm{X})$ at 513 K results in compound $\mathrm{Y}, \mathrm{MnO}_2$ and a gaseous product. $\mathrm{MnO}_2$...

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Among the following four aromatic compounds, which one will have the lowest melting point?

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The coefficient of $t^4$ in the expansion of $\left(\frac{1-t^6}{1-t}\right)^3$ is

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The transfer characteristic curve of a transistor, having input and output resistance $100 \Omega$ and $100 \mathrm{k} \Omega$ respectively, is...

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Among the following, the energy of 2s orbital is lowest in:

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Let $A=\{x \in R: x$ is not a positive integer $\}$. Define a function $f: A \rightarrow R$ as $...

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What will be the major product when m -cresol is reacted with propargyl bromide ( $\mathrm{HC} \equiv \mathrm{C}-\mathrm{CH}_2 \mathrm{Br}$ )...

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A person of mass $M$ is, sitting on a swing of length $L$ and swinging with an angular amplitude $\theta_0$....

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If $...

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Heating of 2-chloro-1-phenylbutane with EtOK/ EtOH gives $X$ as the major product. Reaction of $X$ with $\mathrm{Hg}(\mathrm{OAc})_2 / \mathrm{H}_2 \mathrm{O}$...

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Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the...

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Let $z_0$ be a root of the quadratic equation, $x^2+x+1=0$. If $z=3+6 i z_0^{81}-3 i z_0^{93}$, then arg $z$ is...

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In the Hall-Heroult process, aluminium is formed at the cathode. The cathode is made out of

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The temporary hardness of a water sample is due to compound X. Boiling this sample converts X to compound Y....

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When M1 gram of ice at $-10^{\circ} \mathrm{C}$ (specific heat $=0.5 \mathrm{cal} \mathrm{g}^{-1 \circ} \mathrm{C}^{-1}$ ) is added to $\mathrm{M}_2$...

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If $x=\sin ^{-1}(\sin 10)$ and $y=\cos ^{-1}(\cos 10)$, then $y-x$ is equal to

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Let $f$ be a differentiable function from $R$ to $R$ such that $|f(x)-f(y)| \leq 2|x-y|^{\frac{3}{2}}$, for all $...

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A man (mass $=50 \mathrm{~kg}$ ) and his son (mass $=20 \mathrm{~kg}$ ) are standing on a frictionless surface facing...

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The molar solubility of $\mathrm{Cd}(\mathrm{OH})_2$ is $1.84 \times 10^{-5} \mathrm{M}$ in water. The expected solubility of $\mathrm{Cd}(\mathrm{OH})_2$ in a buffer...

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The IUPAC name for the following compound is

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A progressive wave travelling along the positive $x$-direction is represented by $y(x, t)=A \sin (k x-\omega t+\phi)$. Its snapshot at...

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Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the...

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In comparison to boron, berylium has

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The logical statement $[\sim(\sim p \vee q) \vee(p \wedge r)] \wedge(\sim q \wedge r)$ is equivalent to

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If the system of linear equations x – 4y + 7z = g 3y – 5z = h – 2x...

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The ratio of number of atoms present in a simple cubic, body centered cubic and face centered cubic structure are,...

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If $0 \leq x

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A solution is prepared by dissolving 0.6 g of urea (molar mass $=60 \mathrm{~g} \mathrm{~mol}^{-1}$ ) and 1.8 g of...

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The correct name of the following polymer is

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If the lines x = ay + b, z = cy + d and x = a′z + b′, y...

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$\mathrm{NO}_2$ required for a reaction is produced by the decomposition of $\mathrm{N}_2 \mathrm{O}_5$ in $\mathrm{CCl}_4$ as per the equation, $...

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Let $f:[0,1] \rightarrow R$ be such that $f(x y)=f(x) \cdot f(y)$, for all $x, y \in[0,1]$, and $f(0) \neq 0$....

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The INCORRECT match in the following is

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The correct sequence of amino acids present in the tripeptide given below is : The given tripeptide contains.

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Which of the following combination of statements is true regarding the interpretation of the atomic orbitals? (a) An electron in...

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Which of the following compounds is not aromatic?

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The primary pollutant that leads to photochemical smog is

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For the following reaction, the mass of water produced from 445 g of $\mathrm{C}_{57} \mathrm{H}_{110} \mathrm{O}_6$ is: $...

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The major product of the following reaction is:

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The increasing basicity order of the following compounds is:

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For the reaction, $2 A+B \rightarrow$ products, when the concentration of $A$ and $B$ both were doubled, the rate of...

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Good reducing nature of $\mathrm{H}_3 \mathrm{PO}_2$ is attributed to the presence of:

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The major product formed in the following reaction is:

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The complex that has highest crystal field splitting energy ( $\Delta$ ), is

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An electromagnetic wave is represented by the electric field $\overrightarrow{\mathbf{E}}=\mathrm{E}_0 \hat{n} \sin [\omega t+(6 y-8 z)]$. Taking unit vectors in...

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$$ \text { The correct order of the oxidation states of nitrogen in NO, N2O, NO2, and N2O3 is }...

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A magnetic compass needle oscillates 30 times per minute at a place where the dip is $45^{\circ}$, and 40 times...

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The element having greatest difference between its first and second ionization energies, is

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A point dipole $\hat{p}=-p_0 \hat{x}$ is kept at the origin. The potential and electric field due to this dipole on...

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A galvanometer of resistance $100 \Omega$ has 50 divisions on its scale and has sensitivity of $20 \mu \mathrm{~A} /$...

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For a reaction, $\mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_3(\mathrm{~g})$; Identify dihydrogen $\left(\mathrm{H}_2\right)$ as a limiting reagent in the following reaction mixtures.

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Major products of the following reaction are :

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In a double slit experiment, when a thin film of thickness $t$ having refractive index $\mu$ is introduced in front...

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The species that can have a trans-isomer is : (en = ethane-1, 2-diamine, ox = oxalate)

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Q JEE MAIN 2019

Excessive release of $\mathrm{CO}_2$ into the atmosphere results in

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The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network...

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The major product of the following reaction is :

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Among the following, the INCORRECT statement about colloids is

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A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target...

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Increasing rate of $\mathrm{S}_{\mathrm{N}} 1$ reaction in the following compounds is:

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In which one of the following equilibria, $\mathrm{K}_{\mathrm{P}} \neq \mathrm{K}_{\mathrm{C}}$ ?

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Among the following, the molecule expected to be stabilized by anion formation is $\mathrm{C}_2, \mathrm{O}_2, \mathrm{NO}, \mathrm{F}_2$

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25 g of an unknown hydrocarbon upon burning produces 88 g of $\mathrm{CO}_2$ and 9 g of $\mathrm{H}_2 \mathrm{O}$. This...

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A process will be spontaneous at all temperatures if

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The value of numerical aperture of the objective lens of a microscope is 1.25. If light of wavelength 5000 Å...

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Ethylamine $\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{NH}_2\right)$ can be obtained from Nethylphthalimide on treatment with:

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The major product of the following reaction

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An ‘Assertion’ and a ‘Reason’ are given below. Choose the correct answer from the following options : Assertion (A) :...

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The major product of the following reaction is

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The alloy used in the construction of aircrafts is :

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Q JEE MAIN_2019_

The isoelectronic set of ions is :

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Consider the van der Waals constants, a and b, for the following gases. Which gas is expected to have the...

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The set of all values of $\lambda$ for which the system of linear equations $$ \begin{aligned} & x-2 y-2 z=\lambda...

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In the Hall-Heroult process, aluminium is formed at the cathode. The cathode is made out of

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Consider the hydrated ions of $\mathrm{Ti}^{2+}, \mathrm{V}^{2+}, \mathrm{Ti}^{3+}$, and $\mathrm{Sc}^{3+}$. The correct order of their spin-only magnetic moments is i.

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Decomposition of X exhibits a rate constant of 0.05 g/year. How many years are required for the decomposition of 5...

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The total number of irrational terms in the binomial expansion of $\left(7^{1 / 5}-3^{1 / 10}\right)^{60}$ is :

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The major product of the following reaction is :

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if the sum of the first 15 terms of the series $\left(\frac{3}{4}\right)^3+\left(1 \frac{1}{2}\right)^3+\left(2 \frac{1}{4}\right)^3+3^3+\left(3 \frac{3}{4}\right)^3+\ldots$. is equal to $225 k$,...

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Q JEE MAIN 2019

The compound used in the treatment of lead poisoning is :

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The correct statement regarding the given Ellingham diagram is

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The standard electrode potential $E^{\circ}$ and its temperature coefficient $\left(\frac{d E^{\circ}}{d T}\right)$ for a cell are $2 V$ and $...

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$\lim _{x \rightarrow 1} \frac{\sqrt{\pi}-\sqrt{2 \sin ^{-1} x}}{\sqrt{1-x}}$ is equal to :

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A bacterial infection in an internal wound grows as $\mathrm{N}^{\prime}(\mathrm{t})=\mathrm{N}_0 \exp (\mathrm{t})$, where the time t is in hours. A...

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Q JEE-MAIN 2019

Two solids dissociate as follows $\begin{aligned} & \mathrm{A}(\mathrm{s}) \rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g}) ; \mathrm{K}_{\mathrm{P}_1}=\mathrm{x} \mathrm{atm}^2 \\ & \mathrm{D}(\mathrm{s}) \rightleftharpoons \mathrm{C}(\mathrm{g})+\mathrm{E}(\mathrm{g}) ; \mathrm{K}_{\mathrm{P}_2}=\mathrm{yatm}^2\end{aligned}$...

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Q JEE MAIN 2019

At $100^{\circ} \mathrm{C}$, copper $(\mathrm{Cu})$ has FCC unit cell structure with cell edge length of $\mathrm{x} \AA$. What is the...

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The decreasing order of electrical conductivity of the following aqueous solutions is: 0.1 M Formic acid (A), 0.1 M Acetic...

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Amylopectin is composed of

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If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes...

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Q JEE-MAIN 2019

The increasing order of reactivity of the following compounds towards reaction with alkyl halides directly is

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Consider the following table i \begin{tabular}{lll} Gas & $\mathrm{a} /\left(\mathrm{k} \mathrm{Pa} \mathrm{dm}^6 \mathrm{~mol}^{-1}\right)$ & $\mathrm{b} /\left(\mathrm{dm}^3 \mathrm{~mol}^{-1}\right)$ \\ A &...

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Q JEE MAIN 2019

The equation of a tangent to the parabola, $x^2=8 y$, which makes an angle $\theta$ with the positive direction of...

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The C–C bond length is maximum in :

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Consider the statements S1 and S2: S1: Conductivity always increases with decrease in the concentration of electrolyte. S2 : Molar...

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The integral $\int \frac{3 x+2 x}{\left(2 x^4+3 x^2+1\right)^4} d x$ is equal to (where C is a constant of integration)

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The osmotic pressure of a dilute solution of an ionic compound XY in water is four times that of a...

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The major product of the following reaction is :

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The pair that has similar atomic radii is :

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The molecule that has minimum/no role in the formation of photochemical smog, is

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$\lim _{n \rightarrow \infty}\left(\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\frac{n}{n^2+3^2}+\ldots \ldots+\frac{1}{5 n}\right)$ is equal to :

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Q JEE MAIN 2019

A solution containing 62 g ethylene glycol in 250 g water is cooled to $-10^{\circ} \mathrm{C}$. If $\mathrm{K}_{\mathrm{f}}$ for water...

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The principle of column chromatography is:

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The INCORRECT statement is :

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The given plots represent the variation of the concentration of a reactant R with time for two different reactions (i)...

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Poly- $\beta$-hydroxybutyrate-co- $\beta$-hydroxyvalerate (PHBV) is a copolymer of $\_\_\_\_$ .

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If a circle of radius R pases through the origin O and intersects the coordinate axes at A and B,...

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Which of the following is a condensation polymer?

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The graph between $|\psi|^2$ and r(radial distance) is shown below. This represents i.

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Q JEE MAIN 2019

The increasing order of reactivity of the following compounds towards aromatic electrophilic substitution reaction is

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If ${ }^{\mathrm{n}} \mathrm{C}_4,{ }^{\mathrm{n}} \mathrm{C}_5$ and ${ }^{\mathrm{n}} \mathrm{C}_6$ are in A.P., then n can be :

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Q JEE MAIN 2019

The number of integral values of $m$ for which the quadratic expression, $(1+2 m) x^2-2(1+3 m) x+4(1+m)$, $x \in R$,...

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Q JEE-MAIN 2019

In the following reaction

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Q JEE MAIN_2019_

The oxoacid of sulphur that does not contain bond between sulphur atoms is :

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Q JEE MAIN 2019

The major product of the following reaction is

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Let $z_1$ and $z_2$ be two complex numbers satisfying $\left|z_1\right|=9$ and $\left|z_2-3-4 i\right|=4$. Then the minimum value of $...

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Consider the following statements (a) The pH of a mixture containing 400 mL of 0.1 $\mathrm{M} \mathrm{H}_2 \mathrm{SO}_4$ and 400...

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Q JEE MAIN 2019

If an angle between the line, $\frac{x+1}{2}=\frac{y-2}{1}=\frac{z-3}{-2}$ and the plane, $x-2 y-k z=3$ is $\cos ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)$

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Q JEE MAIN 2019

Among the following, the set of parameters that represents path functions, is (A) q + w (B) q (C) w...

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Q JEE MAIN 2019

In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic?

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Q JEE MAIN 2019

The pH of rain water, is approximately

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Let $S$ be the set of all real values of $\lambda$ such that a plane passing through the points $...

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The temporary hardness of water is due to

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When the first electron gain enthalpy $\left(\Delta_{\mathrm{eg}} \mathrm{H}\right)$ of oxygen is $-141 \mathrm{~kJ} / \mathrm{mol}$, its second electron gain enthalpy...

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The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3,...

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Q JEE MAIN 2019

The major product of the following reaction

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The expression $\sim(\sim p \rightarrow q)$ is logically equivalent to

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Q JEE MAIN 2019

A solution containing 62 g ethylene glycol in 250 g water is cooled to $-10^{\circ} \mathrm{C}$. If $\mathrm{K}_{\mathrm{f}}$ for water...

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Let $Z$ be the set of integers. If $A=\left\{x \in Z: 2^{(x+2)\left(x^2-5 x+9\right)}=1\right\}$ and $B=\{x \in Z:-3

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When the first electron gain enthalpy $\left(\Delta_{e 0} \mathrm{H}\right)$ of oxygen is $-141 \mathrm{~kJ} / \mathrm{mol}$, its second electron gain...

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Q JEE MAIN 2019

There are m men and two women participating in a chess tournament. Each participant plays two games with every other...

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Q JEE MAIN 2019

In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic?

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Q JEE MAIN 2019

If the function f given by $\mathrm{f}(\mathrm{x})=\mathrm{x}^3-3(\mathrm{a}-2) \mathrm{x}^2+3 \mathrm{ax}+7$, for some $\mathrm{a} \in \mathrm{R}$ is increasing in $(0,1]$ and decreasing...

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Q JEE MAIN 2019

For coagulation of arsenious sulphide sol, which one of the following salt solution will be most effective?

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Q JEE-MAIN 2019

The hardness of a water sample (in terms of equivalents of $\mathrm{CaCO}_3$ ) containing $10^{-3} \mathrm{M} \mathrm{CaSO}_4$ is (molar mass...

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Q JEE MAIN 2019

If the standard electrode potential for a cell is 2 V at 300 K , the equilibrium constant $(\mathrm{K})$ for...

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Let f be a differentiable function such that $f(1)=2$ and $f^{\prime}(x)=f(x)$ for all $x \in R$. If $h(x)=f(f(x))$, then $h^{\prime}(1)$...

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A metal on combustion in excess air forms $X$. $X$ upon hydrolysis with water yields $\mathrm{H}_2 \mathrm{O}_2$ and $\mathrm{O}_2$ along...

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The metal d-orbitals that are directly facing the ligands in $\mathrm{K}_3\left[\mathrm{Co}(\mathrm{CN})_6\right]$ are

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Q JEE MAIN 2019

The transition element that has lowest enthalpy of atomisation, is

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Let $S$ and $S^{\prime}$ be the foci of an ellipse and $B$ be any one of the extremities of its...

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The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383...

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Given Gas H2 CH4 CO2 SO2 Critical 33 190 304 630 Temperature/K On the basis of data given above, predict...

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The integral $\int_1^e\left\{\left(\frac{x}{e}\right)^{2 x}-\left(\frac{e}{x}\right)^x\right\} \log _e x d x$ is equal to

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Q JEE MAIN 2019

The metal that forms nitride by reacting directly with $\mathrm{N}_2$ of air, is

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For any given series of spectral lines of atomic hydrogen, let $\Delta \bar{v}=\bar{v}_{\max }-\bar{v}_{\min }$ be the difference in maximum...

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Q JEE MAIN 2019

Which of the following conditions in drinking water causes methemoglobinemia?

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Q JEE-MAIN 2019

Water samples with BOD values of 4 ppm and 18 ppm, respectively, are

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If $\sin ^4 \alpha+4 \cos ^4 \beta+2=4 \sqrt{2} \sin \alpha \cos \beta ; \alpha, \beta \in[0, \pi]$, then $...

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Q JEE MAIN 2019

The major product of the following reaction is $\mathrm{CH}_3 \mathrm{CH}=\mathrm{CHCO}_2 \mathrm{CH}_3 \xrightarrow{\mathrm{LiAlH}_4}$

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Consider the following reversible chemical reactions $...

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Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as...

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Liquid ‘M’ and liquid ‘N’ form an ideal solution. The vapour pressures of pure liquids ‘M’ and ‘N’ are 450...

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If a curve passes through the point $(1,-2)$ and has slope of the tangent at any point $(x, y)$ on...

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The major product obtained in the following reaction is

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In the figure shown, after the switch ‘S’ is turned from position ‘A’ to position ‘B’, the energy dissipated in...

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The tests performed on compound X and their inferences are : Test Inference (a) 2,4-DNP test Coloured precipitate (b) Iodoform...

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Q JEE MAIN 2019

In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair...

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What is the position and nature of image formed by lens combination shown in figure? ( $f_1, f_2$ are focal...

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Q JEE MAIN 2019

For coagulation of arsenious sulphide sol, which one of the following salt solution will be most effective?

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A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected...

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If $...

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Q JEE MAIN 2019

The correct match between Item I and Item II is :

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A particle of mass $m$ moves in a circular orbit in a central potential field $U(r)=\frac{1}{2} k r^2$. If Bohr's...

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The position co-ordinates of a particle moving in a 3-D coordinate system is given by $...

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The one that will show optical activity is (en = ethane-1,2-diamine)

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A point source of light, S is placed at a distance L in front of the centre of plane mirror...

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If the angle of elevation of a cloud from a point P which is 25 m above a lake be...

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The top of a water tank is open to air and its water level is maintained. It is giving out...

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Q JEE MAIN 2019

Magnesium powder burns in air to give

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A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A...

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Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three unit vectors, out of which vectors $\vec{b}$ and $\vec{c}$ are non-parallel. If $\alpha$...

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A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the...

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A particle A of mass ‘m’ and charge ‘q’ is accelerated by a potential difference of 50 V. Another particle...

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In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC...

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The correct structure of histidine in a strongly acidic solution (pH = 2) is

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The element that shows greater ability to form $p \pi-p \pi$ multiple bonds, is

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The number of water molecule(s) not coordinated to copper ion directly in $\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$, is

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8 g of NaOH is dissolved in 18 g of $\mathrm{H}_2 \mathrm{O}$. Mole fraction of NaOH in solution and molality...

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Charge is distributed within a sphere of radius $R$ with volume charge density $\rho(r)=\frac{A}{r^2} e^{\frac{-2 r}{a}}$, where $A$ and a...

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Q JEE MAIN 2019

If the standard electrode potential for a cell is 2 V at 300 K , the equilibrium constant $(\mathrm{K})$ for...

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Q JEE MAIN 2019

The combination of plots which does not represent isothermal expansion of an ideal gas is

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Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror (...

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Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius...

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Q JEE MAIN 2019

The transition element that has lowest enthalpy of atomisation, is

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The standard Gibbs energy for the given cell reaction in kJ mol–1 at 298 K is $\mathrm{Zn}(\mathrm{s})+\mathrm{Cu}^{2+}(\mathrm{aq}) \longrightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{Cu}(\mathrm{s})$, $...

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Q JEE MAIN 2019

The upper stratosphere consisting of the ozone layer protects us from the sun’s radiation that falls in the wavelength region...

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A rod of mass ‘M’ and length ‘2L’ is suspended at its middle by a wire. It exhibits torsional oscillations;...

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A simple pendulum, made of a string of length $I$ and a bob of mass $m$, is released from a...

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The pair that does NOT require calcination is

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Expression for time in terms of G(universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:

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The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383...

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Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod...

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The two monomers for the synthesis of nylon 6, 6 are

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The major product of the following reaction is $\mathrm{CH}_3 \mathrm{C} \equiv \mathrm{CH} \xrightarrow[\text { (ii)DI }]{\text { (i)DCl (1equiv.) }}$

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In the given circuit the internal resistance of the 18 V cells is negligible. If $\mathrm{R}_1=400 \Omega, \mathrm{R}_3=100 \Omega$ and...

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A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What...

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The element that does NOT show catenation is

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$\mathrm{C}_{60}$ , an allotrope of carbon contains

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The correct order of atomic radii is

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Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a...

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A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120...

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The volume strength of $1 \mathrm{M} \mathrm{H}_2 \mathrm{O}_2$ is (Molar mass of $\mathrm{H}_2 \mathrm{O}_2=34 \mathrm{~g} \mathrm{~mol}^{-1}$ )

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Q JEE MAIN 2019

The metal that forms nitride by reacting directly with $\mathrm{N}_2$ of air, is

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A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having...

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If the de Broglie wavelength of the electron in $\mathrm{n}^{\text {th }}$ Bohr orbit in a hydrogenic atom is equal...

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Q JEE MAIN 2019

Which of the following conditions in drinking water causes methemoglobinemia?

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A cylinder of radius $R$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2 R$....

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The correct statement(s) among I to III with respect to potassium ions that are abundant within the cell fluids is/are...

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An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer...

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The displacement of a damped harmonic oscillator is given by $x(t)=e^{-0.1 t} \cos (10 \pi t+\phi)$. Here $t$ is in...

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Q JEE MAIN 2019

Consider the following reversible chemical reactions

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A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle...

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As shown in the figure, two infinitely long, identical wires are bent by $90^{\circ}$ and placed in such a way...

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Given below in the left column are different modes of communication using the kinds of waves given in the right...

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The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and...

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A current of 5 A passes through a copper conductor (resistivity $=1.7 \times 10^{-8} \Omega \mathrm{~m}$ ) of radius of...

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Q JEE-MAIN 2019

The output of the given logic circuit is

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In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure

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Q JEE MAIN 2019

Chlorine on reaction with hot and concentrated sodium hydroxide gives

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In a meter bridge, the wire of length 1 m has a nonuniform cross-section such that, the variation $\frac{\mathrm{dR}}{\mathrm{dl}}$ of...

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Q JEE MAIN 2019

The correct match between Item I and Item II is :

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The electric field of a plane electromagnetic wave is given by $$ \overline{\mathrm{E}}=\mathrm{E}_0 \hat{\mathrm{i}} \cos (\mathrm{kz}) \cos (\omega \mathrm{t}) $$...

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Molecules of benzoic acid $\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{COOH}\right)$ dimerise in benzene. ' w ' g of the acid dissolved in 30...

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Q JEE MAIN 2019

In a car race on straight road, car A takes a time t less than car B at the finish...

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One plano-convex and one plano-concave lens of same radius of curvature ' R ' but of different materials are joined...

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The products formed in the reaction of cumene with $\mathrm{O}_2$ followed by treatment with dil. HCl are :

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The major product of the following reaction is

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The magnetic field associated with a light wave is given, at the origin, by $...

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Q JEE MAIN 2019

For the given cyclic process CAB as shown for a gas, the work done is

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A proton and an $\alpha$-particle (with their masses in the ratio of $1: 4$ and charges in the ratio of...

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A force acts on a 2 kg object so that its position is given as a function of time as...

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The major product in the following conversion is

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A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane...

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There is a uniform spherically symmetric surface charge density at a distance $\mathrm{R}_0$ from the origin. The charge distribution is...

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The energy required to take a satellite to a height ' $h$ ' above Earth surface (radius of Earth $...

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A travelling harmonic wave is represented by the equation $y(x, t)=10^{-3} \sin (50 t+2 x)$, where $x$ and $y$ are...

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Two Carnot engines A and B are operated in series. The first one, A, receives heat at $T_1(=600 \mathrm{~K})$ and...

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The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7,9...

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A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied...

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Let the equations of two sides of a triangle be $3 x-2 y+6=0$ and $4 x+5 y-20=0$. If the orthocentre...

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For a reaction, consider the plot of $\ln \mathrm{k}$ versus $1 / \mathrm{T}$ given in the figure. If the rate...

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Two point charges $\mathrm{q}_1(\sqrt{10} \mu \mathrm{C})$ and $\mathrm{q}_2(-25 \mu \mathrm{C})$ are placed on the x -axis at $\mathrm{x}=1 \mathrm{~m}$ and...

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The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on...

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The galvanometer deflection, when key $K_1$ is closed but $K_2$ is open, equal $\theta_0$ (see figure). On closing $K_2$ also...

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A series AC circuit containing an inductor ( 20 mH ), a capacitor ( $120 \mu \mathrm{~F}$ ) and a...

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The aldehydes which will not form Grignard product with one equivalent Grignard reagent are

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In the figure shown, a circuit contains two identical resistors with resistance $\mathrm{R}=5 \Omega$ and an inductance with $\mathrm{L}=2 \mathrm{mH}$....

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If ‘M’ is the mass of water that rises in a capillary tube of radius ‘r’, then mass of water...

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Q JEE MAIN 2019

The major product of the following reaction is

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A ball is thrown vertically up (taken as + z-axis) from the ground. The correct momentum-height (p-h) diagram is:

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Q JEE MAIN 2019

Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode...

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An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the...

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A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle...

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$\wedge_{\mathrm{m}}^{\circ}$ for $\mathrm{NaCl}, \mathrm{HCl}$ and NaA are $126.4,425.9$ and $100.5 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$, respectively. If the conductivity of 0.001 M...

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The area of the region $A=\{(x, y): 0 \leq y \leq x|x|+1$ and $-1 \leq x \leq 1\}$ in sq....

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Q JEE MAIN 2020

One of the two identical conducting wires of length $L$ is bent in the form of a circular loop and...

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Q JEE MAIN 2019

The major product of the following reaction is

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A data consists of $n$ observations $x_1, x_2, \ldots ., x n$. If $\sum_{i=1}^n\left(x_i+1\right)^2=9 n$ and $\sum_{i=1}^n\left(x_i-1\right)^2=5 n$, then the...

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Q JEE MAIN 2019

The magnetic moment of an octahedral homoleptic Mn(II) complex is 5.9 BM. The suitable ligand for this complex is

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The equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane containing the straight lines $\frac{x}{3}=\frac{y}{4}=\frac{z}{2}$...

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The major product of the following reaction is

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Among the following, the false statement is

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A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length...

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If the circles $x^2+y^2-16 x-20 y+164=r^2$ and $(x-4)^2+(y-7)^2=36$ intersect at two distinct points, then

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Let $\mathrm{a}, \mathrm{b}$ and c be the $7^{\text {th }}, 11^{\text {th }}$ and $13^{\text {th }}$ terms respectively of...

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The number of all possible positive integral values of $\alpha$ for which the roots of the quadratic equation, $...

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A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise...

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A thin disc of mass $M$ and radius $R$ has mass per unit area $\sigma(r)=k r^2$ where $r$ is the...

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The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities...

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The value of acceleration due to gravity at Earth's surface is $9.8 \mathrm{~ms}^{-2}$. The altitude above its surface at which...

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An open vessel at 27°C is heated until two fifth of the air (assumed as an ideal gas) in it...

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In the given circuit, an ideal voltmeter connected across the $10 \Omega$ resistance reads 2 V. The internal resistance r,...

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A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of...

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A moving coil galvanometer allows a full scale current of $10^{-4} \mathrm{~A}$. A series resistance of $2 \mathrm{M} \Omega$ is...

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Let $\ddot{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\sqrt{2} \hat{\mathrm{k}}, \ddot{\mathrm{b}}=\mathrm{b}_1 \hat{\mathrm{i}}+\mathrm{b}_2 \hat{\mathrm{j}}+\sqrt{2} \hat{\mathrm{k}}$ and $\ddot{\mathrm{c}}=5 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\sqrt{2} \hat{\mathrm{k}}$ be three vectors such that the projection vector of...

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Two particles A, B are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angular speed $\omega$....

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The electric field of light wave is given as $...

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Two particles of masses M and 2 M, moving, as shown, with speeds of $10 \mathrm{~m} / \mathrm{s}$ and $...

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A parallel plate capacitor with plates of area $1 \mathrm{~m}^2$ each, are at a separation of 0.1 m . If...

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If $x=3 \tan t$ and $y=3$ sect, then the value of $\frac{d^2 y}{d x^2}$ at $t=\frac{\pi}{4}$, is

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A plane electromagnetic wave having a frequency $v=23.9 \mathrm{GHz}$ propagates along the positive z-direction in free space. The peak value...

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The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure

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A message signal of frequency 100 MHz and peak voltage 100 V is used to execute amplitude modulation on a...

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The sum of the following series $$ 1+6+\frac{9\left(1^2+2^2+3^2\right)}{7}+\frac{12\left(1^2+2^2+3^2+4^2\right)}{9}+\frac{15\left(1^2+2^2+\ldots \ldots+5^2\right.}{11}+\ldots . $$ up to 15 terms, is

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A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the...

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An NPN transistor is used in common emitter configuration as an amplifier with $1 \mathrm{k} \Omega$ load resistance. Signal voltage...

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Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are

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Two particles are projected from the same point with the same speed $u$ such that they have the same range...

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A paramagnetic material has 1028 atoms $/ \mathrm{m}^3$. Its magnetic susceptibility at temperature 350 K is $2.8 \times 10^{-4}$. Its...

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$\int_0^{\pi / 3} \frac{\tan \theta}{\sqrt{2 k \sec \theta}} d \theta=1-\frac{1}{\sqrt{2}},(k>0)$, then the value of $k$ is

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In the given circuit, the charge on $4 \mu \mathrm{~F}$ capacitor will be

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Two radioactive materials A and B have decay constants $10 \lambda$ and $\lambda$, respectively. If initially they have the same...

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The number density of molecules of a gas depends on their distance $r$ from the origin as $n(r)=n_0 e^{\alpha r^4}$....

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A $25 \times 10^{-3} \mathrm{~m}^3$ volume cylinder is filled with 1 mol of $\mathrm{O}_2$ gas at room temperature ( 300...

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A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the...

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Let $\mathrm{A}(4,-4)$ and $\mathrm{B}(9,6)$ be points on the parabola, $\mathrm{y}^2=4 \mathrm{x}$. Let C be chosen on the arc AOB of...

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A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air...

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An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K . The mean...

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n moles of an ideal gas with constant volume heat capacity CV undergo an isobaric expansion by certain volume. The...

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Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively. If, initially a sample...

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Two satellites, $A$ and $B$, have masses $m$ and $2 m$ respectively. $A$ is in a circular orbit of radius...

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A rigid square loop of side ‘a’ and carrying current $\mathrm{l}_2$ is lying on a horizontal surface near a long...

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A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point...

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For each $x \in R$, let $[x]$ be the greatest integer less than or equal to $x$. Then $...

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Three particles of masses, 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle...

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Let a total charge 2 Q be distributed in a sphere of radius R, with the charge density given by...

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A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2...

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The coefficient of $t^4$ in the expansion of $\left(\frac{1-t^6}{1-t}\right)^3$ is

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In a Frank-Hertz experıment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7...

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A stationary source emits sound waves of frequency 500 Hz . Two observers moving along a line passing through the...

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Consider an electron in a hydrogen atom, revolving in its second excited state (having radius 4.65 Å). The de-Broglie wavelength...

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Let $A=\{x \in R: x$ is not a positive integer $\}$. Define a function $f: A \rightarrow R$ as $...

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A plano-convex lens (focal length $f_2$, refractive index $\mu_2$, radius of curvature $R$ ) fits exactly into a planoconcave lens(focal...

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A system of three charges are placed as shown in the figure : If D >> d, the potential energy...

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A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis,...

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Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a...

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lf $$ A=\left[\begin{array}{ccc} e^t & e^{-t} & e^{-t} \sin t \\ e^t & -e^t \cos t-e^{-t} \sin t & -e^{-t}...

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An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCI molecules in its gaseous phase...

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A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force...

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In an amplitude modulator circuit, the carrier wave is given by, $C(t)=4 \sin (20000 \pi t)$ while modulating signal is...

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Let $z_0$ be a root of the quadratic equation, $x^2+x+1=0$. If $z=3+6 i z_0^{81}-3 i z_0^{93}$, then arg $z$ is...

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The ratio of the weights of a body on the Earth's surface to that on the surface of a planet...

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To double the covering range of a TV transmission tower, its height should be multiplied by:

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Consider the LR circuit shown in the figure. If the switch $S$ is closed at $t=0$ then the amount of...

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A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move...

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An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered...

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If both the roots of the quadratic equation $x^2-m x+4=0$ are real and distinct and they lie in the interval...

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A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of...

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Two sources of sound $S_1$ and $S_2$ produce sound waves of same frequency 660 Hz . A listener is moving...

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A particle is moving with speed $v=b \sqrt{x}$ along positive $x$-axis. Calculate the speed of the particle at time $t=\tau$...

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Formation of real image using a biconvex lens is shown below: If the whole set up is immersed in water...

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A transparent cube of side $d$, made of a material of refractive index $\mu_2$, is immersed in a liquid of...

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A particle of mass 20 g is released with an initial velocity $5 \mathrm{~m} / \mathrm{s}$ along the curve from...

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

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A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm...

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A smooth wire of length $2 \pi r$ is bent into a circle and kept in a vertical plane. A...

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When a certain photosensistive surface is illuminated with monochromatic light of frequency $v$, the stopping potential for the photo current...

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

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In the given circuit diagram, the currents, $\mathrm{I}_1=-0.3 \mathrm{~A}, \mathrm{I}_4=0.8 \mathrm{~A}$ and $\mathrm{I}_5=0.4 \mathrm{~A}$, are flowing as shown. The currents...

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Figure shows a DC voltage regulator circuit, with a Zener diode of breakdown voltage = 6 V. If the unregulated...

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A simple harmonic motion is represented by: $$ y=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t) c m $$ The...

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A solid sphere, of radius $R$ acquires a terminal velocity $v_1$ when falling (due to gravity) through a viscous fluid...

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The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of...

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A system of three polarizers $P_1, P_2, P_3$ is set up such that the pass axis of $P 3$ is...

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In a radioactive decay chain, the initial nucleus is ${ }_{90}^{232}$ th at the end there are $6 \alpha$-particles and...

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A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB...

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A Carnot engine has an efficiency of $\frac{1}{6}$. When the temperature of the sink is reduced by $62^{\circ} \mathrm{C}$, its...

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The mean intensity of radiation on the surface of the Sun is about $10^8 \mathrm{~W} / \mathrm{m}^2$. The rms value...

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An electron, moving along the x-axis with an initial energy of 100 eV , enters a region of magnetic field...

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In the circuit shown, find $C$ if the effective capacitance of the whole circuit is to be $0.5 \mu F$....

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A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the...

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One kg of water, at $20^{\circ} \mathrm{C}$, is heated in an electric kettle whose heating element has a mean (temperature...

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A galvanometer, whose resistance is 50 ohm , has 25 divisions in it. When a current of $...

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A spring whose unstretched length is I has a force constant k . The spring is cut into two pieces...

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A vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible thickness....

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In the figure, given that $\mathrm{V}_{\mathrm{BB}}$ supply can vary from 0 to $...

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A moving coil galvanometer, having a resistance G , produces full scale deflection when a current Ig flows through it....

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If one real root of the quadratic equation $81 x^2+k x+256=0$ is cube of the other root, then a value...

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The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently...

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The value of the $\int_{-2}^2 \frac{\sin ^2 x}{\left[\frac{x}{\pi}\right]+\frac{1}{2}}$ (where $[x]$ denotes the greatest integer less than or equal to $x$...

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A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a...

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The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its...

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A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity...

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The sum of the real values of $x$ for which the middle term in the binomial expansion of $\left(\frac{x^3}{3}+\frac{3}{x}\right)^8$ equals...

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Let $f_x(x)=\frac{1}{k}\left(\sin ^k x+\cos ^k x\right)$ for $k=1,2,3, \ldots$. Then for all $x \in R$, the value of $f_4(x)-f_6(x)$ is...

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The maximum value of the function $f(x)=3 x^3-18 x^2+27 x-40$ on the set $S=\left\{x \in R: x^2+30 \leq 11 x\right\}$...

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The direction ratios of normal to the plane through the points $(0,-1,0)$ and $(0,0,1)$ and making an angle $\frac{\pi}{4}$ with...

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

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In a triangle, the sum of lengths of two sides is $x$ and the product of the lengths of the...

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A square is inscribed in the circle $x^2+y^2-6 x+8 y-103=0$ with its sides parallel to the coordinate axes. Then the...

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If tangents are drawn to the ellipse $x^2+2 y^2=2$ at all points on the ellipse other than its four vertices...

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Equation of a common tangent to the parabola $y^2=4 x$ and the hyperbola $x y=2$ is:

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Two integers are selected at random from the set {1, 2, ..., 11}. Given that the sum of selected numbers...

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Two wires A and B are carrying currents $\mathrm{I}_1$ and $\mathrm{I}_2$ as shown in the figure. The separation between them...

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A npn transistor operates as a common emitter amplifier, with a power gain of 60 dB. The input circuit resistance...

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If $\int \frac{\sqrt{1-x^2}}{x^4} d x=A(x)\left(\sqrt{1-x^2}\right)^m+C$, for a suitable chosen integer $m$ and a function $A(x)$, where $C$ is a constant...

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If $x \log _e\left(\log _e x\right)-x^2+y^2=4(y>0)$, then $\frac{d y}{d y}$ at $x=e$ is equal to:

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In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown...

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The value of r for which $...

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In a photoelectric effect experiment the threshold wavelength of light is 380 nm . If the wavelength of incident light...

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Two circles with equal radii are intersecting at the points (0, 1) and (0, –1). The tangent at the point...

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A particle of mass $m$ is moving along a trajectory given by $$ \begin{aligned} & x=x_0+a \cos \omega_1 t \\...

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Let $A=\left(\begin{array}{ccc}0 & 2 q & r \\ p & q & -r \\ p & -q & r\end{array}\right)$. If...

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Let $[\mathrm{x}]$ denote the greatest integer less than or equal to x . Then $...

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A ball is thrown upward with an initial velocity V 0 from the surface of the earth. The motion of...

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The straight line $x+2 y=1$ meets the coordinate axes at A and B. A circle is drawn through A, B...

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

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Let $a_1, a_2, \ldots, a_{10}$ be a G.P. If $\frac{a_3}{a_1}=25$, then $\frac{a_9}{a_5}$ equals

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The area (in sq. units) of the region bounded by the curve $x^2=4 y$ and the straight line $x=4 y-2$...

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Let $\vec{a}=\hat{i}+2 \hat{j}+4 \hat{k}, \vec{b}=\hat{i}+\lambda \hat{j}+4 \hat{k}$ and $\overrightarrow{\mathrm{c}}=2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+\left(\lambda^2-1\right) \hat{\mathrm{k}}$ be coplanar vectors. Then the non-zero vector $...

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The outcome of each of 30 items was observed; 10 items gave an outcome $\frac{1}{2}$-d each, 10 items gave outcome...

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Let $f: R \rightarrow R$ be defined by $f(x)=\frac{x}{1+x^2} x \in R$. Then the range of $r$ is

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The plane containing the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z-1}{3}$ and also containing its projection on the plane $2 x+3 y-z=$ 5 , contains...

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The negation of the Boolean expression $\sim s \vee(\sim r \wedge s)$ is equivalent to:

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Let $f(x)=\left\{\begin{array}{cc}-1, & -2 \leq x

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If $\cos ^{-1} x-\cos ^{-1} \frac{y}{2}=\alpha$, where $1 \leq x \leq 1,-2 \leq y \leq 2$, $x \leq \frac{y}{2}$, then...

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An example of solid sol is.

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Heat treatment of muscular pain involves radiation of wavelength of about 900 nm . Which spectral line of Hatom is...

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The distance of the point having position vector $-\hat{i}+2 \hat{j}+6 \hat{k}$ from the straight line passing through the point (...

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A 10 mg effervescent tablet containing sodium bicarbonate and oxalic acid releases 0.25 ml of $\mathrm{CO}_2$ at $\mathrm{T}=$ 298.15 K...

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The tangent and normal to the ellipse $3 x^2+5 y^2=$ 32 at the point $P(2,2)$ meet the $x$-axis at $Q$...

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Peroxyacetyl nitrate (PAN), an eye irritant is produced by

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Which compound(s) out of following is/are not aromatic?

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If the line $a x+y=c$, touches both the curves $x^2+y^2=1$ and $y^2=4 \sqrt{2} x$, then $|c|$ is equal to :

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The integral $\int_{\pi / 6}^{\pi / 3} \sec ^{2 / 3} x \operatorname{cosec}^{4 / 3} x d x$ is equal...

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The amphoteric hydroxide is

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Let $\lambda$ be a real number for which the system of linear equations $$ \begin{aligned} & x+y+z=6 \\ & 4...

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NaH is an example of

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The polymer obtained from the following reactions is

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If 5 x+9=0 is the directrix of the hyperbola $16 x^2- 9 y^2=144$, then its corresponding focus is :

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Among the following compounds, which one is found in RNA?

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Minimum number of times a fair coin must be tossed so that the probability of getting at least one head...

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A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts...

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The element that usually does NOT show variable oxidation states is

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The correct statements among (a) to (d) regarding $\mathrm{H}_2$ as a fuel are (a) It produces less pollutants than petrol....

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Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the...

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Two blocks of the same metal having same mass and at temperature $T_1$ and $T_2$, respectively, are brought in contact...

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Lines are drawn parallel to the line $4 x-3 y+2=0$, at a distance $\frac{3}{5}$ from the origin. Then which one...

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The number of real roots of the equation $5+\left|2^x-1\right|=2^x\left(2^x-2\right)$ is :

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Match the metals (column I) with the coordination compound(s)/enzyme(s) (column II)

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If $\lim _{x \rightarrow 1} \frac{x^2-a x+b}{x-1}=5$, then $a+b$ is equal to :

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If the plane $2 x-y+2 z+3=0$ has the distances $\frac{1}{3}$ and $\frac{2}{3}$ units from the planes $4 x-2 y+4 z+\lambda=0$...

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An organic compound is estimated through Dumas method and was found to evolve 6 moles of $\mathrm{CO}_2 4$ moles of...

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Let $a_1, a_2, a_3, \ldots .$. be an A.P. with $a_6=2$. Then the common difference of this A.P., which maximises...

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For the chemical reaction $\mathrm{X} \rightleftharpoons \mathrm{Y}$, the standard reaction Gibbs energy depends on temperature T (in K ) as...

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Let $y=y(x)$ be the solution of the differential equation, $\frac{d y}{d x}+y \tan 2 x=x^2+x^2 \tan x$, $x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$,...

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Consider the reaction $$ \mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{~g}) $$ The equilibrium constant of the above reaction is $\mathrm{K}_{\mathrm{P}}$. If...

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For the cell $\mathrm{Zn}(\mathrm{s})\left|\mathrm{Zn}^{2+}(\mathrm{ag}) \| \mathrm{M}^{x+}(\mathrm{ag})\right| \mathrm{M}(\mathrm{s})$, different half cells and their standard electrode potentials are given below If $...

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The correct order of the atomic radii of C, Cs, Al, and S is

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The correct match between items I and II is

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A perpendicular is drawn from a point on the line $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{1}$ to the plane $x+y+z=3$ such that the foot of...

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The major product of the following reaction is:

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The area (in sq. units) of the region bounded by the curves $y=2^x$ and $y=|x+1|$, in the first quadrant is...

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The major product of the following reaction is

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Let $\mathrm{a}, \mathrm{b}$ and c be in G.P. with common ratio r , where $\mathrm{a} \neq 0$ and $0

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If a reaction follows the Arrhenius equation, the plot $\operatorname{lnk} v s \frac{1}{(R T)}$ gives straight line with a gradient...

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If $\int x^5 e^{-x^2} d x=g(x) e^{-x^2}+c$, where $c$ is a constant of integration, then $\mathrm{g}(-1)$ is equal to :

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The chloride that CANNOT get hydrolysed is:

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If both the mean and the standard deviation of 50 observations $x_1, x_2, \ldots x_{50}$ are equal to 16 ,...

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The major product of the following reaction is:

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The smallest natural number n , such that the coefficient of $x$ in the expansion of $\left(x^2+\frac{1}{x^3}\right)^n$ is $...

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The major product of the following reaction is

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The sum $1+\frac{1^3+2^3}{1+2}+\frac{1^3+2^3+3^3}{1+2+3}+\ldots \ldots$ $$ +\frac{1^3+2^3+3^3+\ldots \ldots+15^3}{1+2+3+\ldots \ldots+15}-\frac{1}{2}(1+2+3 \ldots .+15) $$ is equal to :

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The locus of the centres of the circles, which touch the circle, $x^2+y^2=1$ externally, also touch the $y$-axis and lie...

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The correct match between item (I) and item (II) is:

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If $z$ and $w$ are two complex numbers such that $|z w|=1$ and $\arg (z)-\arg (w)=\frac{\pi}{2}$, then :

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The freezing point of a diluted milk sample is found to be $-0.2^{\circ} \mathrm{C}$, while it should have been $...

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The sum of the real roots of the equation $...

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The angles $A, B$ and $C$ of a triangle $A B C$ are in A.P. and $a: b=1: \sqrt{3}$. If...

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The concentration of dissolved oxygen (DO) in cold water can go upto:

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Match the ores (column A) with the metals (column B): \begin{tabular}{ll} \multicolumn{1}{c}{\begin{tabular}{c} (Column A) \\ Ores \end{tabular}} & \multicolumn{1}{c}{\begin{tabular}{l} (Column...

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Let $A$ be a point on the line $\vec{r}=(1-3 \mu) \hat{i}+(\mu-1) \hat{j}+(2+5 \mu) \hat{k}$ and $B(3,2,6)$ be a point in...

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In chromatography, which of the following statements is INCORRECT for $\mathrm{R}_{\mathrm{f}}$ ?

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If the area enclosed between the curves $y=k x^2$ and $x=k y^2,(k>0)$, is 1 square unit. Then $k$ is :

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If the deBroglie wavelength of an electron is equal to $10^{-3}$ times the wavelength of a photon of frequency $...

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The correct statements among (a) to (d) are : (a) Saline hydrides produce H2 gas when reacted with H2O. (b)...

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Let $\vec{a}=2 \hat{i}+\lambda_1 \hat{j}+3 \hat{k}, \vec{b}=4 \hat{i}+\left(3-\lambda_2\right) \hat{j}+6 \hat{k}$ and $\vec{c}=3 \hat{i}+6 \hat{j}+\left(\lambda_3-1\right) \hat{k}$ be three vectors such that $...

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Points I, II and III in the following plot respectively correspond to ( $\mathrm{V}_{\text {mp }}$ : most probable velocity)

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Ice at $-20^{\circ} \mathrm{C}$ is added to 50 g of water at $40^{\circ} \mathrm{C}$. When the temperature of the mixture...

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For each tR, let [t] be the greatest integer less than or equal to t. Then,

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If $5,5 r, 5 r^2$ are the lengths of the sides of a triangle, then $r$ cannot be equal to...

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A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this...

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The minimum amount of O2(g) consumed per gram of reactant is for the reaction: (Given atomic mass : Fe =...

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The plane passing through the point $(4,-1,2)$ and parallel to the lines $\frac{x+2}{3}=\frac{y-2}{-1}=\frac{z+1}{2}$ and $\frac{x-2}{1}=\frac{y-3}{2}=\frac{z-4}{3}$ also passes through the point:

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Which of the following is NOT a correct method of the preparation of benzylamine from cyanobenzene?

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In the given circuit the current through Zener Diode is close to

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Let $\mathrm{n} \geq 2$ be a nutural number and $0

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The noble gas that does NOT occur in the atmosphere is :

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In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number...

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A satellite is revolving in a circular orbit at a height h from the earth surface, such that h

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The correct order of the first ionization enthalpies is :

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The increasing order of nucleophilicity of the following nucleophiles is: (a) $\mathrm{CH}_3 \mathrm{CO}_2^{\ominus}$ (b) $\mathrm{H}_2 \mathrm{O}$ (c) $\mathrm{CH}_3 \mathrm{CO}_3^{\ominus}$ (d)...

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The shortest distance between the point $\left(\frac{3}{2}, 0\right)$ and the curve $y=\sqrt{x},(x>0)$ is

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In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves...

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Air pollution that occurs in sunlight is :

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https://competishun.com/let-f-r-rightarrow-r-be-a-function-such-that-fxx3x2-fprime1x-fprime-prime2fprime-prime-prime3-x-in-r-then-f2-equals/ has infinitely many solutions, then $\beta-\alpha$ equals

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The resistance of the metre bridge AB in given figure is $4 \Omega$. With a cell of emf $\varepsilon=0.5 \mathrm{~V}$...

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Let $f: R \rightarrow R$ be a function such that $f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3), x \in R$. Then...

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The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The...

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Compound $\mathrm{A}\left(\mathrm{C}_9 \mathrm{H}_{10} \mathrm{O}\right)$ shows positive iodoform test. Oxidation of A with $\mathrm{KMnO}_4 / \mathrm{KOH}$ gives acid $\mathrm{B}\left(\mathrm{C}_8 \mathrm{H}_6 \mathrm{O}_4\right)$....

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The equation of a tangent to the hyperbola $4 x^2-5 y^2=20$ parallel to the line $x-y=2$ is

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A liquid of density  is coming out of a hose pipe of radius a with horizontal speed v and...

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The sum of all values of $\theta \in\left(0, \frac{\pi}{2}\right)$ satisfying $\sin ^2 2 \theta+\cos ^4 2 \theta=\frac{3}{4}$ is

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1 g of a non-volatile non-electrolyte solute is dissolved in 100 g of two different solvents A and B whose...

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The major product ‘Y’ in the following reaction is :

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An electromagnetic wave of intensity $50 \mathrm{Wm}^{-2}$ enters in a medium of refractive index ' $n$ ' without any loss....

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If the parabolas $y^2=4 b(x-c)$ and $y \quad l=8 a x$ have a common normal, then which one of the...

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The major product ‘Y’ in the following reaction is :

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A point $P$ moves on the line $2 x-3 y+4=0$. If $Q(1,4)$ and $R(3,-2)$ are fixed points, then the locus...

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Consider the statement: " $P(n): n^2-n+41$ " is prime." Then which one of the following is true?

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Let $f(x)=\left\{\begin{array}{ll}\max \left\{|x|, x^2\right\}, & |x| \leq 2 \\ 8-2|x|, & 2

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An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens...

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The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are...

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In the figure shown below, the charge on the left plate of the $10 \mu \mathrm{~F}$ capacitor is $...

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If the third term in the binomial expansion of $\left(1+x^{\log _2 x}\right)^5$ equals 2560 , then a possible value of...

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If the line $3 x+4 y-24=0$ intersects the $x$-axis at the point $A$ and the $y$-axis at the point $B$,...

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A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only translational...

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Equation of travelling wave on a stretched string of linear density $5 \mathrm{~g} / \mathrm{m}$ is $...

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A body is projected at $t=0$ with a velocity $10 \mathrm{~ms}^{-1}$ at an angle of $60^{\circ}$ with the horizontal. The...

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An equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D, E and F are...

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Consider the quadratic equation $(c-5) x^2-2 c x+(c-4)=0, c \neq 5$. Let $S$ be the set of all integral values...

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An unbiased coin is tossed. If the outcome is a head, then a pair of unbiased dice is rolled and...

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In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V . Calculate the radius of...

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Let $I=\int_a^b\left(x^4-2 x^2\right) d x$ If $I$ is minimum then the ordered pair $(a, b)$ is

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Consider a triangular plot ABC with sides AB = 7 m, BC = 5 m and CA = 6 m....

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A particle undergoing simple harmonic motion has time dependent displacement given by $x(t)=A \sin \frac{\pi t}{90}$ The ratio of kinetic...

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The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which...

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If $\frac{d y}{d x}+\frac{3}{\cos ^2 x} y=\frac{1}{\cos ^2 x}, x \in\left(\frac{-\pi}{3}, \frac{\pi}{3}\right)$ and $y\left(\frac{\pi}{4}\right)=\frac{4}{3}$, they $y\left(-\frac{\pi}{4}\right)$ equals

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The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is

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There are two long co-axial solenoids of same length I . The inner and outer coils have radii $\mathrm{r}_1$ and...

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If $\sum_{\mathrm{i}=1}^{20}\left(\frac{{ }^{20} \mathrm{C}_{\mathrm{i}-1}}{{ }^{20} \mathrm{C}_{\mathrm{i}}+{ }^{20} \mathrm{C}_{\mathrm{i}-1}}\right)^3=\frac{\mathrm{k}}{21}$, then k equals

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If a circle $C$ passing through the point $(4,0)$ touches the circle $x^2+y^2+4 x-6 y=12$ externally at the point $(1$,...

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In a Wheatstone bridge (see fig.), Resistances P and Q are approximately equal. When R $=400 \Omega$, the bridge is...

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For the reaction of $\mathrm{H}_2$ with $\mathrm{I}_2$, the rate constant is $2.5 \times 10^{-4} \mathrm{dm} 3 \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $...

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Three charges Q, +q and +q are placed at the vertices of a right-angle isosceles triangles as shown below. The...

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The number of pentagons in $\mathrm{C}_{60}$ and trigons (triangles) in white phosphorus, respectively, are:

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Two equal resistances when connected in series to a battery, consume electric power of 60 W. If these resistances are...

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The major product obtained in the given reaction is:

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Let $d \in R$, and $$ A\left[\begin{array}{ccc} -2 & 4+d & (\sin \theta)-2 \\ 1 & (\sin \theta)+2 & d...

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A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength $980 \AA$. The radius...

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The correct option among the following is :

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The decreasing order of ease of alkaline hydrolysis for the following esters is

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The highest possible oxidation states of uranium and plutonium, respectively, are :

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A particle is moving along a circular path with a constant speed of 10 ms–1. What is the magnitude of...

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Which primitive unit cell has unequal edge lengths (a ≠ b ≠ c) and all axial angles different from 90°?

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Which of these factors does not govern the stability of a conformation in acyclic compounds?

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Two pi and half sigma bonds are present in

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A hydrated solid X on heating initially gives a monohydrated compound Y. Y upon heating above 373 K leads to...

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A mixture of 100 m mol of $\mathrm{Ca}(\mathrm{OH})_2$ and 2 g of sodium sulphate was dissolved in water and the...

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The given graph shows variation (with distance r from centre) of

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For the reaction, $$ \begin{aligned} & 2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_3(\mathrm{~g}) \\ & \Delta \mathrm{H}=-57.2 \mathrm{~kJ} \mathrm{~mol}^{-1} \text { and...

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The crystal field stabilization energy (CFSE) of $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_2$ and $\mathrm{K}_2\left[\mathrm{NiCl}_4\right]$, respectively, are :

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The effect of lanthanoid contraction in the lanthanoid series of elements by and large means

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The force of interaction between two atoms is given by $\mathrm{F}=\alpha \beta \exp \left(-\frac{\mathrm{x}^2}{\alpha \mathrm{kt}}\right)$; where x is the distance,...

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The correct structure of product ‘P’ in the following reaction is

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Which one of the following graphs between molar conductivity ( $\Lambda_{\mathrm{m}}$ ) versus $\sqrt{\mathrm{C}}$ is correct?

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In the circuit shown, the switch $S_1$ is closed at time $t=0$ and the switch $S_2$ is kept open. At...

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The difference between $\Delta \mathrm{H}$ and $\Delta \mathrm{U}(\Delta \mathrm{H}-\Delta \mathrm{U})$, when the combustion of one mole of heptane(I) is carried...

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An amplitude modulated signal is given by $V(t)=10\left[1+0.3 \cos \left(2.2 \times 10^4 t\right)\right] \sin \left(5.5 \times 10^5 t\right)$. Here $t$...

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Number of stereo centers present in linear and cyclic structures of glucose are respectively :

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The INCORRECT statement is :

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The area (in sq. units) in the first quadrant bounded by the parabola, $y=x^2+1$, the tangent to it at the...

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Water filled in two glasses A and B have BOD values of 10 and 20, respectively. The correct statement regarding...

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The pH of a $0.02 \mathrm{M} \mathrm{NH}_4 \mathrm{Cl}$ solution will be [given $$ \left.\mathrm{K}_{\mathrm{b}}\left(\mathrm{NH}_4 \mathrm{OH}\right)=10^{-5} \text { and } \log...

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Which hydrogen in compound (E) is easily replaceable during brominating reaction in presence of light?

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Let $K$ be the set of all real values of $x$ where the function $f(x)=\sin |x|-|x|+2(x-\pi)$ is not differentiable. Then...

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The correct statement is :

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The solution of the differential equation, $\frac{d y}{d x}=(x-y)^2$, when $y(1)=1$, is

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In the formula $X=5 Y Z^2, X$ and $Z$ have dimensions of capacitance and magnetic field, respectively. What are the...

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Let $\sqrt{3} \hat{i}+\hat{j}, \hat{i}+\sqrt{3} \hat{j}$ and $\beta \hat{i}+(1-\beta) \hat{j}$ respectively be the position vectors of the points $A, B$ and...

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A solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The first part has a...

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All $x$ satisfying the inequality $\left(\cot ^{-1} x\right)^2-7\left(\cot ^{-1} x\right)+10>0$, lie in the interval

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Light is incident normally on a completely absorbing surface with an energy flux of 25 Wcm2. If the surface has...

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If the point $(2, \alpha, \beta)$ lies on the plane which passes through the points $(3,4,2)$ and $(7,0,6)$ and is...

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The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it...

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A submarine experiences a pressure of $5.05 \times 10^6$ Pa at a depth of $\mathrm{d}_1$ in a sea. When it...

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Let S = {1, 2, ...., 20}. A subset B of S is said to be “nice”, if the sum...

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A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. If...

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Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the...

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The magnitude of the magnetic field at the center of an equilateral triangular loop of side 1 m which is...

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Let $S_n=1+q+q^2+\ldots+q^n$ and $T_n=1+\left(\frac{q+1}{2}\right)+\left(\frac{q+1}{2}\right)^2+\ldots .+\left(\frac{q+1}{2}\right)^n$ where $q$ is a real number and $q \neq 1$. If $...

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A coil of self inductance 10 mH and resistance $0.1 \Omega$ is connected through a switch to a battery of...

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If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13,...

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A bag contains 30 white ball and 10 red balls. 16 balls are drawn one by one randomly from the...

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Space between two concentric conducting spheres of radii a and $\mathrm{b}(\mathrm{b}>\mathrm{a})$ is filled with a medium of resistivity $\rho$. The...

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Let $\alpha$ and $\beta$ the roots of the quadratic equation $x^2 \sin \theta-x(\sin \theta \cos \theta+1)+\cos \theta=0\left(0

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The integral $\int_{\pi / 6}^{\pi / 4} \frac{d x}{\sin 2 x\left(\tan ^5 \times \cot ^5 x\right)}$ equals :

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A 2 mW laser operates at a wavelength of 500 nm . The number of photons that will be emitted...

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The number of function f from {1, 2, 3, ...,20} onto {1, 2, 3, ..., 20} such that f(k) is...

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A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures...

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A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E,...

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If 19 th term of a non-zero A.P. is zero, then its $\left(49^{\text {th }}\right.$ term) $(29$ th term $)$...

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When heat $Q$ is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by $...

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Given $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$ for $\triangle A B C$ with usual natation. If $\frac{\cos A}{\alpha}=\frac{\cos B}{\beta}=\frac{\cos C}{12}$, then the ordered triplet $(\alpha$,...

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Water from a tap emerges vertically downwards with an initial speed of $1.0 \mathrm{~ms}^{-1}$. The crosssectional area of the tap...

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Let $(x+10)^{50}+(x-10)^{50} =a_0+a_1 x+a_2 x^2+\ldots+a_{50} x^{50}$, for all $x \in R$ : then $\frac{a_2}{a_0}$ is equal to :

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Two lines $\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-3}{4}$ and $\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4}$ intersect at the point $R$. The reflection of $R$ in the $x y$-plane has coordinates...

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$\lim _{x \rightarrow 0} \frac{x \cot (4 x)}{\sin ^2 x \cot ^2(2 x)}$ is equal to

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If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2,...

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Contrapositive of the statement “If two numbers are not equal, then their squares are not equal.” is :

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Let $f(x)=\frac{x}{\sqrt{a^2+x^2}}-\frac{(d-x)}{\sqrt{b^2+(d-x)^2}}, x \in R$ where $a, b$ and $d$ are non-zero real constants. Then :

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Two blocks $A$ and $B$ of masses $m_A=1 \mathrm{~kg}$ and $\mathrm{m}_{\mathrm{B}}=3 \mathrm{~kg}$ are kept on the table as shown in...

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Let $z$ be a complex number such that $|z|+z=3+i($ where $i=\sqrt{-1})$. Then $|z|$ is equal to :

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In $\mathrm{Li}^{++}$, electron in first Bohr orbit is excited to a level by a radiation of wavelength $\lambda$. When the...

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If the area of the triangle whose one vertex is at the vertex of the parabola, $y^2+4\left(x-a^2\right)=0$ and the other...

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The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the...

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If $\int \frac{x+1}{\sqrt{2 x-1}} d x=f(x) \sqrt{2 x-1}+C$, where $C$ is a constant of integration, then $f(x)$ is equal to...

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If $...

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Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal...

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Which dicarboxylic acid in presence of a dehydrating agent is least reactive to give an anhydride?

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The major product of the following reaction is

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Which of the following is not an example of heterogeneous catalytic reaction?

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The total number of isomers for a square planar complex $\left[\mathrm{M}(\mathrm{F})(\mathrm{Cl})(\mathrm{SCN})\left(\mathrm{NO}_2\right)\right]$ is

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The increasing order of the $\mathrm{pK}_{\mathrm{a}}$ values of the following compounds is

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The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively, are

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Hall-Heroult’s process is given by

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The major product ‘X’ formed in the following reaction is

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The metal used for making X-ray tube window is

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Wilkinson catalyst is $\left(\mathrm{Et}=\mathrm{C}_2 \mathrm{H}_5\right)$

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The type of hybridisation and number of lone pair(s) of electrons of $X e$ in $X e O F_4$, respectively,...

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If dichloromethane (DCM) and water $\left(\mathrm{H}_2 \mathrm{O}\right)$ are used for differential extraction, which one of the following statements is correct?

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Liquids $A$ and $B$ form an ideal solution in the entire composition range. At 350 K , the vapor pressures...

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The values of $\frac{K_p}{K_c}$ for the following reactions at 300 K are, respectively (At $300 \mathrm{~K}, \mathrm{RT}=24.62 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~mol}^{-1}$...

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The electronegativity of aluminium is similar to

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Consider the given plots for a reaction obeying Arrhenius equation $\left(0^{\circ} \mathrm{C}

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Consider the following reduction processes: $$ \begin{aligned} & \mathrm{Zn}^2++2 \mathrm{e}^{-} \rightarrow \mathrm{Zn}(\mathrm{~s}) ; \mathrm{E}^{\circ}=-0.76 \mathrm{~V} \\ & \mathrm{Ca}^{2+}+2 \mathrm{e}^{-} \rightarrow...

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Let $x, y$ be positive real numbers and $m, n$ positive integers. The maximum value of the expression $...

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The chemical nature of hydrogen peroxide is

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The major product of the following reaction is

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A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant...

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A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At...

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A cubical block of side 0.5 m floats on water with $30 \%$ of its volume under water. What is...

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A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string...

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Let $A$ and $B$ be two invertible matrices of order $3 \times 3$. If $\operatorname{det}\left(A B A^{\top}\right)=8$ and $\operatorname{det}\left(A B^{-1}\right)=8$,...

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A potentiometer wire $A B$ having length $L$ and resistance $12 r$ is joined to a cell $D$ of emf...

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A uniform metallic wire has a resistance of $18 \Omega$ and is bent into an equilateral triangle. Then, the resistance...

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The standard reaction Gibbs energy for a chemical reaction at an absolute temperature T is given by $\Delta_{\mathrm{r}} \mathrm{G}^{\circ}=\mathrm{A}-\mathrm{BT}$ Where...

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A parallel plate capacitor is of area $6 \mathrm{~cm}^2$ and a separation 3 mm . The gap is filled with...

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Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on...

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25 ml of the given HCl solution requires 30 mL of 0.1 M sodium carbonate solution. What is the volume...

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The density of a material is SI units is $128 \mathrm{~kg} \mathrm{~m}^{-3}$. In certain units in which the unit of...

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The reaction $\mathrm{MgO}(\mathrm{s})+\mathrm{C}(\mathrm{s}) \rightarrow \mathrm{Mg}(\mathrm{s})+\mathrm{CO}(\mathrm{g})$, for which $\quad \Delta_{\mathrm{r}} \mathrm{H}^{\circ}=+491.1 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta_{\mathrm{r}} \mathrm{S}^{\circ}=198.0 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$, is not feasible...

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A heat source at $T=10^3 K$ is connected to another heat reservoir at $T=10^2 K$ by a copper slab which...

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In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used....

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Let $f$ be a differentiable function from $R$ to $R$ such that $|f(x)-f(y)| \leqslant 2|x-y|^{\frac{3}{2}}$, for all $...

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The higher concentration of which gas in air can cause stiffness of flower buds?

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An insulating, thin rod of length I has a linear charge density $\rho(x)=\rho_0 \frac{x}{I}$ on it. The rod is rotated...

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A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c)...

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Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $\mathrm{t}=0$, a sample has the...

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A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’...

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The coordination number of Th in $\mathrm{K}_4\left[\mathrm{Th}\left(\mathrm{C}_2 \mathrm{O}_4\right)_4\left(\mathrm{OH}_2\right)_2\right]$ is $\left(\mathrm{C}_2 \mathrm{O}_4^{2-}=\right.$ Oxalato $)$

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A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal...

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For the equilibrium

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If the magnetic field of a plane electromagnetic wave is given by (The speed of light $...

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In a Young’s double slit experiment, the ratio of the slit’s width is 4 : 1. The ratio of the...

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A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can...

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The hydride that is NOT electron deficient is

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In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD...

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Three Carnot engines operate in series between a heat source at a temperature $T_1$ and a heat sink at temperature...

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Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the...

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Which of the following compounds reacts with ethylmagnesium bromide and also decolourizes bromine water solution?

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In a Young's double slit experiment with slit separation 0.1 mm , one observes a bright fringe at angle $\frac{1}{40}$...

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In the given circuit the cells have zero internal resistance. The currents (in amperes) passing through resistance $R_1$ and $R_2$...

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The reaction that does NOT define calcination is:

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The logical statement (MF ST-1) $[\sim(\sim p \vee q) \vee(p \wedge r)] \wedge(\sim q \wedge r)$ is equivalent to

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A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible...

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A train moves towards a stationary observer with speed $34 \mathrm{~m} / \mathrm{s}$. The train sounds a whistle and its...

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A magnet of total magnetic moment $10^{-2} \hat{i} \mathrm{~A}-\mathrm{m} 2$ is placed in a time varying magnetic field, $...

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The homopolymer formed from 4-hydroxy-butanoic acids is :

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The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6...

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A block of mass $m$ is kept on a platform which starts from rest with constant acceleration $\frac{g}{2}$ upward, as...

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The relative stability of +1 oxidation state of group 13 elements follows the order :

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The time dependence of the position of a particle of mass $m=2$ is given by $\vec{r}(t)=2 t \hat{i}-3 t^2 \hat{j}$....

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A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m...

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Taj Mahal is being slowly disfigured and discoloured. This is primarily due to :

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Water flows into a large tank with flat bottom at the rate of $10^{-4} \mathrm{~m}^3 \mathrm{~s}^{-1}$. Water is also leaking...

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A bullet of mass 20 g has an initial speed of $1 \mathrm{~ms}^{-1}$, just before it starts penetrating a mud...

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The major product of the following reaction is :

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If the system of linear equations $$ \begin{gathered} x-4 y+7 z=g \\ 3 y-5 z=h \\ -2 x+5 y-9 z=k...

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Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0...

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A plane is inclined at an angle $\alpha=30^{\circ}$ with respect to the horizontal. A particle is projected with a speed...

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A plano convex lens of refractive index $\mu_1$ and focal length $f_1$ is kept in contact with another plano concave...

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$$ \begin{aligned} & \underline{\mathrm{A}} \xrightarrow{4 \mathrm{KOH}, \mathrm{O}_2} \underset{(\text { Green })}{2 \mathrm{~B}}+2 \mathrm{H}_2 \mathrm{O} \\ & \underline{3 \mathrm{~B}} \xrightarrow{4 \mathrm{HCl}}...

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A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field...

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The major product obtained in the following reaction is:

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A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of...

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If $0 \leq x

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The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and...

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To get output ‘1’ at R, for the given logic gate circuit the input values must be

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The number of bridging CO ligand(s) and Co -Co bond(s) in $\mathrm{Co}_2(\mathrm{CO})_8$, respectively are:

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One mole of an ideal gas passes through a process where pressure and volume obey the relation $\mathrm{P}=\mathrm{P}_0\left[1-\frac{1}{2}\left(\frac{\mathrm{v}_0}{\mathrm{v}}\right)^2\right]$. Here $\mathrm{P}_0$...

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$f$ the lines $x=a y+b, z=c y+d$ and $x=a^{\prime} z+b^{\prime}, y=c^{\prime} z+d^{\prime}$ are perpendicular, then

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Two electric dipoles, $A, B$ with respective dipole moments $\overrightarrow{\mathrm{d}}_{\mathrm{A}}=-4 q a \hat{\mathrm{i}}$ and $\overrightarrow{\mathrm{d}}_{\mathrm{B}}=-2 q a \hat{\mathrm{i}}$ are placed...

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Which of the following compounds will produce a precipitate with $\mathrm{AgNO}_3$ ?

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The correct match between Item I and Item II is:

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If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a...

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Let $f:[0,1] \rightarrow R$ be such that $f(x y)=f(x) \cdot f(y)$, for all $x, y \in[0,1]$, and $f(0) \neq 0$....

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If $f(x)=\int \frac{5 x^8+7 x^6}{\left(x^2+1+2 x\right)^2} d x,(x \geq 0)$, and $f(0)=0$, then the value of $f(1)$ is

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If $f: R \rightarrow R$ is a differentiable function and $f(2)=6$, then $...

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If the tangent to the parabola $\mathrm{y}^2=\mathrm{x}$ at a point $(\alpha, \beta),(\beta>0)$ is also a tangent to the ellipse, $...

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The correct match between Item I and Item II is:

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The value of sin10° sin30° sin50° sin70° is

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If the two lines $x+(a-1) y=1$ and $2 x+a^2 y=1(a \in R-\{0,1\})$ are perpendicular, then the distance of their point...

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The area (in sq. units) of the region $A=\left\{(x, y): \frac{y^2}{2} \leq x \leq y+4\right\}$ is

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The correct option with respect to the Pauling electronegativity values of the elements is:

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The value of the integral $\int_0^1 x \cot ^{-1}\left(1-x^2+x^4\right) d x$ is

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The de Broglie wavelength ( $\lambda$ ) associated with a photoelectron varies with the frequency ( $v$ ) of the...

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The position co-ordinates of a particle moving in a 3-D coordinate system is given by x = a cos ωt,...

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Match the following items in column I with the corresponding items in column II.

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The top of a water tank is open to air and its water level is maintained. It is giving out...

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$\mathrm{K}_2 \mathrm{Hgl}_4$ is $40 \%$ ionised in aqueous solution. The value of its van't Hoff factor (i) is :

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A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $\tan ^{-1}\left(\frac{1}{2}\right)$. Water is...

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Two newspapers A and B are published in a city. It is known that 25% of the city population reads...

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A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the...

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Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the...

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The mean and the median of the following ten numbers in increasing order $10,22,26,29,34, x, 42,67,70, y$ are 42 and...

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In the following compound, the favourable site/s for protonation is/are :

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If $p \Rightarrow(q \vee r)$ is false, then truth values of $p, q, r$ are respectively:

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7 Charge is distributed within a sphere of radius $R$ with volume charge density $\rho(r)=\frac{A}{r^2} e^a$, where $A$ and a...

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The reaction $2 X \rightarrow B$ is a zeroth order reaction. If the initial concentration of $X$ is $0.2 M$,...

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The area (in sq. units) of the smaller of the two circles that touch the parabola, $y^2=4 x$ at the...

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Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror (M1)...

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The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic...

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The sum of the series 1 + 2 × 3 + 3 × 5 + 4 × 7 + ......

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Among the colloids cheese (C), milk (M) and smoke (S), the correct combination of the dispersed phase and dispersion medium,...

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The domain of the definition of the function $f(x)=\frac{1}{4-x^2}+\log _{10}\left(x^3-x\right)$ is :

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Given the equilibrium constant : $\mathrm{K}_{\mathrm{C}}$ of the reaction:- $\mathrm{Cu}(\mathrm{s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s})$ is $10 \times 10^{15}$ calculate the...

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A rod of mass ‘M’ and length ‘2L’ is suspended at its middle by a wire. It exhibits torsional oscillations;...

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The common tangent to the circles $x^2+y^2=4$ and $x^2+y^2+6 x+8 y-24=0$ also passes through the point :

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To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force...

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If $f(x)=[x]-\left[\frac{x}{4}\right], x \in R$, where $[x]$ denotes the greatest integer function, then :

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A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear...

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Let P be the plane, which contains the line of intersection of the planes, x + y + z –...

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The circuit shown below contains two ideal diodes, each with a forward resistance of $50 \Omega$. If the battery voltag...

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Expression for time in terms of G(universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:

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Let $z \in C$ be such that $|z|

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A circular disc $D_1$ of mass $M$ and radius $R$ has two identical discs $D_2$ and $D_3$ of the same...

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If the function $f(x)=\left\{\begin{array}{ll}a|\pi-x|+1, & x \leq 5 \\ b|x-\pi|+3, & x>5\end{array}\right.$ is continuous at $x=5$, then the value of...

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Q JEE MAIN 2019

If a unit vector $\vec{a}$ makes angles $\frac{\pi}{3}$ with $\hat{i}, \frac{\pi}{4}$ with $\hat{j}$ and $\theta \in(0, \pi)$ with $\hat{k}$, then...

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The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force...

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A rectangle is inscribed in a circle with a diameter lying along the line 3y = x + 7. If...

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In the given circuit the internal resistance of the 18 V cells is negligible. If $\mathrm{R}_1=400 \Omega, \mathrm{R}_3=100 \Omega$ and...

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Q JEE MAIN 2019

If some three consecutive coefficients in the binomial expansion of $(x+1)^n$ in powers of $x$ are in the ratio $...

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Q JEE MAIN 2019

A particle moves from the point $(2.0 \mathrm{i}+4.0 \mathrm{j}) \mathrm{m}$, at $\mathrm{t}=0$, with an initial velocity $(5.0 \mathrm{i}+4.0 \mathrm{j}) \mathrm{ms}^{-1}$....

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Q JEE MAIN 2019

If $\int e^{\sec x}\left(\sec x \tan x f(x)+\sec x \tan x+\sec ^2 x\right) d x \quad=e^{\sec x} f(x)+C$, then a...

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Q JEE MAIN 2019

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In a double-slit experiment, green light $(5303 \AA)$ falls on a double slit having a separation of $19.44 \mu \mathrm{~m}$...

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Q JEE MAIN 2019

A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the...

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The vertices $B$ and $C$ of a $\triangle A B C$ lie on the line, $\frac{x+2}{3}=\frac{y-1}{0}=\frac{z}{4}$ such that $B C=5$...

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Q JEE MAIN 2019

A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having...

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A pendulum is executing simple harmonic motion and its maximum kinetic energy is $\mathrm{K}_1$. If the length of the pendulum...

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Q JEE MAIN 2019

If $m$ is chosen in the quadratic equation $\left(m^2+1\right) x^2-3 x+\left(m^2+1\right)^2=0$ such that the sum of its roots is greatest,...

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Q JEE MAIN 2019

If the system of equations 2x+3y-z=0, x+ky-2z=0 and $2 x-y+z=0$ has a non-trivial solution $(x, y, z)$, then $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}+k$ is...

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Q JEE MAIN 2019

Seven capacitors, each of capacitance $2 \mu \mathrm{~F}$, are to be connected in a configuration to obtain an effective capacitance...

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Q JEE MAIN 2019

Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their...

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A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by $$ \vec{E}=2 \hat{j}+3...

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A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle...

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The maximum number of possible oxidation states of actinoides are shown by

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

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In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance...

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The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and...

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10 mL of 1 mM surfactant solution forms a monolayer covering $0.24 \mathrm{~cm}^2$ on a polar substrate. If the polar...

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Q JEE MAIN 2019

An amplitude modulated signal is plotted below: Which one of the following best describes the above signal?

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Q JEE MAIN 2019

In the circuit shown, the potential difference between A and B is:

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A thermometer graduated according to a linear scale reads a value $x_0$ when in contact with boiling water, and $...

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A galvanometer having a resistance of $20 \Omega$ and 30 divisions on both sides has figure of merit 0.005 ampere/division....

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Q JEE MAIN 2019

In a car race on straight road, car A takes a time t less than car B at the finish...

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In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation...

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The magnetic field associated with a light wave is given, at the origin, by $...

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Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180°C and B...

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A force acts on a 2 kg object so that its position is given as a function of time as...

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In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 30 nm . The...

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The energy required to take a satellite to a height ' $h$ ' above Earth surface (radius of Earth $...

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In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation...

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The mass and the diameter of a planet are three times the respective values for the Earth. The period of...

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A 27 mW laser beam has a cross-sectional area of $10 \mathrm{~mm}^2$. The magnitude of the maximum electric field in...

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When 100 g of a liquid A at 100°C is added to 50 g of a liquid B at temperature...

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If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young’s modulus will be

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A simple pendulum of length 1 m is oscillating with an angular frequency $10 \mathrm{rad} / \mathrm{s}$. The support of...

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A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is...

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A metal ball of mass 0.1 kg is heated upto $500^{\circ} \mathrm{C}$ and dropped into a vessel of heat capacity...

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A particle of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t=0$, a force...

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p-Hydroxybenzophenone upon reaction with bromine in carbon tetrachloride gives

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An electric field of $1000 \mathrm{~V} / \mathrm{m}$ is applied to an electric dipole at angle of $45^{\circ}$. The value...

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The structures of beryllium chloride in the solid state and vapour phase, respectively, are

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A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of $...

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In the following reaction carbonyl compound $+\mathrm{MeOH} \stackrel{\mathrm{HCl}}{\rightleftharpoons}$ acetal Rate of the reaction is the highest for

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The correct statements among I to III are (I) Valence bond theory cannot explain the color exhibited by transition metal...

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The amorphous form of silica is

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The value of $\lambda$ such that sum of the squares of the roots of the quadratic equation, $x^2+(3-\lambda) x+2=\lambda$ has...

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At a given temperature T , gases $\mathrm{Ne}, \mathrm{Ar}, \mathrm{Xe}$ and Kr are found to deviate from ideal gas behaviour....

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Assertion : For the extraction of iron, haematite ore is used. Reason : Haematite is a carbonate ore of iron.

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In a communication system operating at wavelength 800 nm , only one percent of source frequency is available as signal...

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The value of $\cos \frac{\pi}{2^2} \cdot \cos \frac{\pi}{2^3} \ldots \ldots \cos \frac{\pi}{2^{10}} \cdot \sin \frac{\pi}{2^{10}}$ is

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The layer of atmosphere between 10 km to 50 km above the sea level is called as

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Q JEE MAIN 2019

Q.12 A carbon resistance has a following colour code. What is the value of the resistance?

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Hinsberg’s reagent is

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If mean and standard deviation of 5 observations $x_1, x_2, x_3, x_4, x_5$ are 10 and 3 , respectively, then...

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In an acid-base titration, 0.1 M HCl solution was added to the NaOH solution of unknown strength. Which of the...

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A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its...

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If $\int_0^x f(t) d t=x^2+\int t^2 f(t) d t$ then $f(1 / 2)$ is :

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Molal depression constant for a solvent is $4.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$. The depression in the freezing point of the solvent...

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At a given instant, say $t=0$, two radioactive substances $A$ and $B$ have equal activities. The ratio $\frac{R_B}{R_A}$ of their...

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Which of the following potential energy (PE) diagrams represents the $\mathrm{S}_{\mathrm{N}} 1$ reaction?

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Increasing order of reactivity of the following compounds for $\mathrm{S}_{\mathrm{N}} 1$ substitution is

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A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature $27^{\circ} \mathrm{C}$. Amount of heat...

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The major products A and B for the following reactions are, respectively

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Let N be the set of natural numbers and two functions f and g be defined as $...

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The correct statements among I to III regarding group 13 element oxides are, (I) Boron trioxide is acidic. (II) Oxides...

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Two vertices of a triangle are (0, 2) and (4, 3). If its orthocentre is at the origin, then its...

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Two Carnot engines A and B are operated in series. The first one, A, receives heat at $T_1(=600 \mathrm{~K})$ and...

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Among the following species, the diamagnetic molecule is

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If $\sum_{\mathrm{r}=0}^{25}\left\{{ }^{50} \mathrm{C}_{\mathrm{r}} \cdot{ }^{50-\mathrm{r}} \mathrm{C}_{25-\mathrm{r}}\right\}=\mathrm{K}\left({ }^{50} \mathrm{C}_{25}\right)$, then K is equal to:

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Q JE MAIN 2019

A mass of 10 kg is suspended vertically by a rope trom the root. When a horizontal force is applied...

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Noradrenaline is a / an

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Let $f$ be a differentiable function such tht $f^{\prime}(x)=7-\frac{3 f(x)}{4 x},(x>0)$ and $f(1) \neq 4$. Then $...

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Q JEE MAIN 2019

The one that is not a carbonate ore is

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Two point charges $q_1(\sqrt{10} \mu \mathrm{C})$ and $q_2(-25 \mu \mathrm{C})$ are placed on the $x$-axis at $x=1 \mathrm{~m}$ and $...

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Q JEE MAIN 2019

HF has highest boiling point among hydrogen halides, because it has

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The value of $\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \frac{d x}{[x]+[\sin x]+4}$ where $[t]$ denotes the greatest integer less than or equal to $t$, is...

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A solution of $\mathrm{Ni}\left(\mathrm{NO}_3\right)_2$ is electrolysed between platinum electrodes using 0.1 Faraday electricity. How many mole of Ni will be...

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Let $A=\left[\begin{array}{ccc}2 & b & 1 \\ b & b^2+1 & b \\ 1 & b & 2\end{array}\right]$ where $b>0$....

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What would be the molality of $20 \%$ (mass/mass) aqueous solution of KI? (molar mass of $\mathrm{KI}=166 \mathrm{~g} \mathrm{~mol}^{-1}$ )

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With the usual notation, in $\triangle A B C$, if $\angle A+\angle B=120^{\circ}, a=\sqrt{3}+1$ and $b=\sqrt{3}-1$, then the ratio $...

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During compression of a spring the work done is 10 kJ and 2 kJ escaped to the surroundings as heat....

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Which of the following compounds is a constituent of the polymer

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Let $a_1, a_2, a_3 \ldots a_{10}$ in G.P with $a_i>0$ for $i=1,2, \ldots \ldots, 10$ and $S$ be the set...

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Q JEE MAIN 2019

The peptide that gives positive ceric ammonium nitrate and carbylamine tests is

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Two sides of a parallelogram are along the lines, $x+y=3$ and $x-y+3=0$. If its diagonals intersect at (2,4) then one...

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The major product of the following reaction is :

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Let $S=\left\{(x, y) \in R^2: \frac{y^2}{1+r}-\frac{x^2}{1-r}=1\right\}$, where where $r \neq \pm 1$. Then $S$ represents

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For point charges $-q,+q,+q$ and $-q$ are placed on $y$-axis at $y=-2 d, y=-d, y=+d$ and $y=+2 d$, respectively. The...

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On which of the following lines lies the point of intersection of the line, $\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1}$ and the plane, $...

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Q JEE MAIN 2019

A very long solenoid of radius $R$ is carrying current $I(t)=k t e^{-\alpha t}(k>0)$, as a function of time $...

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The logic gate equivalent to the given logic circuit is

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If $\int x^5 e^{-4 x^3} d x=\frac{1}{48} e^{-4 x^3} f(x)+C$ where $C$ is a constant of integration, then $f(x)$ is...

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Q JEE MAIN 2019

A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates...

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The length of the chord of the parabola $x^2=4 y$ having equation $x-\sqrt{2} y+4 \sqrt{2}=0$ is

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A particle of mass ‘m’ is moving with speed ‘2v’ and collides with a mass ‘2m’ moving with speed ‘v’...

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The curve amongst the family of curves represented by the differential equation, $\left(x^2-y^2\right) d x+2 x y d y=0$ which...

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A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of...

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The value of $\cot \left(\sum_{n=1}^{19} \cot ^{-1}\left(1+\sum_{p=1}^n 2 p\right)\right)$ is

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Two coils ' $P$ ' and ' $Q$ ' are separated by some distance. When a current of $3 A$...

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Let $f:(-1,1) \rightarrow R$ be a function defined by $f(x)=\max \left\{-|x|,-\sqrt{1-x^2}\right\}$. If $K$ be the set of all points at...

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Q JEE MAIN 2019

If the probability of hitting a target by a shooter, in any shot, is $\frac{1}{3}$, then the minimum number of...

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Let $\mathrm{z}=\left(\frac{\sqrt{3}}{2}+\frac{\mathrm{i}}{2}\right)^5+\left(\frac{\sqrt{3}}{2}-\frac{\mathrm{i}}{2}\right)^5$. If $\mathrm{R}(\mathrm{z})$ and $\mathrm{I}(\mathrm{z})$ respectively denote the real and imaginary parts of z , then

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Q JEE MAIN 2019

The plane which bisects the line segment joining the points (–3, –3, 4) and (3, 7, 6) at right angles,...

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The positive value of $\lambda$ for which the co-efficient of $x^2$ in the expression $x^2\left(\sqrt{x}+\frac{\pi}{x^2}\right)^{10}$ is 720 , is

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The number of values of $\theta \in(0, \pi)$ for which the system of linear equations $$ \begin{aligned} & x+3 y+7...

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\text { If the area of an equilateral triangle inscribed in the circle, } x^2+y^2+10 x+12 y+c=0 \text { is...

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Let $\alpha=(\lambda-2) \mathrm{a}+\mathrm{b}$ and $\beta=(4 \lambda-2) \mathrm{a}+3 \mathrm{~b}$ be two given vectors where vectors a and b are non-collinear. The...

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The major product of the following reaction is :

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Which is the most suitable reagent for the following transformation?

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A thin convex lens $L$ (refractive index $=1.5$ ) is placed on a plane mirror $M$. When a pin is...

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Q JEE MAIN 2019

The reaction that is NOT involved in the ozone layer depletion mechanism in the stratosphere is :

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A series AC circuit containing an inductor (20 mH), a capacitor (120 μF) and a resistor (60 Ω) is driven...

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A compound of formula A2B3 has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedral...

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Elevation in the boiling point for 1 molal solution of glucose is 2 K . The depression in the freezing...

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In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength $\lambda=500 \mathrm{~nm}$ is incident...

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The major product of the following reaction

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Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode...

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In a conductor, if the number of conduction electrons per unit volume is $8.5 \times 10^{28} \mathrm{~m}^{-3}$ and mean free...

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One of the two identical conducting wires of length $L$ is bent in the form of a circular loop and...

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What is the IUPAC name of the following compound?

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A moving coil galvanometer has a coil with 175 turns and area 1 cm 2 . It uses a torsion...

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A particle ' P ' is formed due to a completely inelastic collision of particles ' x ' and '...

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For an elementary chemical reaction, $A_2 \underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons}} 2 A$, the expression for $\frac{d[A]}{d t}$ is :

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A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the...

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Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm. coming from a...

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Q JEE MAIN 2019

Haemoglobin and gold sol are examples of :

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The area of a square is $5.29 \mathrm{~cm}^2$. The area of 7 such squares taking into account the significant figures...

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The difference in the number of unpaired electrons of a metal ion in its high spin and low-spin octahedral complexes...

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Two materials having coefficients of thermal conductivity ' 3 K ' and ' K ' and thickness ' d '...

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The major product obtained in the following reaction is:

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A wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When certain amount of an...

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The amount of sugar $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ required to prepare 2 L of its 0.1 M aqueous solution is:

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Q JEE MAIN 2019

Which of the following tests cannot be used for identifying amino acids?

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A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge...

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The physical sizes of the transmitter and receiver antenna in a communication system are:

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The 71st electron of an element X with an atomic number of 71 enters into the orbital:

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The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery...

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The position of a particle as a function of time $t$, is given by $$ x(t)=a t+b t^2-c t^3 $$...

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The number of 2-centre-2-electron and 3-centre-2-electron bonds in B2H6 respectively are:

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A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept...

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What will be the major product in the following mononitration reaction?

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Two cars $A$ and $B$ are moving away from each other in opposite directions. Both the cars are moving with...

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$5.1 \mathrm{~g} \mathrm{NH}_4 \mathrm{SH}$ is introduced in 3.0 L evacuated flask at $327^{\circ} \mathrm{C} .30 \%$ of the solid $...

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$\mathrm{A} \mathrm{He}^{+}$ion is in its first excited state. Its ionization energy is :

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In the reaction of oxalate with permanganate in acidic medium, the number of electrons involved in producing one molecule of...

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The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002...

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Sodium metal on dissolution in liquid ammonia gives a deep blue solution due to the formation of

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A reaction of cobalt (III) chloride and ethylenediamine in a 1 : 2 mole ratio generates two isomeric products A...

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Moment of inertia of a body about a given axis is 1.5 kg m2. Initially the body is at rest....

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The major product of the following reaction is :

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A thin smooth rod of length L and mass M is rotating freely with angular speed 0 about an axis...

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A metal wire of resistance $3 \Omega$ is elongated to make a uniform wire of double its previous length. This...

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The electrolytes usually used in the electroplating of gold and silver, respectively, are :

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$50 \mathrm{~W} / \mathrm{m}^2$ energy density of sunlight is normally incident on the surface of a solar panel. Some part...

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The position vector of a particle changes with time according to the relation $\vec{r}(t)=15 t^2 \hat{i}+\left(4-20 t^2\right) \hat{j}$. What is...

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The specific heats, $\mathrm{C}_{\mathrm{P}}$ and $\mathrm{C}_{\mathrm{V}}$ of a gas of diatomic molecules, A , are given (in units of $...

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The correct match between item ‘I’ and item ‘II’ is :

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A test particle is moving in a circular orbit in the gravitational field produced by a mass density $\rho(r)=\frac{K}{r^2}$. Identify...

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In the cell $\mathrm{Pt}(\mathrm{s})\left|\mathrm{H}_2(\mathrm{~g}, 1 \mathrm{bar})\right| \mathrm{HCl}(\mathrm{aq})|\mathrm{AgCl}(\mathrm{s})| \mathrm{Ag}(\mathrm{s}) \mid \mathrm{Pt}(\mathrm{s})$ the cell potential is 0.92 V when a $10^{-6}$ molal...

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The equation of the line passing through $(-4,3,1)$, parallel to the plane $x+2 y-z-5=0$ and intersecting the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z-2}{-1}$ is...

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The length of the perpendicular from the point ( $2,-$ 1,4) on the straight line, $\frac{x+3}{10}=\frac{y-2}{-7}=\frac{z}{1}$ is

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If a, b and c be three distinct real numbers in G.P. and a + b + c = xb,...

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The ground state energy of hydrogen atom is -13.6 eV . The energy of second excited state of $\mathrm{He}^{+}$ion in...

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The sum of all natural numbers ' $n$ ' such that $100< n1$ is :

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For $x^2 \neq n \pi+1, n \in N$ (the set of natural numbers), the integral $...

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$\lim _{x \rightarrow 0} \frac{\sin ^2 x}{\sqrt{2}-\sqrt{1+\cos x}}$ equals :

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An aromatic compound 'A' having molecular formula $\mathrm{C}_7 \mathrm{H}_6 \mathrm{O}_2$ on treating with aqueous ammonia and heating forms compound '...

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If $\cos ^{-1}\left(\frac{2}{3 x}\right)+\cos ^{-1}\left(\frac{3}{4 x}\right)=\frac{\pi}{2}\left(x>\frac{3}{4}\right)$, then $x$ is equal to :

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The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4,...

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The magnitude of the projection of the vector $2 \hat{i}+3 \hat{j}+\hat{k}$ on the vector perpendicular to the plane containing the...

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The process with negative entropy change is :

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If the Boolean expression $(p \oplus q) \wedge(\sim p \odot q)$ is equivalent to $\mathbf{p} \wedge \mathbf{q}$, where $...

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The sum of the solutions of the equation $|\sqrt{x}-2|+\sqrt{x}(\sqrt{x}-4)+2=0,(x>0)$ is equal to:

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The diameter and height of a cylinder are measured by a meter scale to be $12.6 \pm 0.1 \mathrm{~cm}$ and...

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The maximum volume (in cu. m) of the right circular cone having slant height 3 m is :

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The contrapositive of the statement “If you are born in India, then you are a citizen of India”, is:

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The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to...

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If $A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]$, then the matrix $A^{-50}$ when $\theta=\frac{\pi}{12}$, is equal...

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Let $\quad \mathrm{A}=\left(\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right),(\alpha \in \mathrm{R}) \quad$ such that $...

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Let $f: R \rightarrow R$ be a function defined as $$ f(x)=\left\{\begin{array}{rrr} 5, & \text { if } & x...

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If $\cos (\alpha+\beta)=\frac{3}{5}, \sin (\alpha-\beta)=\frac{5}{13}$ and $0

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Two stars of masses $3 \times 10^{31} \mathrm{~kg}$ each, and at distance $2 \times 10^{11} \mathrm{~m}$ rotate in a plane...

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The equation of a plane containing the line of intersection of the planes $2 x-y-4=0$ and $y+2 z -4=0$ and...

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If $f(x)=\frac{2-x \cos x}{2+x \cos x}$ and $g(x)=\log _e x,(x>0)$ then the value of the integral $...

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A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of...

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The area (in sq. units) of the region $...

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$$ \lim _{y \rightarrow 0} \frac{\sqrt{1+\sqrt{1+y^2}}-\sqrt{2}}{y^4} $$

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If $\alpha$ and $\beta$ be the roots of the equation $x^2-2 x+2=$ 0 , then the least value of $n$...

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Let $A$ and $B$ be two non-null events such that $A \subset$ B. Then, which of the following statements is...

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If $y=y(x)$ is the solution of the differential equation, $x \frac{d y}{d x}+2 y=x^2$ satisfying $y(1)=1$, then $y\left(\frac{1}{2}\right)$ is equal...

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Let $\mathrm{O}(0,0)$ and $\mathrm{A}(0,1)$ be two fixed points. Then the locus of a point P such that the perimeter of...

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Equation of a common tangent to the circle, $x^2+y^2-6 x=0$ and the parabola, $y^2=4 x$, is:

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Consider a Young's double slit experiment as shown in figure. What should be the slit separation $d$ in terms wavelength...

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The greatest value of $c \in R$ for which the system of linear equations $$ \begin{aligned} & x-c y-c z=0...

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The plane through the intersection of the planes x + y + z = 1 and 2x + 3y –...

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All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at...

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The system of linear equations $$ \begin{aligned} & x+y+z=2 \\ & 2 x+3 y+2 z=5 \\ & 2 x+3 y+\left(a^2-1\right)...

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A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from...

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The sum of the series $...

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Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from...

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Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of...

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Let $f:[0,2] \rightarrow R$ be a twice differentiable function such that $f^{\prime \prime}(x)>0$, for all $x \in(0,2)$. If $\phi(x)=f(x)+ \mathrm{f}(2-x)$,...

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If $\alpha=\cos ^{-1}\left(\frac{3}{5}\right), \beta=\tan ^{-1}\left(\frac{1}{3}\right)$, where $0

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A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The...

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Let $y=y(x)$ be the solution of the differential equation, $\left(x^2+1\right)^2 \frac{d y}{d x}+2 x\left(x^2+1\right) y=1$ such that $y(0)=0$. If $...

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Two kg of a monoatomic gas is at a pressure of $4 \times 10^4 \mathrm{~N} / \mathrm{m}^2$. The density of...

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If $f(x)=\log _e\left(\frac{1-x}{1+x}\right),|x|

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The sum of the squares of the lengths of the chords intercepted on the circle, $x^2+y^2=16$, by the lines, $...

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A metal plate of area $1 \times 10^{-4} \mathrm{~m}^2$ is illuminated by a radiation of intensity $...

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If the tangents on the ellipse $4 x^2+y^2=8$ at the points $(1,2)$ and $(\mathrm{a}, \mathrm{b})$ are perpendicular to each other,...

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A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power...

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A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard...

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A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V...

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A particle which is experiencing a force, given by $\vec{F}=3 \vec{i}-12 \vec{j}$, undergoes a displacement of $\overrightarrow{\mathrm{d}}=4 \overrightarrow{\mathrm{i}}$. If the...

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Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable...

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The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate...

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For any $\theta \in\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$, the expression $3(\sin \theta-\cos \theta)^4+6(\sin \theta+\cos \theta)^2+4 \sin ^6 \theta$ equals :

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The actual value of resistance R, shown in the figure is 30 $\Omega$.. This is measured in an experiment as...

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An unknown metal of mass 192 g heated to a temperature of 100°C was immersed into a brass calorimeter of...

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For the circuit shown below, the current through the Zener diode is:

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$\int \frac{\sin \frac{5 x}{2}}{\sin \frac{x}{2}} d x$ is equal to: (where c is a constant of integration)

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Let $\vec{a}=\vec{i}-\vec{j}, \vec{b}=\vec{i}+\vec{j}+\vec{k}$ and $\vec{c}$ be a vector such that $\vec{a} \times \vec{c}+\vec{b}=\overrightarrow{0}$ and $\vec{a} \cdot \vec{c}=4$, then $|\vec{c}|^2$ is...

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A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their...

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A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate axes will lie...

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Let $a_1, a_2 \ldots . a_{30}$ be an A.P., $S=\sum_{i=1}^{30}$ ai and $T=\sum_{i=1}^{15} a_{(2 i-1)}$. If $a_5=27$ and $S-2 T=75$,...

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If $2 y=\left(\cot ^{-1}\left(\frac{\sqrt{3} \cos x+\sin x}{\cos x-\sqrt{3} \sin x}\right)\right)^2, x \in\left(0, \frac{\pi}{2}\right)$ then $\frac{\mathrm{dy}}{\mathrm{dx}}$ is equal to:

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Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20°C to 90°C. Work...

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The value of $\int_0^\pi|\cos x|^3 d x$ is :

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Let $0

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If $S_1$ and $S_2$ are respectively the sets of local minimum and local maximum points of the function, $...

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The sum of the co-efficients of all even degree terms in x in the expansion of $\left(x+\sqrt{x^3-1}\right)^6+\left(x-\sqrt{x^3-1}\right)^6,(x>1)$ is equal to...

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A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond...

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The shortest distance between the line $\mathrm{y}=\mathrm{x}$ and the curve $y^2=x-2$ is :

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The area (in sq. units) bounded by the parabola $y=x^2-1$, the tangent at the point $(2,3)$ to it and the...

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In the following compounds, the decreasing order of basic strength will be

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Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3...

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An organic compound neither reacts with neutral ferric chloride solution nor with Fehling solution. It however, reacts with Grignard reagent...

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Charges –q and +q located at A and B, respectively, constitute an electric dipole. Distance AB = 2a, O is...

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Let $\alpha$ and $\beta$ be two roots of the equation $x^2+2 x+2=0$, then $\alpha^{15}+\beta^{15}$ is equal to

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Let $A=\left\{\theta \in\left(-\frac{\pi}{2}, \pi\right): \frac{3+2 i \sin \theta}{1-2 i \sin \theta}\right.$ is purely imaginary $\}$ Then the sum of the...

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The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by...

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Assertion : Ozone is destroyed by CFCs in the upper stratosphere. Reason : Ozone holes increase the amount of UV...

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Three circles of radii a, b, c (a < b < c) touch each other externally. If they have x-axis...

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If the fractional part of the number $\frac{2^{403}}{15}$ is $\frac{k}{15}$, then $k$ is equal to

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5 students of a class have an average height 150 cm and variance $18 \mathrm{~cm}^2$. A new student, whose height...

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Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and...

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Which of the following amines can be prepared by Gabriel phthalimide reaction?

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The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as $\mathrm{R}_1$ has the colour code...

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The size of the iso-electronic species $\mathrm{Cl}^{-}, \mathrm{Ar}$ and $\mathrm{Ca}^{2+}$ is affected by

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Diborane $\left(\mathrm{B}_2 \mathrm{H}_6\right)$ reacts independently with $\mathrm{O}_2$ and $\mathrm{H}_2 \mathrm{O}$ to produce, respectively:

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At some location on earth the horizontal component of earth’s magnetic field is 18 × 10–6 T. At this location,...

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100 mL of a water sample contains 0.81 g of calcium bicarbonate and 0.73 g of magnesium bicarbonate. The hardness...

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In order to oxidise a mixture of one mole of each of $\mathrm{FeC}_2 \mathrm{O}_4$, $\mathrm{Fe}_2\left(\mathrm{C}_2 \mathrm{O}_4\right)_3$, $\mathrm{FeSO}_4$ and $\mathrm{Fe}_2\left(\mathrm{SO}_4\right)_3$ in...

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If solubility product of $\mathrm{Zr}_3\left(\mathrm{PO}_4\right)_4$ is denoted by $\mathrm{K}_{\mathrm{sp}}$ and its molar solubility is denoted by S , then which...

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Element ‘B’ forms ccp structure and ‘A’ occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral...

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The correct order of hydration enthalpies of alkali metal ions is

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The lanthanide ion that would show color is

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For silver, $\mathrm{C}_{\mathrm{D}}\left(\mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)=23+0.01 \mathrm{~T}$. If the temperature (T) of 3 moles of silver is raised from 300 K to...

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The vapour pressures of pure liquids A and B are 400 and 600 mmHg, respectively at 298 K. On mixing...

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Maltose on treatment with dilute HCl gives

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Coupling of benzene diazonium chloride with 1-naphthol in alkaline medium will give

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Given that $\mathrm{E}_{\mathrm{O}_2 / \mathrm{H}_2 \mathrm{O}}^{\ominus}=+1.23 \mathrm{~V}$; $$ \begin{aligned} & \mathrm{E}_{\mathrm{S}_2 \mathrm{O}_8^{2-} / \mathrm{SO}_4^{2-}}^{\odot}=2.05 \mathrm{~V} \\ & \mathrm{E}_{\mathrm{Br}_2 / \mathrm{Br}^{-}}^{\odot}=+1.09...

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Which is wrong with respect to our responsibility as a human being to protect our environment?

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The correct order of the spin-only magnetic moment of metal ions in the following low-spin complexes, $\left[\mathrm{V}(\mathrm{CN})_6\right]^{4-},\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-},\left[\mathrm{Ru}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ and $\left[\mathrm{Cr}\left(\mathrm{NH}_3\right)_6\right]^{2+}$, is:

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Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving...

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With respect to an ore, Ellingham diagram helps to predict the feasibility of its

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A boy’s catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of crosssection and...

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In an interference experiment the ratio of amplitudes of coherent waves is $\frac{a_1}{a_2}=\frac{1}{3}$. The ratio of maximum and minimum intensities...

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A thermally insulated vessel contains 150 g of water at $0^{\circ} \mathrm{C}$. Then the air from the vessel is pumped...

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A circular coil having $N$ turns and radius $r$ carries a current I. It is held in the XZ plane...

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A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential...

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Two identical beakers A and B contain equal volumes of two different liquids at $60^{\circ} \mathrm{C}$ each and left to...

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For the circuit shown, with $\mathrm{R} 1=1.0 \Omega, \mathrm{R} 2=2.0 \Omega$, $\mathrm{E} 1=2 \mathrm{~V}$ and $\mathrm{E} 2=\mathrm{E} 3=4 \mathrm{~V}$, the...

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A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to...

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The reverse breakdown voltage of a Zener diode is 5.6 V in the given circuit

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The bob of a simple pendulum has mass 2 g and a charge of $5.0 \mu \mathrm{C}$. It is at...

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Four identical particles of mass M are located at the corners of a square of side ‘a’. What should be...

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An alternating voltage $\mathrm{v}(\mathrm{t})=220 \sin 100 \pi \mathrm{t}$ volt is applied to a purely resistive load of $50 \Omega$. The...

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A thin circular plate of mass $M$ and radius $R$ has its density varying as $\rho(r)=\rho_0 r$ with $\rho_0$ as...

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A steel wire having a radius of 2.0 mm , carrying a load of 4 kg , is hanging from...

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The wavelength of the carrier waves in a modern optical fiber communication network is close to :

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Voltage rating of a parallel plate capacitor is 500 V . Its dielectric can withstand a maximum electric field of...

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A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a...

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Four particles $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D with masses $\mathrm{m}_{\mathrm{A}}=\mathrm{m}$, $\mathrm{m}_{\mathrm{B}}=2 \mathrm{~m}, \mathrm{~m}_{\mathrm{C}}=3 \mathrm{~m}$ and $\mathrm{m}_{\mathrm{D}}=4 \mathrm{~m}$ are at the...

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A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time...

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A $200 \Omega$ resistor has a certain color code. If one replaces the red color by green in the code,...

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In figure, the optical fiber is I = 2 m long and has a diameter of $\mathrm{d}=20 \mu \mathrm{~m}$. If...

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Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe...

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Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He+ ions in n...

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A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled...

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In SI units, the dimensions of $\sqrt{\frac{\epsilon_0}{\mu_0}}$ is:

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Two particles move at right angle to each other. Their de Broglie wavelengths are $\lambda_1$ and $\lambda_2$ respectively. The particles...

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Let $f: R \rightarrow R$ be a differentiable function satifying $f^{\prime}(3)+f^{\prime}(2)=0$. Then $\lim _{x \rightarrow 0}\left(\frac{1+f(3+x)-f(3)}{1+f(2-x)-f(2)}\right)^{\frac{1}{x}}$ is equal to :

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If the eccentricity of the standard hyperbola passing through the point (4, 6) is 2, then the equation of the...

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If $\int \frac{d x}{x^3\left(1+x^6\right)^{2 / 3}}=x f(x)\left(1+x^6\right)^{\frac{1}{3}}+C$ where $C$ is a constant of integration, then the function $f(x)$ is equal...

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Let $f(x)=a^x(a>0)$ be written as $f(x)=f_1(x)+f_2(x)$, where $f_1(x)$ is an even function and $f_2(x)$ is an odd function. Then $f_1(x+y)+f_1(x-y)$...

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Let $f(x)=\int_0^x g(t) d t$, where $g$ is a non-zero even function. If $f(x+5)=g(x)$, then $\int_0^x f(t) d t$, equals:

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If $f(1)=1, f^{\prime}(1)=3$, then the derivative of $f(f(f(x)))+(f(x))^2$ at $x=1$ is :

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If the system of linear equations $$ \begin{aligned} & x-2 y+k z=1 \\ & 2 x+y+z=2 \\ & 3 x-y-k...

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The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is

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If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest,...

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If a point R(4, y, z) lies on the line segment joining the points P(2, –3, 4) and Q(8, 0,...

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Let $\mathrm{S}(\alpha)=\left\{(\mathrm{x}, \mathrm{y}): \mathrm{y}^2 \leq \mathrm{x}, 0 \leq \mathrm{x} \leq \alpha\right\}$ and $\mathrm{A}(\alpha)$ is area of the region $\mathrm{S}(\alpha)$. If...

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Suppose that the points $(h, k),(1,2)$ and $(-3,4)$ lie on the line $L_1$. If a line $L_2$ passing through the...

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Given that the slope of the tangent to a curve $y=y(x)$ at any point ( $x, y$ ) is $...

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Let $f:[-1,3] \rightarrow R$ be defined as $$ f(x)=\left\{\begin{array}{cc} |x|+[x], & -1 \leq x

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Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in meters)...

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The sum $\sum_{k=1}^{20} k \frac{1}{2^k}$ is equal to :

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The minimum number of times one has to toss a fair coin so that the probability of observing at least...

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Let the numbers 2, $\mathrm{b}, \mathrm{c}$ be in an A.P. and $...

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The number of integral values of $m$ for which the equation $\left(1+m^2\right) x^2-2(1+3 m) x+(1+8 m)=0$ has no real root...

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If $z=\frac{\sqrt{3}}{2}+\frac{i}{2}(i=\sqrt{-1})$, then $\left(1+i z+z^5+i z^8\right)^9$ is equal to :

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If three distinct numbers $a, b, c$ are in G.P. and the equations $a x^2+2 b x+c=0$ and $...

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The tangent to the parabola $\mathrm{y}^2=4 \mathrm{x}$ at the point where it intersects the circle $\mathrm{x}^2+\mathrm{y}^2=5$ in the first quadrant,...

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If the fourth term in the binomial expansion of $\left(\sqrt{\frac{1}{x^{1+\log _{10} x}}}+x^{\frac{1}{12}}\right)^6$ is equal to 200 , and $x>1$, then...

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The tangent and the normal lines at the point $(\sqrt{3}, 1)$ to the circle $x^2+y^2=4$ and the $x$-axis form a...

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A student scores the following marks in five tests : 45, 54, 41, 57, 43. His score is not known...

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In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis...

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The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3,...

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Which one of the following statements is not a tautology?

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The vector equation of plane through the line of intersection of the planes $x+y+z=1$ and $2 x+3 y+4 z=5$ which...

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The statement that is INCORRECT about the interstitial compounds is

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The percentage composition of carbon by mole in methane is

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The major product obtained in the following reaction is

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The maximum prescribed concentration of copper in drinking water is :

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For a reaction scheme $A \xrightarrow{k_1} B \xrightarrow{k_2} C$, if the rate of formation of $B$ is set to be...

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Among the following molecules/ions, $$ \mathrm{C}_2^{2-}, \mathrm{N}_2^{2-}, \mathrm{O}_2^{2-}, \mathrm{O}_2 $$ Which one is diamagnetic and has the shortest bond length?

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Fructose and glucose can be distinguished by:

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If $p$ is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having...

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For the solution of the gases $w, x, y$ and $z$ in water at $298 K$, the Henrys law constants...

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Which of the following compounds will show the maximum ‘enol’ content?

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Calculate the standard cell potential (in V) of the cell in which following reaction takes place : $$ \mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow...

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The ion that has sp3d2 hybridization for the central atom, is :

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The major product of the following reaction is:

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The calculated spin-only magnetic moments (BM) of the anionic and cationic species of $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]_2$ and $\left[\mathrm{Fe}(\mathrm{CN})_6\right]$, respectively, are:

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5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature becomes 200...

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The IUPAC symbol for the element with atomic number 119 would be :

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Polysubstitution is a major drawback in :

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The covalent alkaline earth metal halide (X = Cl, Br, I) is

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The strength of 11.2 volume solution of $\mathrm{H}_2 \mathrm{O}_2$ is [Given that molar mass of $\mathrm{H}=1 \mathrm{~g} \mathrm{~mol}^{-1}$ and $...

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Which one of the following alkenes when treated with HCl yields majorly an anti Markovnikov product ?

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The structure of Nylon-6 is

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The compound that inhibits the growth of tumors is

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Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The...

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The correct statement about $\mathrm{ICl}_5$ and $\mathrm{ICl}_4^{-}$is :

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The Mond process is used for the :

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0.27 g of a long chain fatty acid was dissolved in $100 \mathrm{~cm}^3$ of hexane. 10 mL of this solution...

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The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is...

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Young’s moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m...

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A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all...

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A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both...

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The ratio of mass densities of nuclei ${ }^{40} \mathrm{Ca}$ and ${ }^{16} \mathrm{O}$ is close to :

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A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines,...

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A positive point charge is released from rest at a distance $r_0$ from a positive line charge with uniform density....

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Calculate the limit of resolution of a telescope objective having a diameter of 200 cm , if it has to...

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Let $\left|\overrightarrow{A_1}\right|=3,\left|\overrightarrow{A_2}\right|=5$ and $\left|\overrightarrow{A_1}+\overrightarrow{A_2}\right|=5$. The value of $\left(2 \overrightarrow{A_1}+3 \overrightarrow{A_2}\right) \cdot\left(3 \overrightarrow{A_1}-2 \overrightarrow{A_2}\right)$ is:

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In the figure shown, what is the current (in Ampere) drawn from the battery? You are given : $$ \begin{aligned}...

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A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure....

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A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of...

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An electric dipole is formed by two equal and opposite charges $q$ with separation $d$. The charges have same mass...

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In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured...

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A rocket has to be launched from earth in such a way that it never returns. If E is the...

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A nucleus $A$, with a finite de-Broglie wavelength $\lambda_A$, undergoes spontaneous fission into two nuclei $B$ and $C$ of equal...

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In the circuit shown, a four wire potentiometer is made of a 400 cm long wire, which extends between A...

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The magnetic field of an electromagnetic wave is given by: $$ \vec{B}=1.6 \times 10^{-6} \cos \left(2 \times 10^7 z+6 \times...

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A circuit connected to an ac source of emf $e=e_0 \sin (100 t)$ with $t$ in seconds, gives a phase...

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If Surface tension (S), Moment of Inertia (I) and Planck’s constant (h), were to be taken as the fundamental units,...

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A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for...

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Two magnetic dipoles $X$ and $Y$ are placed at a separation $d$, with their axes perpendicular to each other. The...

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The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the...

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A parallel plate capacitor has $1 \mu \mathrm{~F}$ capacitance. One of its two plates is given $+2 \mu \mathrm{C}$ charge...

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The electric field in a region is given by $\vec{E}=(A x+B) \hat{i}$, where $E$ is in $N C^{-1}$ and $x$...

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In a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving...

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A body of mass $m_1$ moving with an unknown velocity of $v_1 \hat{i}$, undergoes a collinear collision with a body...

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A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to...

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Consider the set of all lines $p x+q y+r=0$ such that $3 p+2 q+4 r=0$. Which one of the following...

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The major product of the following reaction is

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Aluminium is usually found in +3 oxidation state. In contrast, thallium exists in +1 and +3 oxidation states. This is...

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The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The amount of $\mathrm{PbSO}_4$ electrolyzed in g...

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Arrange the following amines in the decreasing order of basicity

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0.5 moles of gas $A$ and $x$ moles of gas $B$ exert a pressure of 200 Pa in a container...

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A solution of sodium sulfate contains 92 g of $\mathrm{Na}^{+}$ions per kilogram of water. The molality of $\mathrm{Na}^{+}$ions in that...

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For emission line of atomic hydrogen from $n_i=8 \mid$ to $n_f=n$, the plot of wave number $(\vec{v})$ against $\left(\frac{1}{n^2}\right)$ will...

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A water sample has ppm level concentration of the following metals: $\mathrm{Fe}=0.2 ; \mathrm{Mn}=5.0 ; \mathrm{Cu}=3.0 ; \mathrm{Zn}=5.0$. The metal...

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The major product of following reaction is

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Which one of the following statements regarding Henry's law is not correct?

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Major product of the following reaction is

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The following results were obtained during kinetic studies of the reaction ; $2 \mathrm{~A}+\mathrm{B} \rightarrow$ Products The time (in minutes)...

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The isotopes of hydrogen are

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The one that is extensively used as a piezoelectric material is

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The compounds A and B in the following reaction are, respectively

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The correct decreasing order for acid strength is

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According to molecular orbital theory, which of the following is true with respect to $\mathrm{Li}_2{ }^{+}$and $\mathrm{Li}_2{ }^{-}$?

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The increasing order of pKa of the following amino acids in aqueous solution is Gly, Asp, Lys, Arg

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Adsorption of a gas follows Freundlich adsorption isotherm. In the given plot, $x$ is the mass of the gas adsorbed...

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Which amongst the following is the strongest acid?

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Correct statements among a to d regarding silicones are (a) They are polymers with hydrophobic character (b) They are biocompatible...

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The ore that contains both iron and copper is

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The major product of the following reaction is

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The correct match between Item-I and Item-II is

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The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexes is

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Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures T1 and T2...

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In general, the properties that decrease and increase down a group in the periodic table, respectively, are

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Two complexes $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_3(\mathrm{~A})$ and $\left[\mathrm{Cr}\left(\mathrm{NH}_3\right)_6\right]_3(\mathrm{~B})$ are violet and yellow coloured, respectively. The incorrect statement regarding them is

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Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $I$. The...

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Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the...

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For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a...

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A sample of radioactive material A , that has an activity of $10 \mathrm{mCi}\left(1 \mathrm{Ci}=3.7 \times 10^{10}\right.$ decays $\left./ \mathrm{s}\right)$,...

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A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a...

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Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section $5 \mathrm{~mm}_2$, is...

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An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure....

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Three charges +Q, q, +Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis....

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A rod, length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having...

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When the switch S, in the circuit shown, is closed, then the value of current i will be

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An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as...

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A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a...

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If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L,...

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A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force...

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A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of...

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A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point...

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Three blocks $A, B$ and $C$ are lying on a smooth horizontal surface, as shown in the figure. $A$ and...

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A gas can be taken from A and B via two different processes ACB and ADB. When path ACB is...

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Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field....

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Surface of certain metal is first illuminated with light of wavelength $\lambda_1=350 \mathrm{~nm}$ and then, by light of wavelength $...

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A resistance is shown in the figure. Its value and tolerance are given respectively by

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A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume...

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Consider a tank made of glass (refractive index 1.5) with a thick bottom. It is filled with a liquid of...

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A mixture of 2 moles of helium gas (atomic mass $=4 \mathrm{u}$ ), and 1 mole of argon gas (atomic...

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A convex lens is put 10 cm from a light source and it makes a sharp image on a screen,...

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Temperature difference of $120^{\circ} \mathrm{C}$ is maintained between two ends of a uniform rod AB of length 2 L ....

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A conducting circular loop made of a thin wire, has area $3.5 \times 10-3 \mathrm{~m} 2$ and resistance $10 \Omega$....

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A parallel plate capacitor is made of two square plates of side a, separated by a distance d(d

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A heavy ball of mass $M$ is suspended from the ceiling of a car by a light string of mass...

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Amongst $\mathrm{BeF}_2, \mathrm{BF}_3, \mathrm{H}_2 \mathrm{O}, \mathrm{NH}_3, \mathrm{CCl}_4$ and HCl , the number of molecules with non-zero net dipole moment is...

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