Q JEE MAIN 2022

Let $x=\sin \left(2 \tan ^{-1} \alpha\right)$ and $y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$. If $S=\left\{\alpha \in \mathbb{Z}: y^2=1-x\right\}$, then $...

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Q JEE MAIN 2023

Let the function $f(x)=2 x^3+(2 p-7) x^2+3(2 p-9) x-6$ have a maxima for some value of $x0$. Then, the set...

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Q JEE Main 2022

The sum $\sum_{n=1}^{21} \frac{3}{(4 n-1)(4 n+3)}$ is equal to

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Q JEE Main 2022

The remainder when $(11)^{1011}+(1011)^{11}$ is divided by 9 is

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Q JEE Main 2022

The number of bijective functions $f:\{1,3,5,7, \ldots, 99\} \rightarrow\{2,4,6,8, \ldots . ., 100\}$ such that $...

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Q JEE Main 2022

The number of real values of $\lambda$, such that the system of linear equations $$ \begin{aligned} & 2 x-3 y+5...

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Q JEE Main 2023

Let $\stackrel{\mathbb{J}}{\mathrm{a}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$ and $\stackrel{\mathrm{b}}{\mathrm{b}}=3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$ and $\stackrel{n}{\mathrm{c}}$ is a vector such that $...

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Q JEE Main 2023

Let $\alpha_1, \alpha_2, \ldots, \alpha_7$ be the roots of the equation $x^7+3 x^5-13 x^3-15 x=0$ and $...

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Q JEE Main 2023

Let $\alpha=8-14 i, \quad A=\left\{z \in C: \frac{\alpha z-\bar{\alpha} \bar{z}}{z^2-(\bar{z})^2-112 i}=1\right\}$ and $B=\{z \in C:|z+3 i|=4\}$ Then $...

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Q JEE Main 2023

Let $x=\{11,12,13, \ldots, 40,41\}$ and $Y=\{61,62,63, \ldots, 90,91\}$ be the two sets of observations. If $\bar{x}$ and $\bar{y}$ are their...

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Q JEE Main 2023

Let $\left\{a_k\right\}$ and $\left\{b_k\right\}, k \in N$, be two G.P.s with common ratio $r_1$ and $r_2$ respectively such that $a_1=b_1=4$...

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Q JEE Main 2023

Let $A$ be a symmetric matrix such that $|A|=2$ and $...

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Q JEE Main 2023

If the equation of the normal to the curve $y=\frac{x-a}{(x+b)(x-2)}$ at the point $(1,-3)$ is $x-4 y=13$, then the value...

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Q JEE Main 2023

Let $a_1=b_1=1$ and $a_n=a_{n-1}+(n-1), b_n=b_{n-1}+a_{n-1}, \forall n \geq 2$. If $\sum_{n=1}^{10} \frac{b_n}{2^n}$ and $T=\sum_{n=1}^8 \frac{n}{2^{n-1}}$, then $2^7(2 S-$ T )...

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Q JEE Main 2023

A circle with centre $(2,3)$ and radius 4 intersects the line $x+y=3$ at the points $P$ and $Q$. If the...

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Q JEE Main 2023

A triangle is formed by the tangents at the point $(2,2)$ on the curves $y^2=2 x$ and $x^2+y^2=4 x$, and...

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Q JEE Main 2023

The total number of 4-digit numbers whose greatest common divisor with 54 is 2 , is $\_\_\_\_$ .

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Q JEE Main 2023

Consider a function $f: N \rightarrow R$, satisfying $f(1)+2 f(2)+3 f(3)+\ldots+x f(x)=x(x+1) f(x) ; x \geq 2$ with $f(1)=1$. Then...

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Q JEE Main 2023

Let $R$ be a relation defined on $N$ as a $R b$ is $2 a+3 b$ is a multiple of...

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Q JEE Main 2023

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 ,...

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Q JEE Main 2023

Let $y=y(x)$ be the solution of the differential equation $x \log _e x^{\frac{d y}{d x}}+y=x^2 \log _e x,(x>1)$. If $y(2)=2$,...

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Q JEE Main 2023

If the tangent at a point $P$ on the parabola $y^2=3 x$ is parallel to the line $x+2 y=1$ and...

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Q JEE Main 2023

The value of the integral $\int_{1 / 2}^2 \frac{\tan ^{-1} x}{x} d x \quad$ is equal to

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Q JEE MAIN_2023

If the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{1}$ and $\frac{x-a}{2}=\frac{y+2}{3}=\frac{z-3}{1}$ intersects at the point $P$, then the distance of the point $P$ from the...

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Q JEE MAIN_2023

The plane $2 x-y+z=4$ intersects the line segment joining the points $A(a,-2,4)$ and $B(2, b,-3)$ at the point $C$ in...

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Q JEE MAIN_2023

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a...

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Q JEE MAIN_2023

The set of all values of $\lambda$ for which the equation $...

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Q JEE MAIN_2023

The area of the region $$ A=\left\{(x, y):|\cos x-\sin x| \leq y \leq \sin x, 0 \leq x \leq \frac{\pi}{2}\right\}...

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Q JEE MAIN_2023

The set of all values of $t \in R$, for which the matrix

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Q JEE MAIN_2023

Let $f$ and $g$ be twice differentiable functions on $R$ such that $$ \begin{aligned} & f^{\prime \prime}(x)=g^{\prime \prime}(x)+6 x \\...

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Q JEE MAIN_2023

Let $K$ be the sum of the coefficients of the odd powers of $x$ in the expansion of $(1+x)^{99}$. Let...

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Q JEE MAIN_2023

The value of the integral $\int_1^2\left(\frac{t^4+1}{t^6+1}\right) d t$ is:

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Q JEE MAIN_2023

Let $S=\left(w_1, w_2, \ldots\right\}$ be the sample space associated to a random experiment. Let $P\left(w_n\right)=\frac{P\left(w_{n-1}\right)}{2}, n \geq$ 2. Let $...

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Q JEE MAIN_2023

is equal to

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Q JEE MAIN_2023

Shortest distance between the lines $\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}$ and $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}$ is

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Q JEE MAIN_2023

The statement $B \Rightarrow((\sim A) \vee B)$ is not equivalent to :

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Q

Let the area enclosed by the lines $x+y=2, y=0, x=0$ and the curve $f(x)=\min \left\{x^2+\frac{3}{4}, 1+[x]\right\}$ where $[x]$ denotes the...

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Q JEE MAIN 2023

Let $R=\{a, b, c, d, e\}$ and $S=\{1,2,3,4\}$. Total number of onto function $f \mid: R \rightarrow S$ such that...

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Q JEE MAIN 2024

A and B formed in the following reactions are:

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Q JEE MAIN

Let $P_1$ be the plane $3 x-y-7 z=11$ and $P_2$ be the plane passing through the points $(2,-1,0),(2,0,-1)$, and $(5,1,1)$....

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Q JEE MAIN 2023

The ordinates of the points $P$ and $Q$ on the parabola with focus $(3,0)$ and directrix $x=-3$ are in the...

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Q JEE MAIN

Let $m$ and $n$ be the numbers of real roots of the quadratic equations $x^2-12 x+[x]+31=0$ and $...

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Q JEE MAIN 2023

If domain of the function $\log _e\left(\frac{6 x^2+5 x+1}{2 x-1}\right)+\cos ^{-1}\left(\frac{2 x^2-3 x+4}{3 x-5}\right)$ is $(\alpha, \beta) \cup(\gamma, \delta]$, then...

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Q JEE MAIN 2023

Let $[t]$ denote the greatest integer function. If $\int_0^{2.4}\left[X^2\right] d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}+\delta \sqrt{5}$, then $\alpha+\beta+\gamma+\delta$ is equal to $\_\_\_\_$...

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Q JEE-Main 2023

Let $A=\{1,2,3,4,5,6,7\}$. Then the relation $R=\{(x, y) \in A \times A: x+y=7\}$ is

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Q JEE-Main 2023

Let $\mathrm{A}(0,1), \mathrm{B}(1,1)$ and $\mathrm{C}(1,0)$ be the mid - points of the sides of a triangle with in Centre at...

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Q

If $\mathrm{A}=\left[\begin{array}{cc}1 & 5 \\ \lambda & 10\end{array}\right], \mathrm{A}^{-1}=\alpha \mathrm{A}+\beta \mathrm{I}$ and $\alpha+\beta=-2$, then $4 \alpha^2+\beta 2+\lambda^2$ is equal to...

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Q [JEE-Main 2023

If $\alpha>\beta>0$ are the roots of the equation $a x^2+b x+1=0$, and $\lim _{x \rightarrow \frac{1}{\alpha}}\left(\frac{1-\cos \left(x^2+b x+a\right)}{2(1-\alpha x)^2}\right)^{\frac{1}{2}}=\frac{1}{k}\left(\frac{1}{\beta}-\frac{1}{\alpha}\right)$, then...

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Q JEE-Main 2023

The neqation of $(p \wedge(\sim q)) \vee(\sim p)$ is equivalent to

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Q JEE-Main 2023

Let $O$ be the origin and $O P$ and $O Q$ be the tangents to the circle $x^2+y^2-6 x+4 y+8=0$...

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Q JEE-Main 2023

Let the vectors $\overrightarrow{\mathrm{u}}_1=\hat{\mathrm{i}}+\hat{\mathrm{j}}+a \hat{\mathrm{k}}, \overrightarrow{\mathrm{u}}=\hat{\mathrm{i}}+b \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{u}}_3=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ be coplanar. If the vectors $...

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Q JEE MAIN 2023

If the area of the region $\left\{(x, y):\left|x^2-2\right| \leq y \leq x\right\}$ is $A$, then $6 A+16 \sqrt{2}$ is equal...

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Q JEE MAIN 2023

In the figure, $\theta_1+\theta_2=\frac{\pi}{2}$ and $\sqrt{3}(B E)=4(A B)$. If the area of $\triangle C A B$ is $2 \sqrt{3}-3$ unit...

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Q JEE MAIN 2023

The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is...

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Q JEE MAIN_2023

$25^{190}-19^{190}-8^{190}+2^{190}$ is divisible by

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Q JEE MAIN 2023

If the domain of the function $f(x)=\sec ^{-1}\left(\frac{2 x}{5 x+3}\right)$ is $[\alpha, \beta] \cup[\gamma, \delta]$, then $|3 \alpha+10(\beta+\gamma)+21 \delta|$ is...

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Q JEE MAIN 2023

Suppose $a_1, a_2, 2, a_3, a_4$ be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric progression...

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Q JEE MAIN 2023

Let the tangent at any point P on a curve passing through the points $(1,1)$ and $\left(\frac{1}{10}, 100\right)$, intersect positive...

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Q JEE-Main 2023

For $\mathrm{a}, \mathrm{b} \in \mathrm{Z}$ and $|\mathrm{a}-\mathrm{b}| \leq 10$, let the angle between the plane $\mathrm{P}: \mathrm{ax}+\mathrm{y}-\mathrm{z}=\mathrm{b}$ and the line...

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Q JEE MAIN 2023

Let quadratic curve passing through the point $(-1,0)$ and touching the line $y=x$ at $(1,1)$ be $y=f(x)$. Then the x-intercept...

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Q JEE MAIN 2023

Let the foot of perpendicular from the point $\mathrm{A}(4,3,1)$ on the plane $\mathrm{P}: \mathrm{x}-\mathrm{y}+2 \mathrm{z}+3=0$ be N . If $...

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Q JEE MAIN 2023

Let S be the set of values of $\lambda$, for which the system of equations $$ \begin{aligned} & 6 \lambda...

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Q JEE-Main 2023

The area of the quadrilateral ABCD with vertices A(2, 1, 1), B(1, 2, 5), C(–2, –3, 5) and D(1, –6,...

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Q JEE MAIN 2023

Let the equations of two adjacent sides of a parallelogram ABCD be $2 \mathrm{x}-3 \mathrm{y}=-23$ and $5 \mathrm{x}+4 \mathrm{y}=23$. If...

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Q JEE MAIN 2023

The remainder, when $7^{103}$ is divided by 17 is $\_\_\_\_$ $-$

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Q JEE MAIN 2023

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Q JEE MAIN 2023

The foci of a hyperbola are $( \pm 2,0)$ and its eccentricity is $\frac{3}{2}$. A tangent, perpendicular to the line...

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Q JEE MAIN 2023

If $y=y(x)$ is the solution of the differential equation $\frac{d y}{d x}+\frac{4 x}{\left(x^2-1\right)} y=\frac{x+2}{\left(x^2-1\right)^{5 / 2}}, x>1$ such that $...

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Q JEE MAIN 2023

Let the number $(22)^{2022}+(2022)^{22}$ leave the remainder a when divided by 3 and $\beta$ when divided by 7 . Then...

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Q JEE MAIN 2023

Let $S=\left\{z=x+i y: \frac{2 z-3 i}{4 z+2 i}\right.$ is a real number $\}$. Then which of the following is NOT...

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Q JEE MAIN 2024

A light string passing over a smooth light fixed pulley connects two blocks of masses 1 m and 2 m...

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Q JEE MAIN 2023

Let the line $=\frac{x}{1}=\frac{6-y}{2}=\frac{z+8}{5}$ intersect the lines $\frac{x-5}{4}=\frac{y-7}{3}=\frac{z+2}{1}$ and $\frac{x+3}{6}=\frac{3-y}{3}=\frac{z-6}{1}$ at the points $A$ and $B$ respectively. Then the distance...

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Q JEE MAIN 2023

Let the eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is reciprocal to that of the hyperbola $2 x^2-2 y^2=1$. If the ellipse...

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Q JEE-Main 2023

The value of $36\left(4 \cos ^2 9^{\circ}-1\right)\left(4 \cos ^2 27^{\circ}-1\right)\left(4 \cos ^2 81^{\circ}-1\right)\left(4 \cos ^2 243^{\circ}-1\right)$ is

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Q JEE MAIN 2023

If the coefficients of $x$ and $x^2$ in $(1+x)^p(1-x)^q$ are 4 and -5 respectively, then $2 p+3 q$ is equal...

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Q JEE MAIN 2023

Let the eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is reciprocal to that of the hyperbola $2 x^2-2 y^2=1$. If the ellipse...

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Q JEE MAIN 2023

For $\mathrm{x} \in(-1,1]$, the number of solutions of the equation $\sin ^{-1} \mathrm{x}=2 \tan ^{-1} \mathrm{x}$ is equal to

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Q JEE MAIN 2023

Let a curve $y=f(x), x \in(0, \infty)$ pass through the points $P\left(1, \frac{3}{2}\right)$ and $Q\left(a, \frac{1}{2}\right)$. If the tangent at...

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Q JEE MAIN 2023

Let $[\alpha]$ denote the greatest integer $\leq \alpha$. Then $[\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+\ldots .+[\sqrt{120}]$ is equal to $\_\_\_\_$ .

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Q JEE-Main 2023

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

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Q JEE MAIN 2023

For $\alpha, \beta, z \in C$ and $\lambda>1$, if $\sqrt{\lambda-1}$ is the radius of the circle $|z-\alpha|^2+|z-\beta|^2=2 \lambda$, then $|\alpha-\beta|$...

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Q JEE MAIN 2023

Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2,...

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Q JEE MAIN 2023

Let $f(x)=\sum_{k=1}^{10} k x^k, x \in R$. If $2 f(2)+f^{\prime}(2)=119(2)^n+1$, then $n$ is equal to $\_\_\_\_$ .

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Q JEE MAIN 2023

The number of points, where the curve $y=x^5-20 x^3+50 x+2$ crosses the $x$-axis, is $\_\_\_\_$ .

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Q JEE MAIN 2023

Let A= {–4, –3, –2, 0, 1, 3, 4} and R = {(a, b) ∈ A × A : b...

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Q JEE MAIN 2023

If $(20)^{19}+2(21)(20)^{18}+3(21)^2(20)^{17}+\ldots \ldots . .+20(21)^{19}=\mathrm{k}(20)^{19}$, then k is equal to $\_\_\_\_$ .

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Q JEE-Main 2023

Let $S$ be the set of all values of $\theta \in[-\pi, \pi]$ for which the system of linear equations $...

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Q JEE MAIN 2023

The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later,...

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Q JEE MAIN 2023

If the lines and intersect, then the magnitude of the minimum value of 8is _________.

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Q JEE MAIN 2023

The value of $...

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Q JEE MAIN 2023

The value of tan 9° – tan 27° – tan 63° + tan 81° is _________.

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Q JEE-Main 2023

If the number of words, with or without meaning, which can be made using all the letters of the word...

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Q JEE MAIN 2023

Let for a triangle ABC , $$ \begin{aligned} & \overrightarrow{\mathrm{AB}}=-2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \hat{\mathrm{k}} ; \\ & \overrightarrow{\mathrm{CB}}=\alpha \hat{\mathrm{i}}+\beta \hat{\mathrm{j}}+\gamma \hat{\mathrm{k}} \\...

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Q JEE MAIN 2023

Let $f(x)=\frac{x}{\left(1+x^n\right)^{\frac{1}{n}}}, x \in R-\{-1\}, n \in N, n>2$. If $f^n(x)=$ (fofof ..... upto $n$ times) ( $x$ ), then...

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Q JEE MAIN 2023

The area of the region $\left\{(x, y): x^2 \leq y \leq\left|x^2-4\right|, y \geq 1\right\}$ is

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Q JEE MAIN 2023

In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of...

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Q JEE MAIN 2023

If $\operatorname{gcd}(m, n)=1$ and $1^2-2^2+3^2-4^2+\ldots \ldots+(2021)^2-(2022)^2+(2023)^2=1012 m^2 n$, then $m^2-n^2$ is equal to

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Q JEE MAIN 2023

Let $S=\left\{Z \in C: \bar{z}=i\left(z^2+\operatorname{Re}(\bar{z})\right)\right\}$. Then $\sum_{z \in S}|z|^2$ is equal to $\_\_\_\_$ .

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Q JEE MAIN 2023

Let the vectors $\vec{a}, \vec{b}, \vec{c}$ represent three coterminous edges of a parallelopiped of volume $V$. Then the volume of...

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Q JEE MAIN 2023

Let for $\mathrm{A}=\left[\begin{array}{lll}1 & 2 & 3 \\ \mathrm{a} & 3 & 1 \\ 1 & 1 & 2\end{array}\right],|\mathrm{A}|=2$. If...

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Q JEE MAIN 2023

The random valuable X follows binomial distribution B(n, p) for which the difference of the mean and the variance is...

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Q JEE-Main 2023

The absolute difference of the coefficients of $x^{10}$ and $x^7$ in the expansion of $\left\{2 x^2+\frac{1}{2 x}\right\}^{11}$ is equal to

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Q JEE MAIN 2023

If the tangents at the points P and Q on the circle x2 + y2 – 2x + y =...

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Q JEE MAIN 2023

The statement (p ∧(~ q)∨ ((~ p)∧q)∨((~ p)∧(~ q)) is equivalent to

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Q JEE MAIN 2023

Among the statements $(\mathrm{S} 1):(\mathrm{p} \Rightarrow \mathrm{q}) \vee((\sim \mathrm{p}) \wedge \mathrm{q})$ is a tautology $...

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Q JEE MAIN 2023

The range of $f(x)=4 \sin ^{-1}\left(\frac{x^2}{x^2+1}\right)$

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Q JEE MAIN 2023

If the coefficients of $x^7$ in $\left(a x^2+\frac{1}{2 b x}\right)^{11}$ and $x^{-7}$ in $\left(a x-\frac{1}{3 b x^2}\right)^{11}$ are equal, then

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Q JEE MAIN 2023

Let $f(x)$ be a function satisfying $f(x)+f(\pi-x)=\pi^2, \forall x \in R$. Then $\int^\pi f(x) \sin x d x$ is equal...

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Q JEE MAIN 2023

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written...

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Q JEE MAIN 2023

Let $S=\left\{x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right): 9^{1-\tan ^2 x}+9^{\tan ^2 x}=10\right\}$ and $\beta=\sum_{x \in s} \tan ^2\left(\frac{x}{3}\right)$, then $\frac{1}{6}(\beta-14)^2$ is equal to

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Q JEE MAIN 2023

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

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Q JEE MAIN 2023

Let the centre of a circle C be (α, β) and its radius r < 8. Let 3x + 4y...

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Q JEE-Main 2023

Let A $=\left\{\theta \in(0,2 \pi): \frac{1+2 i \sin \theta}{1-i \sin \theta}\right.$ is purely imaginary $\}$. Then the sum of the...

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Q JEE MAIN 2023

Let the line L pass through the point $(0,1,2)$, intersect the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and be parallel to the plane $...

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Q JEE MAIN 2023

Let N be the foot of perpendicular from the point P(1, –2, 3) on the line passing through the points...

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Q JEE MAIN 2023

If the points $P$ and $Q$ are respectively the circumcentre and the orthocentre of a $\triangle A B C$, then...

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Q JEE MAIN 2023

All the letters of the word PUBLIC are written in all possible orders and these words are written as in...

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Q JEE MAIN 2023

If $\mathrm{S}_{\mathrm{n}}=4+11+21+34+50+$ $\_\_\_\_$ to n terms, then $\frac{1}{60}\left(\mathrm{~S}_{29}-\mathrm{S}_9\right)$ is equal to

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Q JEE MAIN 2023

Let $\vec{a}=2 \hat{i}+7 \hat{j}-\hat{k}, \vec{b}=3 \hat{i}+5 \hat{k}$ and $\vec{c}=\hat{i}-\hat{j}+2 \hat{k}$. Let $\vec{d}$ be a vector which is perpendicular to both...

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Q JEE MAIN 2023

Let P be a square matrix such that $\mathrm{P}^2=\mathrm{I}-\mathrm{P}$. For $\alpha, \beta, \gamma, \delta \in \mathrm{N}$, if $\mathrm{P}^\alpha+\mathrm{P}^\beta=\gamma \mathrm{I}-29 \mathrm{P}$...

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Let $|\vec{a}|=2,|\vec{b}|=3$ and the angle between the vectors $\vec{a}$ and $\vec{b}$ be $\frac{\pi}{4}$. Then $|(\vec{a}+2 \vec{b}) \times(2 \vec{a}-3 \vec{b})|^2$ is...

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Let P be the plane passing through the line $\frac{x-1}{1}=\frac{y-2}{-3}=\frac{z+5}{7}$ and the point (2, 4, –3). If the image of...

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The area bounded by the curves y = |x – 1| + |x – 2| and y = 3 is...

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Let $(\alpha, \beta)$ be the centroid of the triangle formed by the lines $15 x-y=82,6 x-5 y=-4$ and $...

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Let $g(x)=f(x)+f(1-x)$ and $f^{\prime \prime}(x)>0, x \in(0,1)$, If $g$ is decreasing in the interval ( $0, \alpha$ ) and increasing...

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For the system of equations $$ \begin{aligned} & x+y+z=6 \\ & x+2 y+\alpha z=10 \end{aligned} $$ $x+3 y+5 z=\beta$, which...

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Let $a_1, a_2, a_{3, \ldots . .}$ be a G.P. of increasing positive numbers. Let the sum of its 6th...

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Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the...

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Let $\alpha, \beta$ be the roots of the equation $x^2-\sqrt{2} x+2=0$. Then $\alpha^{14}+\beta^{14}$ is equal to

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Let $A$ be the point $(1,2)$ and $B$ be any point on the curve $x^2+y^2=16$. If the centre of the...

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The sum of all values of a, for which the points whose position vectors $...

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Let an be the nth term of the series 5 + 8 + 14 + 23 + 35 + 50...

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If $A=\frac{1}{5!6!7!}\left[\begin{array}{lll}5! & 6! & 7! \\ 6! & 7! & 8! \\ 7! & 8! & 9!\end{array}\right]$, then $...

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The plane, passing through the points (0, –1, 2) and (–1, 2, 1) and parallel to the line passing through...

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If the solution curve f(x, y)=0 of the differential equation $...

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Let $A=\{2,3,4\}$ and $B=\{8,9,12\}$. Then the number of elements in the relation $...

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Let the mean and variance of 12 observations be $\frac{9}{2}$ and 4 respectively. Later on, it was observed that two...

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Let the image of the point $\mathrm{P}(1,2,6)$ in the plane passing through the points $\mathrm{A}(1,2,0), \mathrm{B}(1,4,1)$ and $\mathrm{C}(0,5,1)$ be $...

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Let $a \neq b$ be two non-zero real numbers. Then the number of elements in the set $...

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

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For, $\alpha, \beta, \gamma, \delta \in \mathrm{N}$, if $\int\left(\left(\frac{\mathrm{x}}{\mathrm{e}}\right)^{2 \mathrm{x}}+\left(\frac{\mathrm{e}}{\mathrm{x}}\right)^{2 \mathrm{x}}\right) \log _{\mathrm{e}} \mathrm{xdx}=\frac{1}{\alpha}\left(\frac{\mathrm{x}}{\mathrm{e}}\right)^{\beta \mathrm{x}}-\frac{1}{\gamma}\left(\frac{\mathrm{x}}{\mathrm{e}}\right)^{\delta \mathrm{x}}+\mathrm{C}$ Where $e=\sum_{n=0}^{\infty} \frac{1}{n!}$ and...

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Eight persons are to be transported from city A to city B in three cars of different makes. If each...

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$\operatorname{Lim}_{n \rightarrow \infty}\left\{\left(2^{\frac{1}{2}}-2^{\frac{1}{3}}\right)\left(2^{\frac{1}{2}}-2^{\frac{1}{5}}\right) \cdots \cdots\left(2^{\frac{1}{2}}-2^{\frac{1}{2 n+1}}\right)\right\}$ is equal to

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Let $f$ be a continuous function satisfying $\int_0^{t^2}\left(f(x)+x^2\right) d x=\frac{4}{3} t^3, \forall t>0$. Then $f\left(\frac{\pi^2}{4}\right)$ is equal to :

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Among the statements: (S1): $2023^{2022}-1999^{2022}$ is divisible by 8 . $(\mathrm{S} 2): 13(13)^n-11 \mathrm{n}-13$ is divisible by 144 for infinitely...

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Three dice are rolled. If the probability of getting different numbers on the three dice is , where p and...

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If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then...

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A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance...

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A proton with a kinetic energy of 2.0 eV moves into a region of uniform magnetic field of magnitude $...

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Experimentally it is found that 12.8 eV energy is required to separate a hydrogen atom into a proton and an...

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A body is dropped on ground from a height ' $\mathrm{h}_1$ ' and after hitting the ground, it rebounds to...

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Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal...

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A beam of light consisting of two wavelengths $7000 \AA$ and $5500 \AA$ is used to obtain interference pattern in...

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Two concentric circular coils with radii 1 cm and 1000 cm , and number of turns 10 and 200 respectively...

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A simple pendulum with length 100 cm and bob of mass 250 g is executing S.H.M. of amplitude 10 cm...

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A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The...

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A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of...

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As shown in the figure, two parallel plate capacitors having equal plate area of $200 \mathrm{~cm}^2$ are joined in such...

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A metal block of mass m is suspended from a rigid support through a metal wire of diameter $...

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As shown in the figure, the voltmeter reads 2 V across $5 \Omega$ resistor. The resistance of the voltmeter is...

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A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision,...

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The weight of a body on the surface of the earth is 100 N. The gravitational force on it when...

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For an amplitude modulated wave the minimum amplitude is 3V, while the modulation index is 60%. The maximum amplitude of...

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A spherical drop of liquid splits into 1000 identical spherical drops. If$\mathrm{u}_{\mathrm{i}}$ is the surface energy of the original drop...

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A small particle of mass $m$ moves in such a way that its potential energy $U=\frac{1}{2} m \omega^2 r^2$ where...

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A body cools in 7 minutes from 60°C to 40°C. The temperature of the surrounding is 10°C. The temperature of...

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Two long parallel wires carrying currents 8A and 15 A in opposite directions are placed at a distance of 7...

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A student is provided with a variable voltage source V , a test resistor $\mathrm{R}_{\mathrm{r}}=10 \Omega$, two identical galvanometers $\mathrm{G}_1$...

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The rate constant for a first order reaction is $20 \mathrm{~min}^{-1}$. The time required for the initial concentration of the...

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The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at...

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The number of molecules which gives haloform test among the following molecules is _____.

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An object is placed on the principal axis of convex lens of focal length 10 cm as shown. A plane...

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The energy density associated with electric field $E$ and magnetic field $B$ of an electromagnetic wave in free space is...

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Enthalpies of formation of $\mathrm{CCl}_4(\mathrm{~g}), \mathrm{H}_2 \mathrm{O}(\mathrm{g}), \mathrm{CO}_2(\mathrm{~g})$ and $\mathrm{HCl}(\mathrm{g})$ are $-105,-242,-394$ and $-92 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. The magnitude of...

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The number of alkali metal(s), from Li, K, Cs, Rb having ionization enthalpy greater than 400 kJ $\mathrm{mol}^{-1}$ and forming...

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A dipole comprises of two charged particles of identical magnitude $q$ and opposite in nature. The mass ' $m$ '...

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A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of...

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Assume carbon burns according to following equation : $2 \mathrm{C}_{(\mathrm{s})}+\mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{CO}(\mathrm{g})$ When 12 g carbon is burnt in...

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

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Choose the incorrect statement from the following:

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A sample of a metal oxide has formula $\mathrm{M}_{0.83} \mathrm{O}_{100}$. The metal M can exist in two oxidation states +2...

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A stream of a positively charged particles having $\frac{\mathrm{q}}{\mathrm{m}} \times 2 \times 10^{11} \frac{\mathrm{C}}{\mathrm{kg}}$ and velocity $...

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A particle starts with an initial velocity of $10.0 \mathrm{~ms}^{-1}$ along $x$-direction and accelerates uniformly at the rate of $...

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Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6 \times 10^{-27} \mathrm{~kg}$ and radius of...

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At 298 K, the solubility of silver chloride in water is $1.434 \times 10^{-3} \mathrm{~g} \mathrm{~L}^{-1}$. The value of $...

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A capacitor has capacitance 5μF when it’s parallel plates are separated by air medium of thickness d. A slab of...

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Vectors $a \hat{i}+b \hat{j}+\hat{k}$ and $2 \hat{i}-3 \hat{j}+4 \hat{k}$ are perpendicular to each other when $3 a+2 b=7$, the ratio...

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A child of mass 5 kg is going round a merry-goround that makes 1 rotation in 3.14 s. The radius...

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The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same...

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Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its...

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The resistivity of a 0.8 M solution of an electrolyte is $5 \times 10^{-3} \Omega \mathrm{~cm}$ . Its molar conductivity...

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The work functions of Aluminium and Gold are 4.1 eV and 5.1 eV respectively. The ratio of the slope of...

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As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is...

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As shown in the figure, a particle is moving with constant speed $\pi \mathrm{m} / \mathrm{s}$. Considering its motion from...

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" P " is an optically active compound with molecular formula $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}$. When ' P ' is treated...

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A hollow cylindrical conductor has length of 3.14 m , while its inner and outer diameters are 4 mm and...

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In the circuit shown in the figure, the ratio of the quality factor and the band width is ______ s.

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Figure shows a part of an electric circuit. The potentials at points a, b and c are 30 V, 12...

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A hole is drilled in a metal sheet. At $27^{\circ} \mathrm{C}$, the diameter of hole is 5 cm . When...

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

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A block of mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block...

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A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end...

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

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Match List I with List II

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A conducting loop of radius $\frac{10}{\sqrt{\pi}}$ is placed perpendicular to a uniform magnetic field of 0.5T. The magnetic field is...

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The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto...

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Given below are two statements : Statements 1 : The temperature of a gas is $-73^{\circ} \mathrm{C}$. When the gas...

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A capacitor of capacitance $150.0 \mu \mathrm{~F}$ is connected to an alternating source of emf given by $...

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Sea water contains $29.25 \% \mathrm{NaCl}$ and $19 \% \mathrm{MgCl}_2$ by weight of solution. The normal boiling point of the...

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Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of 4 Å. The radius of...

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The orbital angular momentum of an electron in 3 s orbital is $\frac{x h}{2 \pi}$. The value of $x$ is:

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The ratio of sigma and bonds present in pyrophosphoric acid is _______.

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$\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})$ is a first order reaction. The initial pressure of the system was found to be 800...

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The number of incorrect statements from the following is ______

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The number of correct statements from the following is: A. $\mathrm{E}_{\text {cell }}$ is an intensive parameter. B. A negative...

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20 mL of 0.1 M NaOH is added to 50 mL of 0.1 M acetic acid solution. The pH of...

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The volume of hydrogen liberated at STP by treating 2.4 g of magnesium with excess of hydrochloric acid is $\_\_\_\_$...

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The observed magnetic moment of the complex $\left[\mathrm{Mn}(\mathrm{NCS})_6\right]^{\mathrm{x}-}$ is 6.06 BM. The numerical value of x is__

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At 298 K , the standard reduction potential for $\mathrm{Cu}^{2+} / \mathrm{Cu}$ electrode is 0.34 V . Given: $...

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The maximum number of lone pairs of electrons on the central atom from the following species is $\_\_\_\_$ $...

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The total number of intensive properties from the following is $\_\_\_\_$ Volume, Molar heat capacity, Molarity, $\mathrm{E}^\theta$ cell, Gibbs free...

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The sum of oxidation state of the metals in $\mathrm{Fe}(\mathrm{CO})_5, \mathrm{VO}^{2+}$ and $\mathrm{WO}_3$ is ______

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If the formula of Borax is $\mathrm{Na}_2 \mathrm{~B}_4 \mathrm{O}_x(\mathrm{OH})_{4 n} \mathrm{zH}_2 \mathrm{O}$, then $\mathrm{x}+\mathrm{y}+\mathrm{z}=$ $\_\_\_\_$

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$\mathrm{Mg}\left(\mathrm{NO}_3\right)_2 \cdot \mathrm{XH}_2 \mathrm{O}$ and $\mathrm{Ba}\left(\mathrm{NO}_3\right)_2 \cdot \mathrm{YH}_2 \mathrm{O}$, represent formula of the crystalline forms of nitrate salts. Sum of...

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If the boiling points of two solvents X and Y (having same molecular weights) are in the ratio 2 :...

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See the following chemical reaction: $\mathrm{Cr}_2 \mathrm{O}_7^{2-}+\mathrm{XH}^{+}+6 \mathrm{Fe}^{2+} \rightarrow \mathrm{YCr}^{3+}+6 \mathrm{Fe}^{3+}+\mathrm{ZH}_2 \mathrm{O}$

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The number of possible isomeric products formed when 3-chloro-1-butene reacts with HCl through carbocation formation is _____

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The number of correct statements from the following _____ A. For 1s orbital, the probability density is maximum at the...

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The number of species from the following carrying a single lone pair on central atom Xenon is ____ $...

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1 g of a carbonate $\left(\mathrm{M}_2 \mathrm{CO}_3\right)$ on treatment with excess HCl produces 0.01 mol of $\mathrm{CO}_2$. The molar mass...

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0.400 g of an organic compound $(\mathrm{X})$ gave 0.376 g of AgBr in Carius method for estimation of bromine. $\%$...

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The number of correct statements about modern adsorption theory of heterogeneous catalysis from the following is ____ A. The catalyst...

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Which of the following complexes will exhibit maximum attraction to an applied magnetic field?

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For complete combustion of ethene. $\mathrm{C}_2 \mathrm{H}_4(\mathrm{~g})+3 \mathrm{O}_2(\mathrm{~g}) 2 \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{l})$ the amount of heat produced as measured in...

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4.5 moles each of hydrogen and iodine is heated in a sealed ten litre vessel. At equilibrium, 3 moles of...

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The covalency and oxidation state respectively of boron in $\left[\mathrm{BF}_4\right]^{-}$, are

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Number of compounds from the following which will not produce orange red precipitate with Benedict solution is ____. Glucose, maltose,...

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The number of atomic orbitals from the following having 5 radial nodes is ______.7s, 7p, 6s, 8p, 8d

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Match List I with List II 1-Bromopropane is reacted with reagents in List-I to give product in List-II

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If $\mathrm{Ni}^{2+}$ is replaced by $\mathrm{Pt}^{2+}$ in the complex $\left[\mathrm{NiCl}_2 \mathrm{Br}_2\right]^{2-}$, which of the following properties are expected to get...

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Coagulating value of electrolytes $\mathrm{AlCl}_3$ and NaCl for $\mathrm{As}_2 \mathrm{~S}_3$ are 0.09 and 50.04 respectively. The coagulating power of $\mathrm{AlCl}_3$...

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Identify the correct order of standard enthalpy of formation of sodium halides.

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The solubility product of $\mathrm{BaSO}_4$ is $1 \times 10^{-10}$ at 298 K . The solubility of $\mathrm{BaSO}_4$ in 0.1 $...

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

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A compound ‘X’ when treated with phthalic anhydride in presence of concentrated $\mathrm{H}_2 \mathrm{SO}_4$ yields ‘Y’. ‘Y’ is used as...

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What happens when methane undergoes combustion in systems A and B respectively?

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

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The correct group of halide ions which can be oxidized by oxygen in acidic medium is

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For a good quality cement, the ratio of lime to the total of the oxides of Si, Al and Fe...

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The magnetic moment is measured in Bohr Magneton (BM). Spin only magnetic moment of Fe in $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}$ and $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$...

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Given below are two statements: Statement I: SO2 and H2¬O both possess V-shaped structure. Statement II: The bond angle of...

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The correct order of reactivity of following haloarenes towards nucleophilic substitution with aqueous NaOH is: Choose the correct answer from...

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What weight of glucose must be dissolved in 100 g of water to lower the vapour pressure by 0.20 mm...

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Match List I with List II

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Alkali metal from the following with least melting point is:

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Given below are two statements: Statement-I : In the metallurgy process, sulphide ore is converted to oxide before reduction. Statement-II...

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Which of the following are the Green house gases? A. Water vapour B. Ozone C. I2 D. Molecular hydrogen

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The descending order of acidity for the following carboxylic acid is : A. $\mathrm{CH}_3 \mathrm{COOH}$ B. $\mathrm{F}_3 \mathrm{C}-\mathrm{COOH}$ C. $\mathrm{ClCH}_2-\mathrm{COOH}$...

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A solution is prepared by adding 2g of “X” of 1 mole of water. Mass percent of “X” in the...

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The number of incorrect statement/s from the following is ______. A. The successive half-lives of zero order reactions decreases with...

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The major product for the following reaction is

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Compound from the following that will not produce precipitate on reaction with $\mathrm{AgNO}_3$ is:

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Henry Moseley studied characteristic X-ray spectra of elements. The graph which represents his observation correctly is : (Given v =...

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One mole of $\mathrm{P}_4$ reacts with 8 moles of $\mathrm{SOCl}_2$ to give 4 moles of A , x mole of...

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Compound A from the following reaction sequence is:

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The electron in the $\mathrm{n}^{\text {th }}$ orbit of $\mathrm{Li}^{2+}$ is excited to ( $\mathrm{n}+1$ ) orbit using the radiation...

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Which one of the following pairs is an example of polar molecular solids?

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A solid steel ball of diameter 3.6 mm acquired terminal velocity $2.45 \times 10^{-2} \mathrm{~m} / \mathrm{s}$ while falling under...

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

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Given below are two statements: Statement I: Tropolone is an aromatic compound and has 8 electrons. Statement II:  electrons...

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For a metal ion, the calculated magnetic moment is 4.90 BM. This metal ion has ______ number of unpaired electrons.

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

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An aqueous solution of volume $300 \mathrm{~cm}^3$ contains 0.63 g of protein. The osmotic pressure of the solution at 300...

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Given below are two statements: Statements I: Ethene at 333 to 343 K and $6-7 \mathrm{~atm}$ pressure in the presence...

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

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The difference in the oxidation state of Xe between the oxidised product of Xe formed on complete hydrolysis of $\mathrm{XeF}_4$...

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In Hall – Heroult process, the following is used for reducing $\mathrm{Al}_2 \mathrm{O}_3$ :-

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The number of molecules from the following which contain only two lone pair of electrons is $\_\_\_\_$ . $...

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Better method for preparation of BeF2, among the following is: (1) $\left(\mathrm{NH}_4\right)_2 \mathrm{BeF}_4 \xrightarrow{\Delta} \mathrm{BeF}_2$ (2) $\mathrm{BeH}_2+\mathrm{F}_2 \xrightarrow{\Delta} \mathrm{BeF}_2$ (3)...

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

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The number of endothermic process/es from the following is ______ (A) $\mathrm{I}_2(\mathrm{~g}) \rightarrow 2 \mathrm{I}(\mathrm{g})$ (B) $\mathrm{HCl}(\mathrm{g}) \rightarrow \mathrm{H}(\mathrm{g})+\mathrm{Cl}(\mathrm{g})$ (C)...

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An electron revolves around an infinite cylindrical wire having uniform linear change density $2 \times 10^{-8} \mathrm{Cm}^{-1}$ in circular path...

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The total number of stereoisomers for the complex $\left[\mathrm{Cr}(\mathrm{ox})_2, \mathrm{ClBr}\right]^{3-}$ (where ox $=$ oxalate) is:

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

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Major product ‘P’ formed in the following reaction is:

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If the maximum load carried by an elevator is 1400 kg ( 600 kg - Passenger + 800 kg -...

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In alkaline medium, the reduction of permanganate anion involves a gain of _______ electrons.

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

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For a chemical reaction A + B  Product, the order is 1 with respect to A and B. What...

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A force of $-P \hat{k}$ acts on the origin of the coordinate system. The torque about the point $(2,-3)$ is...

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$\mathrm{A}(\mathrm{g}) \rightleftharpoons 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})$ For the given reaction, if the initial pressure is 450 mm Hg and the pressure at...

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A rectangular parallelopiped is measured as $1 \mathrm{~cm} \times 1 \mathrm{~cm} \times 100 \mathrm{~cm}$. If its specific resistance is $...

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Given below are two statements related to Ellingham diagram: Statement-I: Ellingham diagrams can be constructed for formation of oxides, sulfides...

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

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A straight wire AB of mass 40 g and length 50 cm is suspended by a pair of flexible leads...

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A point object, ‘O’ is placed in front of two thin symmetrical coaxial convex lenses L1 and L2 with focal...

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Which of the following compounds is an example of Freon?

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Two plates A and B have thermal conductivities $84 \mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ and $126 \mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ respectively. They have same surface...

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A straight wire carrying a current of 14 A is bent into a semicircular are of radius 2.2 cm as...

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The naturally occurring amino acid that contains only one basic functional group in its chemical structure is

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The correct order of metallic character is:

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A car accelerates from rest to u m/s. The energy spent in this process is E J. The energy required...

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A body of mass 500 g moves along x-axis such that it’s velocity varies with displacement x according to the...

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

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The logic operations performed by the given digital circuit is equivalent to:

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In the wet tests for detection of various cations by precipitation, Ba2+ cations are detected by obtaining precipitate of

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

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Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0...

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

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A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is...

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If 917 Å be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be ____...

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Which hydride among the following is less stable?

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The major product ‘P’ formed in the given reaction is:

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The correct order for acidity of the following hydroxyl compound is: Choose the correct answer from the options given below:

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In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental...

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The correct order of the number of unpaired electrons in the given complexes is A. $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$ B. $\left[\mathrm{FeF}_6\right]^{3-}$

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An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the crosssectional area $24 \mathrm{~cm}^2$....

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Given below are two statements : Statement I: For a planet, if the ratio of mass of the planet to...

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The delicate balance of $\mathrm{CO}_2$ and $\mathrm{O}_2$ is NOT disturbed by:

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In the network shown below, the charge accumulated in the capacitor in steady state will be :

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The statement/s which are true about antagonists from the following is/are :- A. They bind to the receptor site. B....

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Three point charges $q,-2 q$ and $2 q$ are placed on $x$-axis at a distance $x=0, x=\frac{3}{4} R$ and $x=R$...

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Number of water molecules in washing soda and soda ash respectively are:

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The output from a NAND gate having inputs A and B given below will be.

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Which of the following can reduce decomposition of $\mathrm{H}_2 \mathrm{O}_2$ on exposure to light

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An atom absorbs a photon of wavelength 500 nm and emits another photon of wavelength 600 nm. The net energy...

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A bi convex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to...

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The correct reaction profile diagram for a positive catalyst reaction

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The mean free path of molecules of a certain gas at STP is 1500d, where d is the diameter of...

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

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In a Young's double slits experiment, the ratio of amplitude of light coming from slits is 2:1. The ratio of...

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As shown in the figure, a plane mirror is fixed at a height of 50 cm from the bottom of...

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https://competishun.com/the-correct-relationship-between-unit-cell-edge-length-a-and-radius-of-sphere-r-for-facecentred-and-body-centred-cubic-structures-respectively-are/

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The decreasing order of hydride affinity for following carbocations is: Choose the correct answer from the options given below:

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The surface tension of soap solution is $3.5 \times 10^{-2} \mathrm{Nm}^{-1}$. The amount of work done required to increase the...

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The product (P) formed from the following multistep reaction is:

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In the equation $\left[X+\frac{a}{Y^2}\right][Y-b]=R T, X$ is pressure, $Y$ is volume, $R$ is universal gas constant and $T$ is temperature....

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A metallic cube of side 15 cm moving along y-axis at a uniform velocity of $2 \mathrm{~ms}^{-1}$. In a region...

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The reaction used for preparation of soap from fat is:

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A 10$\mu \mathrm{C}$ charge is divided into two parts and placed at 1 cm distance so that the repulsive force...

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A coil has an inductance of 2 H and resistance of $4 \Omega$. A 10 V is applied across the...

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A rectangular block of mass 5 kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1...

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Given below are two statements: Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the...

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The ratio of magnetic field at the centre of a current carrying coil of radius $r$ to the magnetic field...

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A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of...

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A square loop of side 2.0 cm is placed inside a long solenoid that has 50 turns per centimetre and...

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Given below are two statements:- Statement I: In redox titration, the indicators used are sensitive to change in pH of...

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In the reaction give below:

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To radiate EM signal of wavelength $\lambda$ with high efficiency, the antennas should have a minimum size equal to :

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Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature...

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Two identical cells each of emf 1.5 V are connected in series across a $10 \Omega$ resistance. An ideal voltmeter...

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A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time...

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A 600 pF capacitor is charged by 200 V supply. It is then disconnected from the supply and is connected...

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Buna-S can be represented as

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A vehicle of mass 200 kg is moving along a levelled curved road of radius 70 m with angular velocity...

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Given below are two statements:- Statement I: Methyl orange is a weak acid. Statement II: The benzenoid form of methyl...

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A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $...

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If each diode has a forward bias resistance of $25 \Omega$ in the below circuit, Which of the following options...

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A body of mass 5 kg is moving with a momentum of $10 \mathrm{~kg} \mathrm{~ms}^{-1}$. Now a force of 2...

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Given below are two statements: Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor...

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

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A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate,...

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A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m/s (as shown...

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Two planets A and B of radii R and 1.5 R have densities $\rho$ and $\rho / 2$ respectively. The...

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A message signal of frequency 3kHz is used to modulate a carrier signal of frequency 1.5 MHz. The bandwidth of...

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In the given circuit, $...

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In Carius tube, an organic compound ' $X$ ' is treated with sodium peroxide to form a mineral acid '...

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An electron is moving along the positive x-axis. If the uniform magnetic field is applied parallel to the negative z-axis....

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Two projectiles are projected at 30° and 60° with the horizontal with the same speed. The ratio of the maximum...

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Arrange the following gases in increasing order of van der Waals constant ‘a’ A. Ar B. CH4 C. H2O D....

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A steel rod of length 1 m and cross sectional area $10^{-4} \mathrm{~m}^2$ is heated from $0^{\circ} \mathrm{C}$ to $...

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An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid. A. The electron...

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The distance travelled by an object in time t is given by $s=(2.5) t^2$. The instantaneous speed of the object...

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

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Young’s moduli of the material of wires A and B are in the ratio of 1 : 4, while its...

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

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The number density of free electrons in copper is nearly $8 \times 10^{28} \mathrm{~m}^{-3}$. A copper wire has its area...

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In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z-axis...

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Incorrect method of preparation for alcohols from the following is:

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In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

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The correct IUPAC nomenclature for the following compound is

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When vector is subtracted from vector B, it gives a vector equal to 2 . Then the magnitude of vector...

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

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The ratio of wavelength of spectral lines $\mathrm{H}_\alpha$ and $\mathrm{H}_\beta$ in the Balmer series is $\_\_\_\_$ .

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For a periodic motion represented by the equation $Y=\sin \omega t+\cos \omega t$ The amplitude of the motion is

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Number of crystal systems from the following where body centred unit cell can be found, is ____ Cubic, tetragonal, orthorhombic,...

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A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string...

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The current flowing through R2 is:

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The variation of stopping potential (V0) as a function of the frequency (v) of the incident light for a metal...

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Number of isomeric aromatic amines with molecular formula $\mathrm{C}_8 \mathrm{H}_{11} \mathrm{~N}$, which can be synthesized by Gabriel Pathalimide synthesis is...

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A series combination of resistor of resistance $100 \Omega$, inductor of inductance 1 H and capacitor of capacitance $...

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The initial pressure and volume of an ideal gas are $P_0$ and $V_0$. The final pressure of the gas when...

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Among the following the number of compounds which will be give positive iodoform reaction is ____. (a) 1-Phenylbutan-2-one (b) 2-Methylbutan-2-o1...

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The root mean square speed of molecules of nitrogen gas at $27^{\circ} \mathrm{C}$ is approximately: (Given mass of a nitrogen...

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Which of these reactions is not a part of breakdown of ozone in stratosphere?

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The power radiated from a linear antenna of length $(\ell)$ is proportional to (Given, $\lambda=$ Wavelength of wave):

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The ratio of intensities at two points $P$ and $Q$ on the screen in a Young's double slit experiment where...

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A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction...

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Consider the following data

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A bullet of mass 0.1 kg moving horizontally with speed $400 \mathrm{~ms}^{-1}$ hits a wooden block of mass 3.9 kg...

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The energy of He+ ion in its first excited state is. (The ground state energy for the Hydrogen atom is...

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A gas is compressed adiabatically, which one of the following statement is NOT true.

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A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to...

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The amplitude of magnetic field in an electromagnetic wave propagating along y -axis is $6.0 \times 10^{-7} \mathrm{~T}$. The maximum...

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The number of species having a square planar shape from the following is _____.

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The thermodynamic process, in which internal energy of the system remains constant is

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Which of the following have same number of significant figures? (A) 0.00253 (B) 1.0003 (C) 15.0 (D) 163 Choose the...

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Given below are two statements : Statement I : For a planet, if the ratio of mass of the planet...

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An emf of 0.08 V is induced in a metal rod of length 10 cm held normal to a uniform...

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The number of colloidal systems from the following, which will have 'liquid' as the dispersion medium, is ______ Gem stones,...

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The ratio of the de-Broglie wavelengths of proton and electron having same kinetic energy: (Assume mp = me × 1849)

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The standard reduction potential at 298 K for the following half cells are given below: $$ \mathrm{NO}_3^{-}+4 \mathrm{H}^{+}+3 \mathrm{e}^{-} \rightarrow...

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

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In the network shown below, the charge accumulated in the capacitor in steady state will be :

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A spaceship of mass $2 \times 10^4 \mathrm{~kg}$ is launched into a circular orbit close to the earth surface. The...

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The time period of a satellite, revolving above earth’s surface at a height equal to R will be

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In photo electric effect A. The photocurrent is proportional to the intensity of the incident radiation. B. Maximum Kinetic energy...

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https://competishun.com/consider-the-following-pairs-of-solution-which-will-be-isotonic-at-the-same-temperature-the-number-of-pairs-of-solutions-is-are/

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Given below are two statements: Statement-I: Rotation of the earth shows effect on the value of acceleration due to gravity...

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The output from a NAND gate having inputs A and B given below will be.

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

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When one light ray is reflected from a plane mirror with 30° angle of reflection, the angle of deviation of...

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The width of fringe is 2 mm on the screen in a double slits experiment for the light of wavelength...

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The distance between two plates of a capacitor is $d$ and its capacitance is $C_1$, when air is the medium...

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The waves emitted when a metal target is bombarded with high energy electrons are

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The equilibrium composition for the reaction $\mathrm{PCl}_3+\mathrm{Cl}_2 \rightleftharpoons \mathrm{PCl}_5$ at 298 K is given below: $$ \begin{aligned} & {\left[\mathrm{PCl}_3\right]_{\mathrm{leq}}=0.2 \mathrm{~mol}...

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

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A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 m/s at t = 0...

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Given below are two statements: Statement-I: Area under velocity- time graph gives the distance travelled by the body in a...

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Given below are two statements: Statement-I: For diamagnetic substance $-1 \leq \chi \leq 0$, where $\chi$ is the magneticsusceptibility. Statement-II:...

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In an ice crystal, each water molecule is hydrogen bonded to ……... neighbouring molecules.

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Value of work function $\left(\mathrm{W}_0\right)$ for a few metals are given below: The number of metals which will show photoelectric...

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If the radius of the first orbit of hydrogen atom $\mathbf{a}_0$, then de-Broglie's wavelength of electron in $3^{\text {rd }}$...

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In an experiment with Vernier callipers of least count 0.1 mm, when two jaws are joined together the zero of...

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A stone tied to 180 cm long string at its end is making 28 revolutions in horizontal circle in every...

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Which one of the following elements will remain as liquid inside pure boiling water?

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A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational...

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The acceleration due to gravity at height h above the earth if h

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The reaction $2 \mathrm{NO}+\mathrm{Br}_2 \rightarrow 2 \mathrm{NOBr}$ takes places through the mechanism given below: $\mathrm{NO}+\mathrm{Br}_2 \Leftrightarrow \mathrm{NOBr}_2$ (fast) $...

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In the following reaction ‘B’ is

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The temperature at which the kinetic energy of oxygen molecules becomes double than its value at $27^{\circ} \mathrm{C}$ is

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The group of chemicals used as pesticide is

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At 600K, the root mean square (rms) speed of gas X (molar mass = 40) is equal to the most...

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In an ac generator, a rectangular coil of 100 turns each having area $14 \times 10^{-2} \mathrm{~m}^2$ is rotated at...

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The value of x in compound ‘D’ is ___.

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The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h...

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If V is the gravitational potential due to sphere of uniform density on it’s surface, then it’s value at the...

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80 mole percent of MgCl2 is dissociated in aqueous solution. The vapour pressure of 1.0 molal aqueous solution of $\mathrm{MgCl}_2$...

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The volume of 0.02 M aqueous HBr required to neutralize 10.0 mL of 0.01 M aqueous $\mathrm{Ba}(\mathrm{OH})_2$ is (Assume complete...

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As shown in figure, a cuboid lies in a region with electric field $E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k}$ N/C....

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Given below are two statements-

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Three organic compounds A, B and C were allowed to run in thin layer chromatography using hexane and gave the...

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From the figure of column chromatography given below, identify incorrect statements

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In satellite communication, the uplink frequency band used is:

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Formation of which complex, among the following, is not a confirmatory test of $\mathrm{Pb}^{2+}$ ions

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If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will...

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Find out the major product from the following reaction

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A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source...

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A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed...

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During the reaction of permanganate with thiosulphate, the change in oxidation of manganese occurs by value of 3. Identify which...

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A plane electromagnetic wave of frequency 20 MHz propagates in free space along x-direction. At a particular space and time,...

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A car $P$ travelling at $20 \mathrm{~ms}^{-1}$ sounds its horn at a frequency of 400 Hz . Another car $Q$...

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Consider the following reaction that goes from A to B in three steps as shown below:- Choose the correct

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Eight equal drops of water are falling through air with a steady speed of 10 cm/s. If the drops coalesce,...

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Group-13 elements react with $\mathrm{O}_2$ in amorphous form to form oxides of type $\mathrm{M}_2 \mathrm{O}_3(\mathrm{M}=$ element $)$. Which among the...

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The strongest acid from the following is

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Structure of $\mathrm{BeCl}_2$ in solid state, vapour phase and at very high temperature respectively are :-

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Element not present in Nessler's reagent is-

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

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The IUPAC name of $\mathrm{K}_3\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]$ is-

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Ion having highest hydration enthalpy among the given alkaline earth metal ions is-

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Three organic compounds A, B and C were allowed to run in thin layer chromatography using hexane and gave the...

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An analyst wants to convert. 1L HCI of pH = 1 to a solution of HCI of pH 2. The...

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In an oligopeptide named Alanylglycylphenyl alanyl isoleucine, the number of sp2 hybridised carbon is ___.

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Every planet revolves around the sun in an elliptical orbit : A. The force acting on a planet is inversely...

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Given below are two statements : Statement I : Stopping potential in photoelectric effect does not depend on the power...

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The resistance of a wire is 5$\Omega$ . It’s new resistance in ohm if stretched to 5 times of it’s...

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Two objects are projected with same velocity ‘u’ however at different angles$\alpha$ and $\beta$ with the horizontal. If$\alpha+\beta=90^{\circ}$, the ratio...

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Amongst the following, the number of species having the linear shape is ____. $...

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The velocity of a particle executing SHM varies with displacement (x) as $4 v^2=50-x^2$.. The time period of oscillations is...

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A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg . The area of cross section of...

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If the CFSE of $\left[\mathrm{Ti}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}$ is $-96.0 \mathrm{~kJ} / \mathrm{ml}$, this complex will absorb maximum at wavelength ___ nm.(nearest...

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The equivalent resistance between A and B as shown in figure is:

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A 2 meter long scale with least count of 0.2 cm is used to measure the locations of objects on...

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The mass of NH3 produced when 131.8 kg of cyclohexanecarbaldehyde undergoes Tollen's test is ____ kg. (Nearest Integer) Molar Mass...

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A radio-active material is reduced to $1 / 8$ of its original amount in 3 days. If $...

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The distance travelled by a particle is related to time t as$x=4 t^2$. The velocity of the particle at t...

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If the potential difference between B and D is zero, the value of x is $\Omega$. The value of n...

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In Dumas method for the estimation of $\mathrm{N}_2$, the sample is heated with copper oxide and the gas evolved is...

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The trajectory of projectile, projected from the ground is given by $y=x-\frac{x^2}{20}$. Where $x$ and $y$ are measured in meter....

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One mole of an ideal gas at 350K is in a 2.0 L vessel of thermally conducting walls, which are...

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Which of the following elements have half-filled f-orbitals in their ground state ? (Given : atomic number Sm = 62;...

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For a given transistor amplifier circuit in CE configuration $\mathrm{V}_{c c}=1 \mathrm{~V}, \mathrm{R}_{\mathrm{G}}=1 \mathrm{k} \Omega, \mathrm{R}_{\mathrm{b}}=100 \mathrm{k} \Omega$ and $\beta=$...

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The major product ‘P’ formed in the following sequence of reaction is

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A metal M crystallizes into two lattices:- face centred cubic (fee) and body centred cubic (fcc) with unit cell edge...

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A wire of length 1 m moving with velocity 8 m/s at right angles to a magnetic field of 2T....

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Which one of the following statements is incorrect ?

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The spin only magnetic moment of $\left[\mathrm{Mn}\left(\mathrm{H}_2 \mathrm{O}\right)_8\right]^{2+}$ complexes is $\_\_\_\_$ B.M. (Nearest integer) (Given : Atomic no. of Mn...

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A faulty thermometer reads 5°C in melting ice and 95°C in steam. The correct temperature on absolute scale will be...

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

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Testosterone, which is a steroidal hormone, has the following structure The total number of asymmetric carbon atom/s in testosterone is_______

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An organic compound $[\mathrm{A}]\left(\mathrm{C}_4 \mathrm{H}_{11} \mathrm{~N}\right)$, shows optical activity and gives $\mathrm{N}_2$ gas on treatment with $\mathrm{HNO}_2$. The compound [A]...

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$1 \times 10^{-5} \mathrm{M} \mathrm{AgNO}_3$ is added to 1 L of saturated solution of AgBr . The conductivity of this...

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A body of mass is taken from earth surface to the height h equal to twice the radius of earth...

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For particle P revolving round the centre O with radius of circular path r and angular velocity , as shown...

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The half-life of a radioactive substance is $T$. The time taken, for disintegrating $\frac{7}{8}$ th part of its original mass...

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Given below are two statements: Statement I: Boron is extremely hard indicating its high lattice energy Statement II: Boron has...

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A person travels $x$ distance with velocity $v_1$ and then $x$ distance with velocity $v_2$ in the same direction ....

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$20 \%$ of acetic acid is dissociated when its 5 g is added to 500 mL of water. The depression...

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The number of incorrect statement/s from the following is/are $\_\_\_\_$ A. Water vapours are adsorbed by anhydrous calcium chloride. B....

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Electric potential at a point ' P ' due to a point charge of $5 \times 10^{-9} \mathrm{C}$ is 50...

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When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of water. What...

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Consider the following radioactive decay process The mass number and the atomic number A6 are given by :

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$A \rightarrow B$ The above reaction is of zero order. Half life of this reaction is 50 min. The time...

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The electrode potential of the following half cell at 298 K . $\mathrm{X}\left|\mathrm{X}^{2+}(0.001 \mathrm{M})\right|\left|\mathrm{Y}^{2+}(0.01 \mathrm{M})\right| \mathrm{Y}$ is $\_\_\_\_$ $...

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A first order reaction has the rate constant, $\mathrm{k}=4.6 \times 10^{-3} \mathrm{~s}^{-1}$. The number of correct statement/s from the following...

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If two charges $q_1$ and $q_2$ are separated with distance ' $d$ ' and placed in a medium of dielectric...

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Among the following, the number of tranquilizer/s is/are _________.

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The volume of HCl , containing $73 \mathrm{~g} \mathrm{~L}^{-1}$, required to completely neutralise NaOH obtained by reacting 0.69 g of...

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The strength of 50 volume solution of hydrogen peroxide is $\_\_\_\_$ $\mathrm{g} / \mathrm{L}$ (Nearest integer). Given: Molar mass of...

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Given below are two statements : Statement I : If the Brewster's angle for the light propagating from air to...

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The normal rain water is slightly acidic and its pH value is 5.6 because of which one of the following...

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The equilibrium constant for the reaction $\mathrm{Zn}(\mathrm{s})+\mathrm{Sn}^{2+}(\mathrm{aq}) \rightleftharpoons \mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{Sn}(\mathrm{s})$ is $1 \times 10^{20}$ at 298 K . The magnitude of...

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Based on the given figure, the number of correct statement/s is/are _______ A. Surface tension is the outcome of equal...

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A short peptide on complete hydrolysis produces 3 moles of glycine (G), two moles of leucine (L) and two moles...

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As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal...

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Number of compounds from the following which will not dissolve in cold $\mathrm{NaHCO}_3$ and NaOH solutions but will dissolve in...

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Assume that the radius of the first Bohr orbit of hydrogen atom is $0.6 \AA$. The radius of the third...

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

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0.3 g of ethane undergoes combustion at $27^{\circ} \mathrm{C}$ in a bomb calorimeter. The temperature of calorimeter system (including the...

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The graph of $\log \frac{x}{m}$ vs $\log p$ for an adsorption process is a straight line inclined at an angle...

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A metal M forms hexagonal close-packed structure. The total number of voids in 0.02 mol of it is $\_\_\_\_$ $...

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$\mathrm{Pt}(\mathrm{s}) \mathrm{H}_2(\mathrm{~g})(1 \mathrm{bar})\left|\mathrm{H}^{+}(\mathrm{aq})(1 \mathrm{M})\right|\left|\mathrm{M}^{3+}(\mathrm{aq}), \mathrm{M}^{+}(\mathrm{aq})\right| \mathrm{Pt}(\mathrm{s})$ $$ \text { The Ecell for the given cell is } 0.1115 \mathrm{~V} \text...

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A null point is found at 200 cm in potentiometer when cell in secondary circuit is shunted by $5 \Omega$....

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A travelling wave is described by the equation y(x, t) = [0.05 sin (8x – 4t] m. The velocity of...

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Consider the following equation : $$ 2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_3(\mathrm{~g}), \Delta \mathrm{H}=-190 \mathrm{~kJ} $$ The number of factors which...

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The denticity of the ligand present in the Fehling's reagent is_______.

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The element playing significant role in neuromuscular function and interneuronal transmission is :

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The bond order and magnetic property of acetylide ion are same as that of

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Number of hydrogen atoms per molecule of a hydrocarbon A having 85.8% carbon is _________ (Given : Molar mass of...

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$\mathrm{O}-\mathrm{O}$ bond length in $\mathrm{H}_2 \mathrm{O}_2$ is $X$ than the $\mathrm{O}-\mathrm{O}$ bond length in $\mathrm{F}_2 \mathrm{O}_2$. The $\mathrm{O}-\mathrm{H}$ bond length...

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When 0.01 mol of an organic compound containing $60 \%$ carbon was burnt completely, 4.4 g of CO2was produced. The...

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A circular loop of radius r is carrying current I A. The ratio of magnetic field at the centre of...

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

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For electron gain enthalpies of the elements denoted as $\Delta_{\mathrm{eq}} \mathrm{H}$, the incorrect option is:

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Correct statements for the given reaction are: A. Compound 'B' is aromatic B. The completion of above reaction is very...

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If $\vec{E}$ and $\vec{K}$ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector...

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Lead storage battery contains $38 \%$ by weight solution of $\mathrm{H}_2 \mathrm{SO}_4$. The van't Hoff factor is 2.67 at this...

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

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Total number of acidic oxides among $\mathrm{N}_2 \mathrm{O}_3, \mathrm{NO}_2, \mathrm{~N}_2 \mathrm{O}, \mathrm{Cl}_2 \mathrm{O}_7, \mathrm{SO}_2, \mathrm{CO}, \mathrm{CaO}, \mathrm{Na}_2 \mathrm{O}$ and NO...

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A current carrying rectangular loop PQRS is made of uniform wire. The length PR = QS = 5 cm and...

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Total number of moles of AgCl precipitated on addition of excess of $\mathrm{AgNO}_3$ to one mole each of the following...

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Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium -1 ) and...

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

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For conversion of compound $\mathrm{A} \rightarrow \mathrm{B}$, the rate constant of the reaction was found to be $...

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2-hexene $\xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}]{\text { (i) } \mathrm{O}_3}$ Products The two products formed in above reaction are...

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As per given figure, a weightless pulley P is attached on a double inclined frictionless surface. The tension in the...

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Which one of the following sets of ions represents a collection of isoelectronic species? (Given : Atomic Number : $...

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An organic compound undergoes first order decomposition. If the time taken for the 60% decomposition is 540 s, then the...

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

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A. During charging of battery, PbSO4 on anode is converted into $\mathrm{PbO}_2$ . B. During charging of battery, PbSO4 on...

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On heating, $\mathrm{LiNO}_3$ gives how many compounds among the following? $\mathrm{Li}_2 \mathrm{O}, \mathrm{N}_2, \mathrm{O}_2, \mathrm{LiNO}_2, \mathrm{NO}_2 \mid$

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A modulating signal is a square wave, as shown in the figure. If the carrier wave is given as $...

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Iron oxide FeO , crystallises in a cubic lattice with a unit cell edge length of 5.0 A . If...

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

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1 mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27^{\circ} \mathrm{C}$. The work...

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28.0 L of $\mathrm{CO}_2$ is produced on complete combustion of 16.8 L gaseous mixture of ethane and methane at $...

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1 g of a liquid is converted to vapour at $3 \times 10^5 \mathrm{~Pa}$ pressure. If $10 \%$ of the...

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$1 \mathrm{~L}, 0.02 \mathrm{M}$ solution of $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{SO}_4\right] \mathrm{Br}$ is mixed with $1 \mathrm{~L}, 0.02 \mathrm{M}$ solution of $...

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Match List I with List II

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A particle of mass 250 g executes a simple harmonic motion under a periodic force F = (–25 x) N....

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In figure, a straight line is given for Freundrich Adsorption $(y=3 x+2.505)$. The value of $\frac{1}{n}$ and $\log K$ are...

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Formulae for Nessler's reagent is:

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Given below are two statements: Statement I : Nickel is being used as the catalyst for producing syn gas and...

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The number of pairs of the solution having the same value of the osmotic pressure from the following is ________....

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A 100 m long wire having cross-sectional area $6.25 \times 10^{-4} \mathrm{~m}^2$ and Young’s modulus is $10^{10} \mathrm{Nm}^{-2}$ is subjected...

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The starting material for convenient preparation of deuterated hydrogen peroxide $\left(\mathrm{D}_2 \mathrm{O}_2\right)$ in laboratory is:

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

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A metal block of base area $0.20 \mathrm{~m}^2$ is placed on a table, as shown in figure. A liquid film...

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

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Given below are two statements: Statement I: During Electrolytic refining, the pure metal is made to act as anode and...

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The weight of a body at the surface of earth is 18 N. The weight of the body at an...

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Number of compounds giving (i) red colouration with ceric ammonium nitrate and also (ii) positive iodoform test from the following...

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Which of the following relations are correct? Choose the most appropriate answer from the options given below :

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An inductor of inductance $2 \mu \mathrm{H}$ is connected in series with a resistance, a variable capacitor and an AC...

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The structures of major products A, B and C in the following reaction are sequence

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From the photoelectric effect experiment, following observations are made. Identify which of these are correct A. The stopping potential depends...

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Boric acid in solid, whereas $\mathrm{BF}_3$ is gas at room temperature because of

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The Lewis acid character of boron tri halides follows the order:

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Following tetrapeptide can be represented as (F, L, D, Y, I, Q, P are one letter codes for amino acids)

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A particle executes simple harmonic motion between x = –A and$x=+A$. If time taken by particle to go from$x=0$ to...

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Match List I with List II:

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The industrial activity held least responsible for global warming is :

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The number of given orbitals which have electron density along the axis is _______ px, py, pz, dxy, dyz dxz,

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A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration...

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Arrange the following orbitals in decreasing order of energy ? (A) n = 3, l = 0, m = 0...

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Reaction of propanamide with $\mathrm{Br}_2 / \mathrm{KOH}(\mathrm{ag})$ produces:

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The water quality of a pond was analysed and its BOD was found to be 4. The pond has

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

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A chloride salt solution acidified with dil. $\mathrm{HNO}_3$ gives a curdy white precipitate, $[A]$, on addition of $\mathrm{AgNO}_3$. $[\mathrm{A}]$ on...

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Bond dissociation energy of $\mathrm{E}-\mathrm{H}$ bond of the " $\mathrm{H}_2 \mathrm{E}$ " hydrides of group 16 elements (given below), follows...

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For a charged spherical ball, electrostatic potential inside the ball varies with r as $\mathrm{V}=2 a \mathrm{r}^2+\mathrm{b}$. Here, a and...

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Two bodies are projected from ground with same speeds $40 \mathrm{~ms}^{-1}$ at two different angles with respect to horizontal. The...

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Compound $\mathrm{A}, \mathrm{C}_5 \mathrm{H}_{10} \mathrm{O}_5$, given a tetraacetate with $\mathrm{Ac}_2 \mathrm{O}$ and oxidation of A with $\mathrm{Br}_2-\mathrm{H}_2 \mathrm{O}$ gives an...

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Which element is not present in Nessler's reagent ?

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The concentration of dissolved Oxygen in water for growth of fish should be more than ppm and Biochemical Oxygen Demand...

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$\mathrm{KMnO}_4$ oxidises I- in acidic and neutral/faintly alkaline solution, respectively to

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Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the...

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The displacement equations of two interfering waves are given by $y_1=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{cm}$ and $...

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In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student...

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The isomeric deuterated bromide with molecular formula C4H8DBr having two chiral carbon atoms is

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

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Evaluate the following statements for their correctness. (A) The elevation in boiling point temperature of water will be same for...

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A solution of $\mathrm{CrO}_5$ in amyl alcohol has a $\_\_\_\_$ colour

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Two parallel plate capacitors $\mathrm{C}_1$ and $\mathrm{C}_2$ each having capacitance of $10 \mu \mathrm{~F}$ are individually charged by a 100...

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‘A’ in the given reaction is

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

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A particle of mass 100 g is projected at time $\mathrm{t}=0$ with a speed $20 \mathrm{~ms}^{-1}$ at an angle $45^{\circ}$...

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If the pKa of lactic acid is 5 , then the pH of 0.005 M calcium lactate solution at $...

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The energy levels of an atom is shown is figure. Which one of these transitions will result in the emission...

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Given below are two statements : Statement I : Sulphanilic acid gives esterification test for carboxyl group. Statement II :...

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The wave function $(\Psi)$ of 2 s is given by $$ \Psi_{2 s}=\frac{1}{2 \sqrt{2 \pi}}\left(\frac{1}{a_0}\right)^{1 / 2}\left(2-\frac{r}{a_0}\right) e^{-r / 2...

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Given below are two statements : Statement I: Upon heating a borax bead dipped in cupric sulphate in a luminous...

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According to MO theory the bond orders for $\mathrm{O}_2^{2-} . \mathrm{CO}$ and $\mathrm{NO}^{+}$respectivelv, are

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For the given circuit, in the steady state, $\left|\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{D}}\right|=$ $\_\_\_\_$ V.

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One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the...

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Find out the major product from the following reaction.

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The complex cation which has two isomers is :

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

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When two resistance $\mathrm{R}_1$ and $\mathrm{R}_2$ connected in series and introduced into the left gap of a meter bridge and...

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Find out the major products from the following reaction sequence.

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Cyclohexylamine when treated with nitrous acid yields (P). On treating (P) with PCC results in (Q). When (Q) is heated...

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If the binding energy of ground state electron in a hydrogen atom is 13.6 eV , then, the energy required...

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Chlorides of which metal are soluble in organic solvents:

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The Total pressure observed by mixing two liquid A and B is 350 mm Hg when their mole fractions are...

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Match List I with List II

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A square loop of area $25 \mathrm{~cm}^2$ has a resistance of $10 \Omega$. The loop is placed in uniform magnetic...

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Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm...

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

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A hydrocarbon 'X' with formula $\mathrm{C}_6 \mathrm{H}_8$ uses two moles of $\mathrm{H}_2$ on catalytic hydrogenation of its one mole. On...

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A point charge of 10 μC is placed at the origin. At what location on the X-axis should a point...

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A ball is dropped from a height of 20 m. If the coefficient of restitution for the collision between ball...

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When the hydrogen ion concentration [H+] changes by a factor of 1000, the value of pH of the solution _______.

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A water heater of power 2000 W is used to heat water. The specific heat capacity of water is $...

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When a hydrocarbon A undergoes combustion in the presence of air, it requires 9.5 equivalents of oxygen and produces 3...

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The graph which represents the following reaction is : $\left(\mathrm{C}_6 \mathrm{H}_5\right)_3 \mathrm{C}-\mathrm{Cl} \xrightarrow[\text { Pyyidine }]{\mathrm{OH}^{-}}\left(\mathrm{C}_6 \mathrm{H}_5\right)_3 \mathrm{C}-\mathrm{OH}$

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The equation of a circle is given by $x^2+y^2=a^2$, where $a$ is the radius. If the equation is modified to...

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The $\mathrm{Cl}-\mathrm{Co}-\mathrm{Cl}$ bond angle values in a fac $-\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}_3\right]$ complex is/are:

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Two light waves of wavelengths 800 and 600 nm are used in Young's double slit experiment to obtain interference fringes...

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Which of the following compounds are not used as disinfectants? (A) Chloroxylenol (B) Bithional (C) Veronal (D) Prontosil (E) Terpineol...

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Total number of tripeptides possible by mixing of valine and proline is _________

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Potassium dichromate acts as a strong oxidizing agent in acidic solution. During this process, the oxidation state changes from

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Match List I with List II:

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The one giving maximum number of isomeric alkenes on dehydrohalogenation reaction is (excluding rearrangement)

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

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All structures given below are of vitamin C. Most stable of them is :

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A series LCR circuit consists of R $=80 \Omega \mathrm{X}_{\mathrm{L}}=100 \Omega$ and $\mathrm{X}_{\mathrm{C}}=40 \Omega$. The input voltage is $...

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Consider a block kept on an inclined plane (inclined at 45°) as shown in the figure. If the force required...

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Maximum number of isomeric monochloro derivatives which can be obtained from 2, 2, 5, 5-tetramethylhexane by chlorination is _______

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Incorrect statement for the use of indicators in acid–base titration is : (1) Methyl orange may be used for a...

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Given below are two statements: Statement I: In a typical transistor, all three regions emitter, base and collector have same...

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The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite...

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Find out the major product for the following reaction.

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The correct order of bond enthalpy ( $\mathrm{kJ} \mathrm{mol}^{-1}$ ) is :

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Maximum number of electrons that can be accommodated in shell with n = 4 are:

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Sum of $\pi$-bonds present in peroxodisulphuric acid and pyrosulphuric acid is

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For the given figures, choose the correct options:

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In the following halogenated organic compounds the one with maximum number of chlorine atoms in its structure is :

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In the above conversion of compound (X) to product (Y), the sequence of reagents to be used will be:

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The number of statement/s which are the characteristics of physisorption is ___________. A. It is highly specific in nature B....

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In a reaction reagents 'X' and 'Y' respectively are

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A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with...

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A doctor prescribed the drug Equanil to a patient. The patient was likely to have symptoms of which disease?

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$\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ paper acidified with dilute $\mathrm{H}_2 \mathrm{SO}_4$ turns green when exposed to

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Match List I with List II

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The hybridization and magnetic behaviour of cobalt ion in $\left.\left[\mathrm{Co}\left(\mathrm{NH}_3\right)\right]^3\right]^{3+}$ complex, respectively is

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An indicator ' $x$ ' is used for studying the effect of variation in concentration of iodide on the rate...

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Decreasing order towards SN1 reaction for the following compounds is:

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Match List I with List II.

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The surface of water in a water tank of cross section area $750 \mathrm{~cm}^2$ on the top of a house...

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Statement I : When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic...

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Identify the correct statements about alkali metals. A. The order of standard reduction potential ( $\mathrm{M}^{+} \mid \mathrm{M}$ ) for...

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A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise...

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

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Match List–I and List–II. Choose the correct answer from the options given below:

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A cubical volume is bounded by the surfaces $x=0, x=a, y=0, y=a, z=0, z=a$. The electric field in the region...

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Which one among the following metals is the weakest reducing agent ?

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The most stable carbocation for the following is:

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Choose the correct colour of the product for the following reaction.

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As shown in the figure, in Young's double slit experiment, a thin plate of thickness $\mathrm{t}=10 \mid \mathrm{a} \cdot \mathrm{m}$...

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A convex lens of refractive index 1.5 and focal length 18 cm in air is immersed in water. The change...

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Match List I with List II

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Which will undergo deprotonation most readily in basic medium?

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Which of the following reaction is correct ?

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A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of...

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Three identical resistors with resistance $\mathrm{R}=12 \Omega$ and two identical inductors with sell inductance L = 5 mH are connected...

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The set of correct statements is: (i) Manganese exhibits +7 oxidation state in its oxide. (ii) Ruthenium and Osmium exhibit...

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In the given circuit the value of $\left|\frac{I_1+I_3}{I_2}\right|$ is:

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Heat energy of 184 kJ is given to ice of mass 600 g at $-12^{\circ} \mathrm{C}$, Specific heat of ice...

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Given below are two statements : Statement I : Pure Aniline and other arylamines are usually colourless. Statement II :...

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A block is fastened to a horizontal spring. The block is pulled to a distance $x=10 \mathrm{~cm}$ from its equilibrium...

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A. Ammonium salts produce haze in atmosphere. B. Ozone gets produced when atmospheric oxygen reacts with chlorine radicals. C. Polychlorinated...

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A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13...

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Correct statement is :

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A body of mass 10 kg is moving with an initial speed of $20 \mathrm{~m} / \mathrm{s}$. The body stops...

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Match List–I and List–II. Choose the correct answer from the options given below:

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Given below are two statements: Statement I: Electromagnetic waves are not deflected by electric and magnetic field. Statement IIn: The...

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

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A square shaped coil of area $70 \mathrm{~cm}^2$ having 600 turns rotates in a magnetic field of $0.4 \mathrm{wbm}^{-2}$, about...

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If a copper wire is stretched to increase its length by 20°%. The percentage increase in resistance of the wire...

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Considering a group of positive charges, which of the following statements is correct?

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Find out the major products from the following reactions.

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

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A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he...

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Nucleus a having $Z=17$ and equal number of protons and neutrons has 1.2 MeV binding energy per nucleon. Another nucleus...

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Under the same load, wire $A$ having length 5.0 m and cross section $2.5 \times 10^{-5} \mathrm{~m}^2$ stretches uniformly by...

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30.4 kJ of heat is required to melt one mole of sodium chloride and the entropy change at the melting...

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As shown in the figure, a point charge Q is placed at the centre of conducting spherical shell of inner...

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Moment of inertia of a dise of mass $M$ and radius ' $R$ ' about any of its diameter is...

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Choose the correct representation of conductometric titration of benzoic acid vs sodium hydroxide.

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The number of correct statements from the following is ____ (A) Conductivity always decreases with decrease in concentration for both...

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A body of mass 1 kg begins to move under the action of a time dependent force $...

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Correct order of spin only magnetic moment of the following complex ions is: (Given At. No. Fe: 26, Co:27)

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The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

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Statement 1 : Dipole moment is a vector quantity and by convention it is depicted by a small arrow with...

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With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the...

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

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A force $F=\left(5+3 y^2\right)$ acts on a particle in the $y$-direction, where $F$ is newton and $y$ is in meter....

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For a reversible reaction $\mathrm{A} \rightleftharpoons \mathrm{B}$, the $\Delta \mathrm{H}_{\text {forward reaction }}=20 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The activation energy of the...

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

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A parallel plate capacitor with air between the plate has a capacitance of 15pF. The separation between the plate becomes...

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

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The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The...

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20 mL of 0.5 M NaCl is required to coagulate 200 mL of $\mathrm{AS}_2 \mathrm{~S}_3$ solution in 2 hours. The...

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What is the mass ratio of ethylene glycol (C2H6O2, molar mass = 62 g/mol) required for making 500 g of...

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Given below are two statements: Statement I : The decrease in first ionization enthalpy from B to Al is much...

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The energy released per fission of nucleus of 240X is 200 MeV. The energy released if all the atoms in...

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For a train engine moving with speed of $20 \mathrm{~ms}^{-1}$ the driver must apply brakes at a distance of 500...

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An alternating voltage source V = 260 sin (628t) is connected across a pure inductor of 5 mH. Inductive reactance...

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

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The vapour pressure of $30 \%(\mathrm{w} / \mathrm{v})$ aqueous solution of glucose is $\_\_\_\_$ mm Hg at $25^{\circ} \mathrm{C}$. [Given:...

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C P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150...

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The modulation index for an A.M. wave having maximum and minimum peak to peak voltages of 14 mV and 6...

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

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A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass...

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The total number of isoelectronic species from the given set is ____. $...

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The threshold frequency of metal is $f_0$. When the light of frequency $2 f_0$ is incident on the metal plate,...

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

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

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A point charge 2 × $10^{-2}$ C is moved from P to S in a uniform electric field of 30...

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A uniform solid cylinder with radius R and length L has moment of inertia I1, about the axis of cylinder....

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In Chromyl chloride, the oxidation state of chromium is (+) ____.

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The ratio of average electric energy density and total average energy density of electromagnetic wave is:

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A body weight W, is projected vertically upwards from earth's surface to reach a height above the earth which is...

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Which of the following represents the correct order of metallic character of the given elements ?

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The total change in the oxidation state of manganese involved in the reaction of $\mathrm{KMnO}_4$ and potassium iodide in the...

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An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin....

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If two vectors $\vec{P}=\hat{i}+2 m \hat{j}+m \hat{k}$ and $\vec{Q}=4 \hat{i}-2 \hat{j}+m \hat{k}$ are perpendicular to each other. Then, the value...

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For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume,...

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If the two metals $A$ and $B$ are exposed to radiation of wavelength 350 nm . The work functions of...

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Given below are two statements :- Statement I: In froth floatation method a rotating paddle agitates the mixture to drive...

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In which of the following reactions the hydrogen peroxide acts as a reducing agent?

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The volume (in mL ) of $0.1 \mathrm{M} \mathrm{AgNO}_3$ required for complete precipitation of chloride ions present in 20 mL...

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In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature;...

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The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity...

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If the velocity of light c, universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The...

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Identify the correct statements from the following: (A) Work done by a man in lifting a bucket out of a...

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Match List I with List II

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The number of s-electrons present in an ion with 55 protons in its unipositive state is

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Given below are two statements Statement I: For transmitting a signal, size of antenna (l) should be comparable to wavelength...

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A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding...

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Figures (a), (b), (c) and (d) show variation of force with time. The impulse is highest in figure

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A fully loaded boeing aircraft has a mass of 5.4 × $10^5$ kg. Its total wing area is $500 \mathrm{~m}^2$.....

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Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each...

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

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A student has studied the decomposition of a gas AB 3 at $25^{\circ} \mathrm{C}$. He obtained the following data. The...

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A metal surface of 100 cm2 area has to be coated with nickel layer of thickness 0.001 mm. A current...

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An electron of a hydrogen like atom, having $Z=4$, jumps from $4^{\text {th }}$ energy state to $2^{\text {nd }}$...

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A long conducting wire having a current I flowing through it, is bent into a circular coil of N turns....

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A thin prism P1 with an angle 6° and made of glass of refractive index 1.54 is combined with another...

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

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The escape velocities of two planets $A$ and $B$ are in the ratio $1: 2$. If the ratio of their...

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KMnO4 is titrated with ferrous ammonium sulphate hexahydrate in presence of dilute H2SO4. Number of water molecules produced for 2...

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Which of the following cannot be explained by crystal field theory?

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Among the following compounds, the one which shows highest dipole moment is

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$t_{87.5}$ is the time required for the reaction to undergo $87.5 \%$ completion and $t_{50}$ is the time required for...

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Choose the correct length $(\mathrm{L})$ versus square of time period $\left(\mathrm{T}^2\right)$ graph for a simple pendulum executing simple harmonic motion.

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What is the number of unpaired electron(s) in the highest occupied molecular orbital of the following species : $...

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Which one amongst the following are good oxidizing agents? Choose the most appropriate answer from the options given below :

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A certain quantity of real gas occupies a volume of 0.15 dm3 at 100 atm and 500 K when its...

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

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Choose the correct statement about Zener diode:

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20 mL of calcium hydroxide was consumed when it was reacted with 10 mL of unknown solution of H2SO4. Also...

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For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is...

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The velocity time graph of a body moving in a straight line is shown in figure. The ratio of displacement...

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The homoleptic and octahedral complex of $\mathrm{Co}^{2+}$ and $\mathrm{H}_2 \mathrm{O}$ has $\_\_\_\_$ unpaired electron(s) in the $t_{2 g}$ set of...

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Let the mean of the data \begin{tabular}{|l|l|l|l|l|l|} \hline$x$ & 1 & 3 & 5 & 7 & 9 \\ \hline...

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An organic compound gives 0.220 g of CO2 and 0.126 g of H2O on complete combustion. If the % of...

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The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by $$ \begin{aligned} &...

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Force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases...

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Which of the following expressions is correct in case of a CsCI unit cell (edge length'a')?

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

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Let $\vec{a}=3 \hat{i}+\hat{j}-\hat{k}$ and $\vec{c}=2 \hat{i}-3 \hat{j}+3 \hat{k}$. If $\vec{b}$ is a vector such that $\vec{a}=\vec{b} \times \vec{c}$ and $|\vec{b}|^2=50$,...

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The complex with highest magnitude of crystal field splitting energy $\left(\Delta_0\right)$ is

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The time taken by an object to slide down 45° rough inclined plane is n times as it takes to...

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Let the image of the point $\left(\frac{5}{3}, \frac{5}{3}, \frac{8}{3}\right)$ in the plane $x-2 y+z-2=0$ be $P$. If the distance of...

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A cell of emf 90 V is connected across series combination of two resistors each of $100 \Omega$ resistance. A...

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For a solid rod, the Young's modulus of elasticity is $3.2 \times 10^{11} \mathrm{Nm}^{-2}$ and density is $...

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A flask contains hydrogen and oxygen in the ratio of 2 : 1 by mass at temperature 27°C. The ratio...

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Let $m_1$ and $m_2$ be the slopes of the tangents drawn from the point $P(4,1)$ to the hyperbola $H: \frac{y^2}{25}-\frac{x^2}{16}=1$....

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Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be:

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For the given logic gates combination, the correct truth table will be

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The sum of lone pairs present on the central atom of the interhalogen $\mathrm{IF}_5$ and $\mathrm{IF}_7$ is ______.

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A2 + B2  2AB. kJ mol–1 AB, A2 and B2 are diatomic molecule. If the bond enthalpies of A2,...

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The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed...

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A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the...

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The number of seven digit positive integers formed using the digits 1,2,3 and 4 only and sum of the digits...

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25.0 mL of 0.050 M Ba(NO3)2 is mixed with 25.0 mL of 0.020 M NaF. Ksp of BaF2 is 0.5...

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A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of...

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The Young's modulus of a steel wire of length 6 m and cross-sectional area $3 \mathrm{~mm}^2$, is $...

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A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$ is...

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Solution of 12 g of non-electrolyte (A) prepared by dissolving it in 1000 mL of water exerts the same osmotic...

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The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density (p) of liquid...

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A body is moving with constant speed, in a circle of radius 10 m. The body completes one revolution in...

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For the given reaction The total number of possible products formed by tertiary carbocation of A is ____.

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Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a...

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In potassium ferrocyanide, there are ____ pairs of electrons in the $\mathrm{t}_{2 \mathrm{~g}}$ set of orbitals

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The ratio of de-Broglie wavelength of an -particle and a proton accelerated from rest by the same potential is $\frac{1}{\sqrt{m}}$,...

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The H amount of thermal energy is developed by a resistor in 10 s when a current of 4A is...

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For a body projected at an angle with the horizontal from the ground, choose the correct statement. (1) Gravitational potential...

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If the degree of dissociation of aqueous solution of weak monobasic acid is determined to be 0.3, then the observed...

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The pair of lanthanides in which both elements have high third -ionization energy is:

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When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours...

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At 300 K, the rms speed of oxygen molecules is $\sqrt{\frac{\alpha+5}{\alpha}}$ times to that of its average speed in the...

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What happens when a lyophilic sol is added to a lyophobic sol?

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A metallic rod of length 'L' is rotated with an angular speed of ‘’ normal to a uniform magnetic field...

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A block of kg is attached to a string whose other end is attached to the wall. An unknown force...

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In an electrochemical reaction of lead, at standard temperature, if $\mathrm{E}_{\left(\mathrm{Pb}^{2+} / \mathrm{Pb}\right)}^0=\mathrm{m}$ Volt and $\mathrm{E}_{\left(\mathrm{Pb}^{4+} / \mathrm{Pb}\right)}^0=\mathrm{n}$ Volt, then...

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$\mathrm{FeO}_4^{2-} \xrightarrow{+2.2 \mathrm{~V}} \mathrm{Fe}^{3+} \xrightarrow{+0.70} \mathrm{Fe}^{2+} \xrightarrow{-0.45} \mathrm{Fe}^0$ $\mathrm{E}_{\mathrm{FeO}_4^{2-} / \mathrm{Fe}^{2+}}^\theta$ is $\mathrm{x} \times 10^{-3} \mathrm{~V}$ The value of x...

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The energy of an electron in the first Bohr orbit of hydrogen atom is –2.18×10–18 J. Its energy in the...

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The major product formed in the Friedel-Craft acylation of chlorobenzene is .

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$0.004 \mathrm{M} \mathrm{K}_2 \mathrm{SO}_4$ solution is isotonic with 0.01 M glucose solution. Percentage dissociation of $\mathrm{K}_2 \mathrm{SO}_4$ is $\_\_\_\_$ (Nearest...

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Given below are two statements: Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from...

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Which of the following statements are not correct? A. The electron gain enthalpy of F is more negative than that...

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In the following reactions, the total number of oxygen atoms in X and Y is ______ $...

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Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number...

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A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field....

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$\mathrm{KClO}_3+6 \mathrm{FeSO}_4+3 \mathrm{H}_2 \mathrm{SO}_4 \rightarrow \mathrm{KCl}+3 \mathrm{Fe}_2\left(\mathrm{SO}_4\right)_3+3 \mathrm{H}_2 \mathrm{O}$ The above reaction was studied at 300 K by monitoring the...

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A long solenoid is formed by winding 70 turns cm–1. If 2.0 A current flows, then the magnetic field produced...

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According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the...

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A solution of sugar is obtained by mixing 200 g of its 25% solution and 500 g of its 40%...

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In the reaction given below:

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As shown in the figure, a long straight conductor with semicircular arc of radius $\frac{\pi}{10} \mathrm{~m}$ is carrying current $...

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The number of incorrect statement/s about the black body from the following is _______ (A) Emit or absorb energy in...

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Solid fuel used in rocket is a mixture of $\mathrm{Fe}_2 \mathrm{O}_3$ and Al (in ratio 122 ). The heat evolved...

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Be (OH)2 react with Sr(OH)2 to yield an ionic salt. [JEE (Main) 13-4-23_S1] [SB_M] M0derate Choose the incorrect option related...

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CIF5 at room temperature is a:

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The number of hyperconjugation structures involved to stabilize carbocation formed in the above reaction is _____.

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https://competishun.com/given-below-are-two-statements-one-is-labelled-as-assertion-a-and-the-other-is-labelled-as-reason-r-brassertion-a-two-metallic-spheres-are-charged-to-the-same-potential-one-of-them-is-hollow-and-another-is-solid-and-both-have-the-same-radii-solid-sphere-will-have-lower-charge-than-the-hollow-one-brreason-r-capacitance-of-metallic-spheres-depend-on-the-radii-of-spheres-in-the-light-of-the-above-statements-choose-the-correct-answer-from-the-options-given-below/

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The ratio x/y on completion of the above reaction is ____.

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The sum to 20 terms of the series $2.2^2-3^2+2.4^2-5^2+2.6^2-\ldots \ldots$ is equal to $\_\_\_\_$ .

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Which one of the following is most likely a mismatch?

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The logic gate equivalent to the given circuit diagram is :

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Let for $\mathrm{x} \in \mathbb{R}, \mathrm{So}(\mathrm{x})=\mathrm{x}$, $S_k(x)=C_k x+k \int_0^x S_{k-1}(t) d t$, where $...

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An atomic substance A of molar mass $12 \mathrm{~g} \mathrm{~mol}^{-1}$ has a cubic crystal structure with edge length of 300...

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A Carnot engine operating between two reservoirs has efficiency $\frac{1}{3}$. When the temperature of cold reservoir raised by $x$, its...

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The ratio of spin-only magnetic moment values

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D-(+)-Glyceraldehyde $$ \text { D-(+)-Glyceraldehyde } \xrightarrow[\text { (ii) } \mathrm{H}_2 \mathrm{O} / \mathrm{H}^{+}]{\text {(i) } \mathrm{HCN}} $$ (iii) $\mathrm{HNO}_3$...

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Let $\omega=\mathrm{z} \overline{\mathrm{z}}+\mathrm{k} 1 \mathrm{z}+\mathrm{k} 2 \mathrm{z}+\lambda(1+\mathrm{j}), \mathrm{k}_1, \mathrm{k} 2 \in \mathbb{R}$. Let $\operatorname{Re}(\omega)=0$ be the circle C of radius...

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

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

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A mixture of 1 mole of $\mathrm{H}_2 \mathrm{O}$ and 1 mole of CO is taken in a 10 litre container...

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If $S=\left\{x \in \mathbb{R}: \sin ^{-1}\left(\frac{x+1}{\sqrt{x^2+2 x+2}}\right)-\sin ^{-1}\left(\frac{x}{\sqrt{x^2+1}}\right)=\frac{\pi}{4}\right\}$, then $\sum_{x \in \mathbb{R}}\left(\sin \left(x^2+x+5\right) \frac{\pi}{2}\right)-\cos \left(\left(x^2+x+5\right) \pi\right)$ is equal to $\_\_\_\_$...

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Which of the following statement is correct for paper chromatography?

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2-Methyl propyl bromide reacts with C2H5O– and gives 'A' whereas on reaction with C2H5OH it gives 'B'. The mechanism followed...

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Let $\alpha$ be the constant term in the binomial expansion of $\left(\sqrt{x}-\frac{6}{x^{\frac{3}{2}}}\right)^n, n \leq 15$. If the sum of the...

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In the following reaction ‘X’ is $...

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For a good quality cement, the ratio of silica to alumina is found to be

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Let $f(x)=\int \frac{d x}{\left(3+4 x^2\right) \sqrt{4-3 x^2}},|x|0$, then $\alpha^2+\beta^2$ is equal to. $\_\_\_\_$ .

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The complex

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Let the equation of plane passing through the line of intersection of the planes $x+2 y+a z=2$ and $x-y +z=3$...

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The radical which mainly causes ozone depletion in the presence of UV radiations is:

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During water-gas shift reaction

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Consider the triangles with vertices $A(2,1) B(0,0)$ and $C(t, 4), t \in[0,4]$. It the maximum and the minimum perimeters of...

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In the above reaction. Left hand side and right hand side rings are named as 'A' and 'B' respectively. They...

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Arrange the following compounds in increasing order of rate of aromatic electrophilic substitution reaction

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Which is not true for arginine?

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If the area bounded by the curve $2 y^2=3 x$, lines $x+y=3, y=0$ and outside the circle $(x-3)^2+y^2=2$ is $A$,...

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Let $y=y_1(x)$ and $y=y_2(x)$ be the solution curves of the differential equation $\frac{d y}{d x}=y+7$ with initial conditions $y_1(0)=y_2(0)=1$ respectively....

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Given below are two statements: Statement I: If BOD is 4 ppm and dissolved oxygen is 8 ppm, then it...

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Match the following

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If the line $x=y=z$ intersects the line $...

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If the distance of the earth from Sun is 1.5 × $10^6$ km. Then the distance of an imaginary planet...

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Let $s 1, s 2, s s_{3000-u s 10}$ respectively be the sum to 12 terms of 10 A.P.s whose...

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The number of elements in the set $\left\{n \in N: 10 \leq n \leq 100\right.$ and $3^n-3$ is a multiple...

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Given below are two statements: [JEE (Main) 11-4-23_S1] [PB (N&O)_E] Ea$...

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An $\alpha$-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in...

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Among the following compounds, the one which shows highest dipole moment is

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major product 'A' formed in the above reaction is

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Let A = {1, 2, 3, 4} and R be a relation on the set A × A defined by...

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Let an ellipse with centre $(1,0)$ and latus rectum of length $\frac{1}{2}$ have its major axis along $x$-axis. If its...

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Which of the following complex has a possibility to exist as meridional isomer?

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Let the plane $P$ contain the line $2 x+y-z-3=0=5 x-3 y+4 z+9$ and be parallel to the line $\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}$. Then...

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Thin layer chromatography of a mixture shows the following observation:

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Among the following compounds, the one which shows highest dipole moment is

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A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different,...

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Match List-I with List-II:

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Let $\gamma_1$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of...

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If the sum of the series

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In the extraction process of copper, the product obtained after carrying out the reactions

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The electric potential at the centre of two concentric half rings of radii $\mathrm{R}_1$ and $\mathrm{R}_2$, having same linear charge...

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If the domain of the function Then $36|\alpha+\beta|$ is equal to-

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Let S be the set of all $(\lambda, \mu)$ for which the vectors $\lambda \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}, \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\mu \hat{\mathrm{k}}$ and $...

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For compound having the formula GaAICI4, the correct option from the following is

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$\int_0^1 \frac{1}{\left(5+2 x-2 x^2\right)\left(1+e^{(2-4 x)}\right)} d x=\frac{1}{\alpha} \log _e\left(\frac{\alpha+1}{\beta}\right), \alpha, \beta>0$, then $\alpha^4-\beta^4$ is equal to:

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Match List-I with List-II: [JEE (Main) 11-4-23_S1] [CB_E] Ea$...

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A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal...

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Let the foot of perpendicular of the point $\mathrm{P}(3,-2-9)$ on the plane passing through the points $(-1,-2,-3),(9,3,4),(9,-2,1)$ be $...

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If $(\alpha, \beta)$ is the orthocentre of the triangle ABC with vertices $\mathrm{A}(3,-7), \mathrm{B}(-1,2)$ and $\mathrm{C}(4,5)$, then $9 \alpha-6 \beta+60$...

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Let the system of linear equations has a unique solution $x=\alpha, y=\beta, z=\gamma$. Then the distance of the point $...

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The shortest distance between the lines $\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}$ and $\frac{x-4}{1}=\frac{y-1}{-2}=\frac{z+3}{0}$ is

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Negation of $p \wedge(q \wedge \sim(p \wedge q))$ is

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$$ \text { The number of common tangents, to the circles } x^2+y^2-18 x-15 y+131=0 \text { and } x^2+y^2-6...

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$$ \text { If the set }\left\{\operatorname{Re}\left(\frac{z-\bar{z}+z \bar{z}}{2-3 z+5 \bar{z}}\right): z \in \mathbb{C}, \operatorname{Re}(z)=3\right\} \text { is equal to the...

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In the above conversion the correct sequence of reagents to be added is

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Let $B=\left[\begin{array}{ccc}1 & 3 & \alpha \\ 1 & 2 & 3 \\ \alpha & \alpha & \alpha\end{array}\right], \alpha>2$ be...

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

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Let $\vec{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \vec{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}$ and $\vec{c}=2 \hat{i}-\hat{j}+4 \hat{k}$. If a vector $\vec{d}$ satisfies $...

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Which of the following statement(s) is/are correct? (A) The pH of $1 \times 10^{-8} \mathrm{M} \mathrm{HCl}$ solution is 8 ....

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Fractional part of the number $\frac{4^{2022}}{15}$ is equal to

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For $x \in R$, two real valued functions $f(x)$ and $g(x)$ are such that, $g(x)=\sqrt{x}+1$ and $f g(x)=x+3-\sqrt{x}$. Then $f(0)$...

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Decreasing order of reactivity towards electrophilie substitution for the following compounds is :

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Given below are two statements: Statement-I Permutit process is more efficient compared to the synthetic resin method for the softening...

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Let P Q be a focal chord of the parabola $y^2=36 x$ of length 100 , making an acute angle...

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Let $A_1$ and $A_2$ be two arithmetic means and $G_1, G_2, G_3$ be three geometric means of two distinct positive...

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

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Given below are two statements Statement-I: According to Bohr's model of hydrogen atom, the angular momentum of an electron in...

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A metal chloride contains 55.0% of chlorine by weight. 100 mL vapours of the metal chloride at STP weigh 0.57...

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Let the determinant of a square matrix A of order m be m – n, where m and n satisfy...

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A molecule undergoes two independent first order reactions whose respective half lives are 12 min and 3 min. If both...

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Given below are two statements: Statements: $\mathrm{SbCl}_5$ is more covalent than $\mathrm{SbCl}_3$ Statements: The higher oxides of halogens also tend...

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The number of $\mathrm{P}-\mathrm{O}-\mathrm{P}$ bonds in $\mathrm{H}_4 \mathrm{P}_2 \mathrm{O}_7,\left(\mathrm{HPO}_3\right)_3$ and $\mathrm{P}_4 \mathrm{O}_{10}$ are respectively.

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Let $\left(a+b x+c x^2\right)^{10}=\sum_{i=0}^{20} p_i x^i, a, b, c \in \mathbb{N}$. If $p_1=20$ and $p_2=210$, then $2(a+b+c)$ is equal to

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Consider the following sequence of reactions:The product ‘B’ is

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The density of alkali metals is in the order

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The area of the region enclosed by the curve $f(x)=\max \{\sin x, \cos x\}-\pi \leq x \leq \pi$ and the...

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The number of real roots of the equation $x|x|-5|x+2|+6=0$, is

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Consider the following statements: (A) NF3 molecule has a trigonal planar structure. (B) Bond length of N2 is shorter than...

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Let the tangent and normal at the point $(3 \sqrt{3}, 1)$ on the ellipse $\frac{x^2}{36}+\frac{y^2}{4}=1$ meet the $y$-axis at the...

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Let $[x]$ denote the greatest integer function and $f(x)=\max \{1+x+[x], 2+x, x+2[x]\}, 0 \leq x \leq 2$. Let $m$ be...

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Let $x=x(y)$ be the solution of the differential equation $2(y+2) \log _e(y+2) d x+\left(x+4-2 \log _e(y+2)\right) d y=0, y>-1$ with...

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The possibility of photochemical smog formation will be minimum at

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For the differentiable function $f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}$, let $3 f(x)+2 f\left(\frac{1}{x}\right)=\frac{1}{x}-10$, then $\left|f(3)+f^{\prime}\left(\frac{1}{4}\right)\right|$ is equal to

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The product formed in the following multistep reaction is

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The sum of all the roots of the equation is :$\left|x^2-8 x+15\right|-2 x+7=0$ is :

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Match List I with List II:

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For the system of linear equations $$ \begin{aligned} & 2 x+4 y+2 a z=b \\ & x+2 y+3 z=4 \\...

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Statement $(P \Rightarrow Q) \wedge(R \Rightarrow Q)$ is logically equivalent to

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Let $A B C D$ be a quadrilateral. If $E$ and $F$ are the mid points of the diagonals $...

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The mismatched combinations are A. Chlorophyll - Co B. Water hardness - EDTA C. Photography - $[\mathrm{Ag}(\mathrm{CN}) 2]^{-}$ D. Wilkinson...

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If the equation of the plane passing through the line of intersection of the planes 2x - y + z...

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The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one...

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Let $I(x)=\int \frac{x^2\left(x \sec ^2 x+\tan x\right)}{(x \tan x+1)^2} d x$. If $I(0)=0$ the $I\left(\frac{\pi}{4}\right)$ is equal to

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Let S be the set of all values of $\lambda$, for which the shortest distance between the lines $\frac{x-\lambda}{0}=\frac{y-3}{4}=\frac{x+6}{1}$ and...

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Given below are two statements: Statement-I Permutit process is more efficient compared to the synthetic resin method for the softening...

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A coin is biased so that the head is 3 times as likely to occur as tail. This coin is...

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Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{i}}\right] 2 \times 2$ where $\mathrm{a}_{\mathrm{i}} \neq 0$ for all $\mathrm{i}, \mathrm{j}$ and $\mathrm{A}^2=\mathrm{I}$. Let a be the sum...

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The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1, 3, 5, 8,...

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In the reaction given below

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The distance of the point $(-1,2,3)$ from the plane $\vec{r} \cdot(\hat{i}-2 \hat{j}+3 \hat{k})=10$ parallel to the line of the shortest...

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The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of...

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Let $A=\left[\begin{array}{lll}0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0\end{array}\right]$, where $...

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The number of following statement/s which is/are incorrect is______.

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The sum of the first 20 terms of the series 5 +11 + 19 + 29 + 41 + ......

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The negation of the statement $((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A$ is

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If a and b are the roots of equation $x^2-7 x-1=0$, then the value of $\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}$ is equal to

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If $\int_{-0.15}^{0.15}\left|100 \mathrm{x}^2-1\right| \mathrm{dx}=\frac{\mathrm{k}}{3000}$, then k is equal to $\_\_\_\_$ .

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From the top A of a vertical wall AB of height 30 m, the angles of depression of the top...

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Three bulbs are filled with CH4, CO2 and Ne as shown in the picture. The bulbs are connected through pipes...

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Let $H_n=\frac{x^2}{1+n}-\frac{y^2}{3+n}=1, n \in N$. Let $k$ be the smallest even value of $n$ such that the eccentricity of $H_k$...

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The number of relations, on the set {1, 2, 3} containing (1, 2) and (2,3), which are reflexive and transitive...

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The set of all $a \in \mathbb{R}$ for which the equation $x|x-1|+|x+2|+a=0$ has exactly one real root is :

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The number of ordered triplets of the truth values of $p, q$ and $r$ such that the truth value of...

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The titration curve of weak acid vs. strong base with phenolphthalein as indictor) is shown below. The Kphenolphthalein = 4...

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The straight lines $I_1$ and $I_2$ pass through the origin and trisect the line segment of the line L: 9x...

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Let the positive numbers $a_1, a_2, a_3, a_4$ and $a_5$ be in a G.P. Let their mean and variance be...

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The number of integral terms in the expansion of $\left(3^{\frac{1}{2}}+5^{\frac{1}{4}}\right)^{680}$ is equal to

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$\max _{0 \leq x \leq \pi}\left\{x-2 \sin x \cos x+\frac{1}{3} \sin 3 x\right\}=$

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Let $\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{b}=2 \hat{i}-2 \hat{j}-2 \hat{k}$ and $\vec{c}=-\hat{i}+4 \hat{j}+3 \hat{k}$. If $\vec{d}$ is a vector perpendicular to...

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XeF4 reacts with SbF5 to form $\mathrm{XeF}_4$ reacts with $\mathrm{SbF}_5$ to form $\left[\mathrm{XeF}_{\mathrm{m}}\right]^{n+}\left[\mathrm{SbF}_{\mathrm{y}}\right]^{z-}$

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Let a line $I$ pass through the origin and be perpendicular to the lines $...

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Let $D_k=\left|\begin{array}{ccc}1 & 2 k & 2 k-1 \\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2\end{array}\right|$....

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In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in...

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$\int_0^{\infty} \frac{6}{e^{3 x}+6 e^{2 x}+1}$

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If the ratio of the fifth term from the begining to the fifth term from the end in the expansion...

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

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For $m, n>0$, let $\alpha(m, n)=\int_0^2 t^m(1+3 t)^n d t$. If $11 \alpha(10,6)+18 \alpha(11,5)=p(14)^6$, then $p$ is equal to

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Let $I(x)=\int \sqrt{\frac{x+7}{x}} d x$ and $I(9)=12+7 \log _e 7$. If $I(1)=\alpha+7 \log _e(1+2 \sqrt{2})$, then $\alpha^4$ is equal to...

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The vapour pressure vs. temperature curve for a solution solvent system is shown below. The boiling point of the solvent...

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The number of bent-shaped molecule/s from the following is ______. $\mathrm{N}_3^{-}, \mathrm{NO}_2^{-}, \mathrm{I}_3^{-}, \mathrm{O}_3, \mathrm{SO}_2$

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

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Let $S=109+\frac{108}{5}+\frac{107}{5^2}+\ldots \ldots \ldots+\frac{2}{5^{107}}+\frac{1}{5^{108}}$. Then the value of $\left(16 S-(25)^{-54}\right)$ is equal to $\_\_\_\_$ .

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The number of given statement/s which is/are correct is____.

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Let the plane $x+3 y-2 z+6=0$ meet the co-ordinate axes at the points A,B,C. It the orthocentre of the triangle...

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The number of correct statement/s involving equilibria in physical process from the following is (A) Equilibrium is possible only in...

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If ${ }^{2 n} C_3 \cdot{ }^n C_3=10: 1$, then the ratio $\left(n^2+3 n\right):\left(n^2-3 n+4\right)$ is

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The mean of the coefficients of $x, x^2$ $\_\_\_\_$ $x^7$ in the binomial expansion of $(2+x)^9$ is $\_\_\_\_$ .

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When a 60 W electric heater is immersed in a gas for 100s in a constant volume container with adiabatic...

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The incorrect statement regarding the reaction given below is

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Identify the correct order of reactivity for the following pairs towards the respective mechanism Choose the correct answer from the...

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Let $[x]$ be the greatest integer $\leq x$. Then the number of points in the interval $(-2,1)$, where the function...

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A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If...

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Let the mean and variance of 8 numbers x, y, 10, 12, 6, 12, 4, 8, be 9 and 9.25...

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Let $x_1, x_2$ $\_\_\_\_$ $x_{100}$ be in an arithmetic progression, with $x_1=2$ and their mean equal to 200 . If...

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Suitable reaction condition for preparation of Methyl phenyl ether is

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Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three...

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Let $\lambda_1, \lambda_2$ be the values of $\lambda$ for which the points $\left(\frac{5}{2}, 1, \lambda\right)$ and $(-2,0,1)$ are at equal...

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The number of elements in the set $S=\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^2 \theta+2=0\right\}$...

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The major product ‘P’ formed in the given reaction is

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The number of following factors which affect the percent covalent character of the ionic bond is____

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A fair n (n > 1) faces die is rolled repeatedly until a number less than n appears. If the...

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If the solution curve of the differential equation $\left(y-2 \log _e x\right) d x+\left(x \log _e x^2\right) d y=0, x>1$...

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Molar mass of the hydrocarbon $(X)$ which on ozonolysis consumes one mole of $O_3$ per mole of $(X)$ and gives...

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Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i}+\hat{j}, \hat{i}+\hat{k}$...

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The enthalpy change for the adsorption process and micelle formation respectively are

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In a triangle $A B C$, if $\cos A+2 \cos B+\cos C=2$ and the lengths of the sides opposite to...

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For elements B, C, N, Li, Be, O and F the correct order of first ionization enthalpy is

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Given below are two statements: Statement I: Lithium and Magnesium do not form superoxide Statement II: The ionic radius of...

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The number of molecules and moles in 2.8375 litres of $\mathrm{O}_2$ at STP are respectively

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Consider a circle $C_1: x^2+y^2-4 x-2 y=\alpha-5$. Let its mirror image in the line $y=2 x+1$ be another circle $...

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Let $(\alpha, \beta, \gamma)$ be the image of the point $\mathrm{P}(2,3,5)$ in the plane $2 \mathrm{x}+\mathrm{y}-3 \mathrm{z}=6$. Then $\alpha+\beta+\gamma$ is...

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Where Nu = Nucleophile Find out the correct statement from the options given below for the above 2 reactions.

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Match List I with List I is reacted with reagents in List I to form products in List II.

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

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Two dice A and B are rolled, Let the numbers obtained on A and B be $\alpha$ and $\beta$ respectively....

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

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Let $A$ be a $2 \times 2$ matrix with real entries such that $A^{\prime}=\alpha A+I$, where $\alpha \in \mathbb{R}-\{-1,1\}$. If...

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Let A = {0, 3, 4, 6, 7, 8, 9, 10} and R be the relation defined on A such...

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The set which does not have ambidentate ligand(s) is

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Four gases A, B, C and D have critical temperatures 5.3, 33.2, 126.0 and 154.3 K respectively. For their adsorption...

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The compound which does not exist is:

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The correct order of electronegativity for given elements is:

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If the point $\left(\alpha, \frac{7 \sqrt{3}}{3}\right)$ lies on the curve traced by the mid-points of the line segments of the...

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If $a_n$ is the greatest term in the sequence $a_n=\frac{n^3}{n^4+147}, n=1,2,3 \ldots \ldots$, then $a$ is equal to $\_\_\_\_$ .

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‘A’ and ‘B’ in the below reaction are:

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A is

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Given: (A) $2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_2(\mathrm{~g})$ in $\quad \Delta \mathrm{H}_1^{\ominus}=-\mathrm{x} \mathrm{kJ} \mathrm{mol}^{-1}$ (B) C (graphite) $+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})$; $...

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

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Let $5 f(x)+4 f\left(\frac{1}{x}\right)=\frac{1}{x}+3, x>0$. Then $18 \int_1^2 f(x) d x$ is equal to :

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The largest natural number $n$ such that $3^n$ divides $66!$ is $\_\_\_\_$

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Match List I with List II

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25 mL of silver nitrate solution (1 M) is added dropwise to 25 mL of potassium iodide (1.05 M) solution....

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The octahedral diamagnetic low spin complex among the following is

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Let $f:[2,4] \rightarrow \mathbb{R}$ be a differentiable function such that $...

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Let $\vec{a}=6 \hat{i}+9 \hat{j}+12 \hat{k}, \vec{b}=\alpha \hat{i}+11 \hat{j}-2 \hat{k}$, and $\vec{c}$ be vectors such that $...

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Let C be the circle in the complex plane with centre $z_0=\frac{1}{2}(1+3 i)$ and radius $r=1$. Let $z_1=1+i$ and the...

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

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In ammonium-phosphomolybdate, the oxidation state of Mo is + ………………

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Which halogen is known to cause the reaction given below: $2 \mathrm{Cu}^{2+}+4 \mathrm{X}^{-} \rightarrow \mathrm{Cu}_2 \mathrm{X}_2(\mathrm{~s})+\mathrm{X}_k$

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If 5 moles of $\mathrm{BaCl}_2$ is mixed with 2 moles of $\mathrm{Na}_3 \mathrm{PO}_4$, the maximum number of moles of $\mathrm{Ba}_3\left(\mathrm{PO}_4\right)_2$...

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Let $[t]$ denotes the greatest integer $\leq t$. If the constant term in the expansion of $\left(3 x^2-\frac{1}{2 x^5}\right)^7$ is...

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The correct order of spin only magnetic moments for the following complex ions is

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When a solution of mixture having two inorganic salts was treated with freshly prepared ferrous sulphate in acidic medium, a...

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Let $[t]$ denotes the greatest integer $\leq t$. Then $...

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Which of the following statements are correct? (A) The $\mathrm{M}^{3+} / \mathrm{M}^{2+}$ reduction potential for iron is greater than manganese...

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What is the purpose of adding gypsum to cement?

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Let the plane $P: 4 x-y+z=10$ be rotated by an angle $\frac{\pi}{2}$ about its line of intersection with the plane...

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For the adsorption of hydrogen on platinum, the activation energy is 30 kJ $\mathrm{mol}^{-1}$ and for the adsorption of hydrogen...

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The polymer X–consists of linear molecules and is closely packed. It is prepared in the presence of triethylaluminium and titanium...

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In chromyl chloride, the number of d-electrons present on chromium is same as in (Given atomic no. of Jii 22,...

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Given below are two reactions, involved in the commercial production of dihydrogen $\left(\mathrm{H}_2\right)$. The two reactions are carried out at...

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Let $A=\left[\begin{array}{cc}1 & \frac{1}{51} \\ 0 & 1\end{array}\right]$. If $...

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If for $z=\alpha+i \beta=|z+2|=z+4(1+i)$, then $\alpha+\beta$ and $\alpha \beta$ are the roots of the equation

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Area of the region $\left\{(x, y): x^2+(y-2)^2 \leq 4, x^2 \geq 2 y\right\}$ is

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L-isomer of tetrose $X\left(\mathrm{C}_4 \mathrm{H}_8 \mathrm{O}_4\right)$ gives positive Schiff's test and has two chiral carbons. On acetylation. ' X '...

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Number of ambidentate ligands in a representative metal complex $\left[\mathrm{M}(\mathrm{en})(\mathrm{SCN})_4\right]$ is [en = ethylenediamine]

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The area of the region enclosed by the curve $y=x^3$ and its tangent at the point $(-1,-1)$ is

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

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$\lim _{x \rightarrow 0}\left(\left(\frac{1-\cos ^2(3 x)}{\cos ^3(4 x)}\right)\left(\frac{\sin ^3(4 x)}{\left(\log _e(2 x+1)\right)^5}\right)\right)$ is equal to $\_\_\_\_$

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The value of log K for the reaction A ⇋ B at 298 K is____. (Nearest integer) Given: $$ \begin{aligned}...

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The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^2 \geq 0$ is

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The sum, of the coefficients of the first 50 terms in the binomial expansion of $(1-x)^{100}$, is equal to

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Let the number of elements in sets A and B be five and two respectively. Then the number of subsets...

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The number of elements in the set $\left\{n \in \mathbb{Z}:\left|n^2-10 n+19\right|

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Mass of Urea $\left(\mathrm{NH}_2 \mathrm{CONH}_2\right)$ required to be dissolved in 1000 g of water to reduce the vapour pressure of...

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The one that does not stabilize $2^{\circ} \text { and } 3^{\circ}$ structures of proteins is

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Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played...

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

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Match List I with List II

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The area of the region $\left\{(x, y): x^2 \leq y \leq 8-x^2, y \leq 7\right\}$ is -

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Consider ellipses $E_k: k x^2+k^2 y^2=1, k=1,2, \ldots \ldots, 20$. Let $C_k$ be the circle which touches the four chords...

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Given below are two statements Statement-I: Aqueous solution of $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ is preferred as a primary standard in volumetric...

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If the mean of the frequency distribution then its variance is ______.

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Among the two statements $(\mathrm{S} 1) \sim(\mathrm{p} \Rightarrow \mathrm{q}) \wedge(\mathrm{q} \wedge(\sim \mathrm{q}))$ is a contradiction and $$ (S 2) \sim(p...

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The negation of the statement $((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A$ is

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The shortest distance between the lines $\frac{x-4}{4}=\frac{y+2}{5}=\frac{z+3}{3}$ and $\frac{x-1}{3}=\frac{y-3}{4}=\frac{z-4}{2}$ is -

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Let ij $\mathrm{S}=\left\{\mathrm{M}=\left[a_{i j}\right], a_{i j} \in\{0,1,2\}, 1 \leq \mathrm{i}_k \mathrm{j} \leq 2\right\}$ be a sample space and $...

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Consider the graph of Gibbs free energy G vs Extent of reaction. The number of statement/s from the following which...

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Isomeric amines with molecular formula $\mathrm{C}_8 \mathrm{H}_{11} \mathrm{~N}$ give the following tests Isomer (P) ⇒ Can be prepared by Gabriel...

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Let $y=p(x)$ be the parabola passing through the points $(-1,0),(0,1)$ and $(1,0)$. If the area of the region $...

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The reaction Ea$y occurs in which of the given galvanic cell. $$ \frac{1}{2} \mathrm{H}_2(\mathrm{~g})+\mathrm{AgCl}(\mathrm{~s}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{Ag}(\mathrm{~s}) $$...

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An organization awarded 48 medals in event ‘A’, 25 in event ‘B’ and 18 in event ‘C’. If these medals...

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

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Negation of $(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$ is

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Let $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be three distinct positive real numbers such that $(2 \mathrm{a})^{\log _{\mathrm{a}} \mathrm{a}}=(\mathrm{bc})^{\log _{\mathrm{a}} \mathrm{b}}$ and $...

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

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Number of bromo derivatives obtained on treating ethane with excess of \mathrm{Br}_2, in diffused sunlight is…

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The pair from the following pairs having both compounds with net non-zero dipole moment is

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Let w1 be the point obtained by the rotation of z1 = 5 + 4i about the origin through a...

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The number of permutations, of the digits 1, 2, 3, …..7 without repetition, which neither contain the string 153 nor...

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Which of the following complex is octahedral, diamagnetic and the most stable?

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https://competishun.com/let-d-be-the-domain-of-the-function-fxsin-1leftlog-_3-xleftfrac62-log-_3-x-5-xrightright-if-the-range-of-the-function-g_i-d-rightarrow-r-defined-by-gxx-xleftxright-is-the-greatest-integer-function-is-alpha-beta-then-alpha2frac5beta-is-equal-to/

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The wavelength of an electron of kinetic energy $4.50 \times 10^{-29} \mathrm{~J}$ is $\_\_\_\_$ $\times 10^{-5} \mathrm{~m}$. (Nearest integer) Given:...

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The set of all $a \in \mathbb{R}$ for which the equation $x|x-1|+|x+2|+a=0$ has exactly one real root is :

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Let $A=\left[\begin{array}{ccc}2 & 1 & 0 \\ 1 & 2 & -1 \\ 0 & -1 & 2\end{array}\right]$. If |adj...

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Let a common tangent to the curves $y^2=4 x$ and $(x-4)^2+y^2=16$ touch the curves at the points $P$ and $Q$....

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For any vector $\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}$, with $10\left|a_i\right|

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Lime reacts exothermally with water to give A which has low solubility in water. Aqueous solution of ' $A$ '...

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For the reaction; $\mathrm{RCH}_2 \mathrm{Br}+\mathrm{I}^{-} \xrightarrow{\text { Acetone }} \mathrm{RCH}_2 \mathrm{I}+\mathrm{Br}_{\text {major }}^{-}$ The correct statement is:

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If the local maximum value of the function $f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^2 x}, x \in\left(0, \frac{\pi}{2}\right)$, is $\frac{k}{e}$, then...

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The major product formed in the following reaction is:

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Let $S_k=\frac{1+2+\ldots \ldots+K}{K}$ and $\sum_{j=1}^n S_j^2=\frac{n}{A}\left(B n^2+C n+D\right)$, where $A, B, C, D \in N$ and $A$ has least value....

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$\max _{0 \leq x \leq \pi}\left\{x-2 \sin x \cos x+\frac{1}{3} \sin 3 x\right\}$

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The sum of all those terms, of the arithmetic progression 3, 8, 13,…… 373, which are not divisible by 3,...

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Prolonged heating is avoided during the preparation of ferrous ammonium sulphate to

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For a concentrated solution of a weak electrolyte $\left(\mathrm{K}_{\text {eq }}=\right.$ equilibrium constant $) \mathrm{A}_2 \mathrm{~B}_3$ of concentration ‘c’, the...

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Using column chromatography, mixture of two compounds ‘A’ and ‘B’ was separated. ‘A’ eluted first, this indicates ‘B’ has

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Let $a, b, c$ be three distinct real numbers, none equal to one. If the vectors $a \hat{i}+\hat{j}+\hat{k}, \hat{i}+b \hat{j}+\hat{k}$...

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The water gas on reacting with cobalt as a catalyst forms

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If the coefficients of the three consecutive terms in the expansion of $(1+x)^n$ are in the ratio $1: 5: 20$,...

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The number of triplets (x, y, z). where x, y, z are distinct non negative integers satisfying x + y...

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Let $P\left(\frac{2 \sqrt{3}}{\sqrt{7}}, \frac{6}{\sqrt{7}}\right), Q, R$ and $S$ be four points on the ellipse $9 x^2+4 y^2=36$. Let $P Q$...

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$\int_0^{\infty} \frac{6}{e^{3 x}+6 e^{2 x}+11 e^x+6} d x$

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The major product formed in the following reaction is

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The coefficient of $x^7$ in $\left(1-x+2 x^3\right)^{10}$ is $\_\_\_\_$

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Let $f(x)=\left[x^2-x\right]+|-x+[x]|$, where $x \in \mathbb{R}$ and $[t]$ denotes the greatest integer less than or equal to $t$. Then, f...

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If the points with vectors $\alpha \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+13 \hat{\mathrm{k}}, 6 \hat{\mathrm{i}}+11 \hat{\mathrm{j}}+11 \hat{\mathrm{k}}, \frac{9}{2} \hat{\mathrm{i}}+\beta \hat{\mathrm{j}}-8 \hat{\mathrm{k}}$ are collinear, then...

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From the given transfer characteristic of a transistor in CE configuration, the value of power gain of this configuration is...

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An are PQ of a circle subtends a right angle at its centre O . The mid point of the...

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Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B...

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Strong reducing and oxidizing agents among the following, respectively, are

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Sulphur (S) containing amino acids from the following are (a) isoleucine (b) cysteine (c) lysine (d) methionine (e) glutamic acid

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A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of...

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

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Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum...

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A fish rising vertically upward with a uniform velocity of $8 \mathrm{~ms}^{-1}$, observes that a bird is diving vertically downward...

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Let $\alpha, \beta$ be the roots of the quadratic equation $x^2+\sqrt{6} x+3=0$. Then $\frac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}$ is

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Let $f(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x}, x \in[0, \pi]-\left\{\frac{\pi}{4}\right\}$. Then $f\left(\frac{7 \pi}{12}\right) f^{\prime \prime}\left(\frac{7 \pi}{12}\right)$ is equal to -

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Choose the halogen which is most reactive towards SN1 reaction in the given compounds (A, B, C & D) https://cdn.mathpix.com/snip/images/Yncz2qqJvofkemQ1n38mek_cPtAhdHxXY_XI_KioLLI.original.fullsize.png

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Let the tangent to the curve $x^2+2 x-4 y+9=0$ at the point P(1, 3) on it meet the y-axis at...

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If $I(x)=\int e^{\sin 2} x(\cos x \sin 2 x-\sin x) d x$ and $I(0)=1$, then $I\left(\frac{\pi}{3}\right)$ is equal to

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n the given figure, an inductor and a resistor are connected in series with a battery of emf E volt....

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Let R be a rectangle given by the lines $x=0, x=2, y=0$ and $y=5$. Let $A(\alpha, 0)$ and $...

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The number of five digit numbers, greater than 40000 and divisible by 5, which can be formed using the digits...

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Which of the following options are correct for the reaction $2\left[\mathrm{Au}(\mathrm{CN})_2\right]^{-}(\mathrm{aq})+\mathrm{Zn}(\mathrm{s}) \rightarrow 2 \mathrm{Au}(\mathrm{s})+\left[\mathrm{Zn}(\mathrm{CN})_4\right]^{2-}{ }_{(\mathrm{aq})}$ A. Redox reaction B. Displacement...

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A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel...

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Let the image of the point P(1, 2, 3) in the plane 2x – y + z = 9 be...

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The number of arrangements of the letter of the word “INDEPENDENCE” in which all the vowels always occur together is-

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If equation of the plane that contains the point $(-2,3,5)$ and is perpendicular to each of the planes $...

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Which of the following represent the Freundlich adsorption isotherms?

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Let A={1, 2, 3, 4,.....10} and B = {0, 1, 2, 3, 4}. The number of elements in the relation...

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The radius of $2^{\text {nd }}$ orbit of $\mathrm{He}^{+}$of Bohr's model is $\mathrm{r}_1$ and that of fourth orbit of Be...

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Let two vertices of triangle ABC be $(2,4,6)$ and $(0,-2,-5)$, and its centroid be $(2,1,-1)$. If the image of third...

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

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When a resistance of $5 \Omega$ is shunted with a moving coil galvanometer, it shows a fullscale deflection for a...

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In a bolt factory, machines A, B and C manufacture respectively 20%, 30% and 50% of the total bolts. of...

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64 identical drops each charged upto potential of 10 mV are combined to form a bigger dorp. The potential of...

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The coefficient of $x^{18}$ in the expansion of $\left(x^4-\frac{1}{x^3}\right)^{15}$ is $\_\_\_\_$

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The value of the integral $\int_{-\log _e 2}^{\log _e 2} \mathrm{e}^{\mathrm{x}}\left(\log _{\mathrm{e}}\left(\mathrm{e}^{\mathrm{x}}+\sqrt{1+\mathrm{e}^{2 \mathrm{x}}}\right)\right) \mathrm{dx}$ is equal to

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Match List I with List II

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If the coefficient of $x^7$ in $\left(a x-\frac{1}{b x^2}\right)^{13}$ and the coefficient of $x^{-5}$ in $\left(a x+\frac{1}{b x^2}\right)^{13}$ are equal,...

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At a given point of time the value of displacement of a simple harmonic oscillator is given as $...

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

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The number of ways, in which 5 girls and 7 boys can be seated at a round table so that...

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Let y = y(x) be a solution of the differential equation (xcos x)dy + (xysinx + ycos x – l)dx...

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A potential $V_0$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_1$. The wire is...

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The negation of the statement $(p \vee q)^{\wedge}(q \vee(\sim r))$ is

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The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J....

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Let $P$ be the point of intersection of the line $\frac{x+3}{3}=\frac{y+2}{1}=\frac{1-z}{2}$ and the plane $x+y+z=2$. If the distance of the...

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The major products A and B from the following reactions are:

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

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Compound P is neutral. Q gives effervescence with $\mathrm{NaHCO}_3$ while R reacts with Hinsbergs reagent to give solid soluble in...

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Given below are two statements: one is labelled as assertion and the other is labelled as reason. Assertion: Loss of...

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The setting time of Cement is increased by adding

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Glycerine of density $1.25 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ is flowing through the conical section of pipe. The area of crosssection...

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Which of the following metals can be extracted through alkali leaching technique?

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Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them....

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The possibility of photochemical smog formation is more at

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Let $\alpha, \beta, \gamma$ be the three roots of the equation $x^3+b x+c=0$. If $\beta \gamma=1=-\alpha$, then $...

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Let the point $(p, p+1)$ lie inside the region $...

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${ }_{92}^{238} \mathrm{~A}|\rightarrow|_{90}^{234} \mathrm{~B}+{ }_2^4 \mathrm{D}+\mathrm{Q}$ In the given nuclear reaction, the approximate amount of energy released will be :...

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For the system of linear equations 2x - y + 3z = 5 3x + 2y – z = 7...

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The current flowing through a conductor connected across a source is 2A and 1.2 A at 0oC and 100oC respectively....

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

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Let $P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right], A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ and $Q=P Q P^{\top}$. If...

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If the area of the region $\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) ; 2 \mathrm{y}-\mathrm{y}^2 \leq \mathrm{x}^2 \leq 2 \mathrm{y}, \mathrm{x} \geq \mathrm{y}\right\}$ is...

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Two wires each of radius 0.2 cm and negligible mass, one made of steel and other made of brass are...

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In the given figure the total charge stored in the combination of capacitors is $100 \mu \mathrm{C}$. The value of...

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Which graph represents the difference between total energy and potential energy of a particle executing SHM Vs it’s distance from...

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A common example of alpha decay is The energy released $(Q)$ during the alpha decay of ${ }_{92}^{238} U$ is...

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The slope of tangent at any point $(x, y)$ on a curve $y=y(x)$ is $\frac{x^2+y^2}{2 x y}, x>0$. If $y(2)=0$,...

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The number of ways of giving 20 distinct oranges to 3 children such that each child gets atleast one orange...

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10 resistors each of resistance 10 can be connected in such as to get maximum and minimum equivalent resistance. The...

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The difference between electron gain enthalpies will be maximum between:

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For the following circuit and given inputs A and B, choose the correct option for output ‘Y’

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Let $C(\alpha, \beta)$ be the circumcenter of the triangle formed by the lines $$ \begin{aligned} & 4 x+3 y=69 \\...

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Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively [a < b <...

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A block of mass 10 kg is moving along x-axis under the action of force F = 5x N. The...

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A circle passing through the point P($\alpha, \beta$) in the first quadrant touches the two coordinate axes at the points...

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Polymer used in orlon is:

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If $A$ is a $3 \times 3$ matrix and $|A|=2$, then $\left|3 \operatorname{adj}\left(|3 A| A^2\right)\right|$ is equal to

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The decay constant for a radioactive nuclide is 1.5 × 10–5 s–1. Atomic of the substance is 60g mole–1, (NA...

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There is an air bubble of radius 1.0 mm in a liquid of surface tension $0.075 \mathrm{Nm}^{-1}$ and density 1000...

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The standard electrode potential of M+/M in aqueous solution does not depend on

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A transverse harmonic wave on a string is given by y(x, t) = 5 sin(6t + 0.003x) where x and...

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Under isothermal condition, the pressure of a gas is given by \mathrm{P}=\mathrm{a} \mathrm{~V}^{-3}, where a is a constant and V...

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An electron in a hydrogen atom revolves around its nucleus with a speed of $6.76 \times 10^6 \mathrm{~ms}^{-1}$ in an...

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$96 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$ is equal to

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Let $a \in Z$ and [t] be the greatest integer $\leq$ t. Then the number of points, where the function...

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A 1m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular...

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

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Let R be the focus of the parabola $\mathrm{y}^2=20 \mathrm{x}$ and the line $\mathrm{y}=m \mathrm{x}+c$ intersect the parabola at two...

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The refractive index of a transparent liquid filled in an equilateral hollow prism is 2 . The angle of minimum...

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The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross-section. Cross sectional areas at...

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Let the complex number $z=x+i y$ be such that $\frac{2 z-3 i}{2 z+i}$ is purely imaginary. If $x+y^2=0$, then $y^4+y^2-y$...

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A conducting circular loop is placed in a uniform magnetic field of 0.4 T with its plane perpendicular to the...

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The current required to be passed through a solenoid of 15 cm length and 60 turns in order to demagnetise...

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Let $A=\{x \in R ;[x+3]+[x+4] \leq 3\},\left\{x \in R: 3^x\left(\sum_{t=1}^{\infty} \frac{3}{10^t}\right)^{x-3}

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A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping....

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A line segment AB of length l moves such that the points A and B remain on the periphery of...

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If the equation of the plane containing the line $x+2 y+3 z-4=0=2 x+y-z+5$ and perpendicular to the plane $...

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Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio...

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A compound is formed by two elements X and Y. The element Y forms cubic close packed arrangement and those...

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As per given figure $A, B$ and $C$ are the first, second and third excited energy level of hydrogen atom...

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Let the position vectors of the points A, B, C and D be $...

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For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$. The value of...

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Let $f$ be a differentiable function such that $x^2 f(x)-x=4 \int_0^x t f(t) d t, f(1)=\frac{2}{3}$. Then $18 f(3)$ is...

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A body of mass $(5 \pm 0.5) \mathrm{kg}$ is moving with a velocity of $(20 \pm 0.4) \mathrm{m} / \mathrm{s}$....

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Let $I(x)=\int \frac{(x+1)}{x\left(1+x e^x\right)^2} d x, x>0$, If $\lim _{x \rightarrow \infty} I(x)=0$, then $I(1)$ is equal to

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For a certain organ pipe, the first three resonance frequencies are in the ratio of $1: 3: 5$ respectively. If...

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The fundamental frequency of vibration of a string stretched between two rigid support is 50 Hz . The mass of...

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The rms speed of oxygen molecule in a vessel at particular temperature is $\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v$, where u is the average...

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Let the ellipse $E_{\text {in }} x^2+9 y^2=9$ intersect the positive $x$ - and $y$-axes at the points $A$ and...

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One vertex of a rectangular parallelopiped is at the origin O and the lengths of its edges along x, y...

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In the circuit diagram shown in figure given below, the current flowing through resistance $3 \Omega$ is $\frac{x}{3} A$. is...

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Given below are two statements: Statement-I : When the frequency of an a.c. source in a series LCR circuit increases,...

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A network of four resistances is connected to 9V battery, as shown in figure. The magnitude of voltage difference between...

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A square piece of tin of side 30 cm is to be made into a box without top by cutting...

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

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If $2 x^y+3 y^x=20$, then $\frac{d y}{d x}$ at $(2,2)$ is equal to

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The ratio of escape velocity of a planet to the escape velocity of earth will be: Given: Mass of the...

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A projectile fired at 30° to the ground is observed to be at same height at time 3s and 5s...

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A 20 cm long metallic rod is rotated with 210 rpm about an axis normal to the rod passing through...

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A disc is rolling without slipping on a surface. The radius of the disc is R. At t = 0,...

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The position-time graphs for two students A and B returning from the school to their homes are shown in figure...

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If $f(x)=\frac{\left(\tan 1^0\right) x+\log _e(123)}{x \log _e(1234)-\left(\tan 1^0\right)}, x>0$, then the least value of $f(f(x))+f\left(f\left(\frac{4}{x}\right)\right)$ is

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In the given circuit, the current (I) through the battery will be :

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The magnetic field B crossing normally a square metallic plate of area $4 \mathrm{~m}^2$ is changing with time as shown...

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A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted...

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A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the particle is and...

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If the system of equations x + y + az = b 2x + 5y + 2z = 6 x...

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A single slit of width $a$ is illuminated by a monochromatic light of wavelength 600 nm . The value of...

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Two charges each of magnitude 0.01 C and separated by a distance of 0.4 mm constitute an electric dipole. If...

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

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The de Broglie wavelength of a molecule in a gas at room temperature (300 K) is 1. If the temperature...

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The length of wire becomes $\mathrm{I}_1$ and $\mathrm{I}_2$ when 100 N and 120 N tensions are applied respectively. If $...

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Let a1, a2, a3 ...... an be n positive consecutive terms of an arithmetic progression. If d > 0 is...

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Let $O$ be the origin and the position vector of the point $P$ be $-\hat{i}-2 \hat{j}+3 \hat{k}$. If the position...

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A thermodynamic system is taken through cyclic process. The total work done in the process is :

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A bullet 10 g leaves the barrel of gun with a velocity of 600 m/s. If the barrel of gun...

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

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An object is placed at a distance of 12 cm in front of a plane mirror. The virtual and erect...

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The speed of a wave produced in water is given by $v=\lambda^{\mathrm{a}} \mathrm{g}^{\mathrm{b}} \rho^{\mathrm{c}}$. Where $\lambda, \mathrm{g}$ and $\rho$ are...

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The sum of all the roots of the equation $\left|x^2-8 x+15\right|-2 x+7=0$ is :

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A solid sphere of mass 500 g and radius 5 cm is rotated about one of its diameter with angular...

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A nucleus with mass number 242 and binding energy per nucleon as 7.6 MeV breaks into fragment each with mass...

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The difference between threshold wavelengths for two metal surfaces A and B having work function $\phi_A=9 e \mathrm{~V}$ and $...

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A ball is thrown vertically upward with an initial velocity of $150 \mathrm{~m} / \mathrm{s}$. The ratio of velocity after...

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The energy of an electromagnetic wave contained in a small volume oscillates with

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A current of 2 A flows through a wire of cross-sectional area $25.0 \mathrm{~mm}^2$. The number of free electrons in...

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A vector in $x$ - $y$ plane makes an angle of $30^{\circ}$ with $y$-axis. The magnitude of $y$-component of vector...

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A planet having mass 9 Me and radius $4 \mathrm{Re}_{\mathrm{e}}$, where Me and Re are mass and radius of earth...

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As shown in the figure. a configuration of two equal point charges (q0 = +2μ C) is placed on an...

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A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when...

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The magnetic intensity at the centre of a long current carrying solenoid is found to be $1.6 \times 10^3 \mathrm{Am}^{-1}$....

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Match List I with List II of electromagnetic waves with corresponding wavelength range:Choose the correct answer from the options given...

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The equivalent capacitance of the combination shown is

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The ratio of powers of two motors is $\frac{3 \sqrt{x}}{\sqrt{x}+1}$, that are capable of raising 300 kg water in 5...

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A force $\vec{F}=(2+3 x) \hat{i}$ acts on a particle in the x direction where F is in newton and x...

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An oscillating LC circuit consists of a 75 mH inductor and a $1.2 \mu \mathrm{~F}$ capacitor. If the maximum charge...

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The position vector of a particle related to time $t$ is given by $$ \overrightarrow{\mathrm{r}}=\left(10 t \hat{\mathrm{i}}+15 t^2 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}\right)...

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Given below are two statements: Statement I : A truck and a car moving with same kinetic energy are brought...

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The equation of wave is given by $Y=10^{-2} \sin 2 \pi\left(160 t-0.5 x+\frac{\pi}{4}\right)$ Where x and Y are in m...

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An air bubble of diameter 6 mm rises steadily through a solution of density $1750 \mathrm{~kg} / \mathrm{m}^3$ at the...

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Given below are two statements:

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Two trains ‘A’ and ‘B’ of length ‘l’ and ‘4l’ are travelling into a tunnel of length ‘L’ in parallel...

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The position of a particle related to time is given by $x=\left(5 t^2-4 t+5\right) m$. The magnitude of velocity of...

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An organ pipe 40 cm long is open at both ends. The speed of sound in air is $360 \mathrm{~ms}^{-1}$....

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The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens...

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The source of time varying magnetic field may be (A) a permanent magnet (B) an electric field changing linearly with...

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An engine operating between the boiling and freezing points of water will have 1. efficiency more than 27%

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If the equation of the plane passing through the line of intersection of the planes 2x - y + z...

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The moment of inertia of semicircular ring about an axis, passing through the center and perpendicular to the plane of...

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A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and...

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Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r & 3r respectively....

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A vessel of depth ‘d’ is half filled with oil of refractive index $\mathrm{n}_1$ and the other half is filled...

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Two radioactive elements A and B initially have same number of atoms. The half life of A is same as...

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$\operatorname{Let} I(x)=\int \frac{x^2\left(x \sec ^2 x+\tan x\right)}{(x \tan x+1)^2} d x$. If $I(0)=0$ the $I\left(\frac{\pi}{4}\right)$ is equal to

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The momentum of a body is increased by 50%. The percentage increase in the kinetic energy of the body is...

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Given below are two statements:

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A body cools from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in 5 minutes. The temperature of the surrounding is $20^{\circ} \mathrm{C}$....

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A wire of length ' $L$ ' and radius ' $r$ ' is clamped rigidly at one end. When the...

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Different combination of 3 resistors of equal resistance R are shown in the figures. The increasing order for power dissipation...

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An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at...

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Two vertical parallel mirrors A and B are separated by 10 cm. A point object O is placed at a...

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Three force $F_1=10 \mathrm{~N}, F_2=8 \mathrm{~N}, F_3=6 \mathrm{~N}$ are acting on a particle of mass 5 kg . The forces...

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Let $\mathrm{A}=\left[a_{i j}\right]_{2 \times 2}$ where $a_{i j} \neq 0$ for all $\mathrm{j}_i \mathrm{j}$ and $\mathrm{A}^2=\mathrm{I}$. Let a be the...

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An electric dipole of dipole moment is $6.0 \times 10^{-6} \mathrm{Cm}$ placed in a uniform electric field of $...

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Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The...

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

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Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the...

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Proton $(P)$ and electron $(e)$ will have same de-Broglie wavelength when the ratio of their momentum is (assume, $\mathrm{m}_{\mathrm{p}}=1849 \mathrm{~m}$...

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Which of the following Maxwell’s equations is valid for time varying conditions but not valid for static conditions :

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The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of...

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The equivalent resistance of the circuit shown below between points a and b is:

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A wire of resistance $160 \Omega$ is melted and drawn in wire of one-fourth of its length. The new resistance...

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A cylindrical wire of mass $(0.4 \pm 0.01) \mathrm{g}$ has length $(8 \pm 0.04) \mathrm{cm}$ and radius $...

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The sum of the first 20 terms of the series 5 +11 + 19 + 29 + 41 + ......

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Given below are two statements: Statements I : Astronomical unit (Au). Parsec (Pc) and Light year (ly) are units for...

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Match List I with List II:

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An air bubble of volume $1 \mathrm{~cm}^3$ rises from the bottom of a lake 40 m deep to the surface...

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Given below are two statements: Statement-I : The diamagnetic property depends on temperature. Statement-II : The included magnetic dipole moment...

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On a temperature scale ‘X’. The boiling point of water is 65° X and the freezing point is –15°X. Assume...

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The engine of a train moving with speed $10 \mathrm{~ms}^{-1}$ towards a platform sounds a whistle at frequency 400 Hz...

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Given below are two statement: Statement-wir if the number of turns in the coil of a moving coil galvanometer is...

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A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric...

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The straight lines l1 and l2 pass through the origin and trisect the line segment of the line L: 9x...

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A proton and an $\alpha$-particle are accelerated from rest by 2 V and 4 V potentials, respectively. The ratio of...

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Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a...

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Two forces having magnitude A and $\frac{\mathrm{A}}{2}$ are perpendicular to each other. The magnitude of their resultant is-

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The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement (x) starting from mean...

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A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they...

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If the $\mathrm{r} . \mathrm{m}$ s speed of chlorine molecule is $490 \mathrm{~m} / \mathrm{s}$ at $27^{\circ} \mathrm{C}$, the rass...

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Let $\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{b}=2 \hat{i}-2 \hat{j}-2 \hat{k}$ and $\vec{c}=-\hat{i}+4 \hat{j}+3 \hat{k}$. If $\vec{d}$ is a vector perpendicular to...

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The current sensitivity of moving coil galvanometer is increased by 25%. This increase is achieved only by changing in the...

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An ideal transformer with purely resistive load operates at 12 kV on the primary side. It supplies electrical energy to...

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The angular momentum for the electron in Bohr’s orbit is L. If the electron is assumed to revolve in second...

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Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius R, with distance r from...

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In an $\mathrm{n}-\mathrm{p}-\mathrm{n}$ common emitter (CE) transistor the collector current changes from 5 mA to 16 mA for the change...

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The free space inside a current carrying toroid is filled with a material of susceptibility $2 \times 10^{-2}$. The percentage...

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If the ratio of the fifth term from the begining to the fifth term from the end in the expansion...

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A carrier wave of amplitude 15V is modulated by a sinusoidal base band signal of amplitude 3V. The ratio of...

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A steel rod has a radius of 20 mm and a length of 2.0 m. A force of 62.8 kN...

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The amplitude of $15 \sin (1000 \pi \mathrm{t})$ is modulated by $10 \sin (4 \pi \mathrm{t})$ signal. The amplitude modulated...

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In this figure the resistance of the coil of galvanometer $G$ is $2 \Omega$. The emf of the cell is...

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A metallic surface is illuminated with radiation of wavelength $\lambda$, the stopping potential is $V_0$.. If the same surface is...

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The range of the projectile projected at an angle of 15° with horizontal is 50 m. If the projectile is...

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The radius of fifth orbit of the Li++ is _____ $\times 10^{-12} \mathrm{~m}$. Take radius of hydrogen atom $=0.51 \AA$

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Dimension of $\frac{1}{\mu_0 \epsilon_0}$ should be equal to

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A person driving car at a constant speed of 15 m/s is approaching a vertical wall. The person notices a...

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The critical angle for a denser-rarer interface is 45°. The speed of light in rarer medium is $...

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A zener diode of power rating 1.6 W is to be used as voltage regulator. If the zener diode has...

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If ${ }^{2 n} C_3 \cdot{ }^n C_3=10: 1$, then the ratio $\left(n^2+3 n\right):\left(n^2-3 n+4\right)$ is

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Two satellites A and B move round the earth in the same orbit. The mass of A is twice the...

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Given below are two statements: Statement-I: If E be the total energy of a satellite moving around the earth, then...

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Two identical circular wires of radius 20 cm and carrying current $\sqrt{2} \mathrm{~A}$ are placed in perpendicular planes as shown...

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A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If...

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1 kg of water at 100°C is converted into steam at 100°C by boiling at atmospheric pressure. The volume of...

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For a nucleus having mass number A and atomic number Z A. The surface energy per nucleon (bs) = a1A2/3...

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Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth from...

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A particle of mass 10 g moves in a straight line with retardation 2x, where x is the displacement in...

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Let $5 f(x)+4 f\left(\frac{1}{x}\right)=\frac{1}{x}+3, x>0$. Then $18 \int_1^2 f(x) d x$ is equal to :

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An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12...

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For the logic circuit shown, the output waveform at Y is:

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Inert gases have positive electron gain enthalpy. Its correct order is

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The correct order in aqueous medium of basic strength in case of methyl substituted amines is :

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As per the given graph choose the correct representation for curve A and curve B. {Where $X_C$ = reactance of...

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A transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive...

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Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio...

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A parallel plate capacitor of capacitance 2 F is charged to a potential V. The energy stored in the capacitor...

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https://competishun.com/number-of-moles-of-agcl-formed-in-the-following-reaction-is-_____-bra-hrefhttp-competishun-com-wp-content-uploads-2026-01-raj2002-156-pngimg-srchttp-competishun-com-wp-content-uploads-2026-01-raj2002-156-300x72-png-alt-width300-height72-classalignnone-size-medium-wp-image-15243-a/

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A 12 V battery connected to a coil of resistance $6 \Omega$ through a switch, drives a constant current in...

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Some amount of dichloromethane ($\mathrm{CH}_2 \mathrm{Cl}_2$) is added to 671.141 mL of chloroform ($\mathrm{CH} \mathrm{Cl}_3$) to prepare 2.6 × 10–3M...

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The logic performed by the circuit shown in figure is equivalent to :

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Uracil is base present in RNA with the following structure. % of N in uracil is ______. Given: Molar mass...

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A body is released from a height equal to the radius (R) of the earth. The velocity of the body...

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A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from...

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Given below are two statements: Statement I : The equivalent resistance of resistors in a series combination is smaller than...

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A trisubstituted compound 'A', $C_(10)H_(12)O_2$ gives neutral $FeCl_3$ test positive. Treatment of compound 'A' with NaOH and $CH_3Br$ gives $CnH_(14)O_2$,...

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For independent process at 300 K. The number of non-spontaneous process from the following is ______.

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The radii of two planets ‘A’ and ‘B’ are ‘R’ and ‘4R’ and their densities are $\rho$ and $...

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(A flask contains Hydrogen and Argon in the ratio 2:1 by mass. The temperature of the mixture is 30°C. The...

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Identify the product formed (A and E)

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The length of a metallic wire is increased by 20% and its area of cross section is reduced by 4%....

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For designing a voltmeter of range 50 V and an ammeter of range 10 mA using a galvanometer which has...

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At any instant the velocity of a particle of mass 500 g is $\left(2 t \hat{\mathrm{i}}+3 t^2 \hat{\mathrm{j}}\right) \mathrm{ms}^{-1}$. If...

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The d-electronic configuration of $\left[\mathrm{CoCl}_4\right]^{2-}$ in tetrahedral crystal field is $\mathrm{e}^{\mathrm{m}} \mathrm{t}_2{ }^{\mathrm{n}}$. Sum of ' m ' and 'number...

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A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m within water...

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The de Broglie wavelength of an electron having kinetic energy $E$ is $\lambda$. If the kinetic energy of electron becomes...

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When $\mathrm{Fe}_{0.93} \mathrm{O}$ is heated in presence of oxygen, it converts to $\mathrm{Fe}_2 \mathrm{O}_3$. The number of correct statement/s from...

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A series LCR circuit is connected to an ac source of 220V, 50Hz. The circuit contain a resistance $...

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The half-life of a radioactive nucleus is 5 years, The fraction of the original sample that would decay in 15...

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At 298 K , a 1 litre solution containing 10 mmol of $\mathrm{Cr}_2 \mathrm{O}_7^{2-}$ and 100 mmol of $\mathrm{Cr}^{3+}$ shows...

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The height of transmitting antenna is 180 m and the height of the receiving antenna is 245 m. The maximum...

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The number of correct statement/s from the following is _______.

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Two identical particles each of mass ‘m’ go round a circle of radius a under the action of their mutual...

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The angular momentum for the electron in Bohr’s orbit is L. If the electron is assumed to revolve in second...

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600 mL of 0.01 M HCl is mixed with 400 mL of 0.01 M $H_2SO_4$. The pH of the mixture...

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In a linear simple harmonic motion (SHM) (A) Restoring force is directly proportional to the displacement. (B) The acceleration and...

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If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of...

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An aluminium rod with Young's modulus $Y=7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^2$ undergoes elastic strain of $0.04 \%$. The energy...

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5 g of NaOH was dissolved in deionized water to prepare a 450 mL stock solution. What volume (in mL)...

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The electric field due to a short electric dipole at a large distance (r) from center of dipole on the...

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The weight of a body on the earth is 400 N. Then weight of the body when taken to a...

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The dissociation constant of acetic is $\mathrm{x} \times 10^{-5}$. When 25 mL of $0.2 \mathrm{M} \mathrm{CH}_3 \mathrm{COONa}$ solution is mixed...

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Given below are two statements: [JEE-Main 08-4-2023_(M)_KTG_M] M0derate Statement-I: If heat is added to a system, its temperature must increase....

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Which of the following is true about freons ?

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In a reflecting telescope, a secondary mirror is used to:

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A TV transmitting antenna is 98 m high and the receiving antenna is at the ground level. If the radius...

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The total pressure of a mixture of non-reacting gases X (0.6 g) and Y (0.45 g) in a vessel is...

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Given below are two statements : Statement I : Noradrenaline is a neurotransmitter Statement II : Low level of noradrenaline...

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When 2 litre of ideal gas expands isothermally into vacuum to a total volume of 6 litre, the change in...

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Form the v-t graph shown. The ratio of distance to displacement in 25s of motion

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oxidation sate of phosphorus in hypophosphoric acid is + ________.

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A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed...

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Decreasing order of the hydrogen bonding in following forms of water is correctly represented by A. Liquid water B. Ice...

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How many of the transformation given below would result in aromatic amines?

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The induced emf can be produced in a coil by A. moving the coil with uniform speed inside magnetic field...

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The number of electrons involved in the reduction of permanganate to manganese dioxide in acidic medium is________.

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The energy of one mole of photons of radiation of frequency $2 \times 10^{12} \mathrm{~Hz} \mathrm{in} \mathrm{J} \mathrm{mol}^{-1}$ is $\_\_\_\_$...

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A mass m is attached to two springs as shown in figure. The spring constants of two springs are $\mathrm{K}_1$...

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For reaction : $\mathrm{SO}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_3(\mathrm{~g}), \mathrm{K}_{\mathrm{P}}=2 \times 10^{12}$ at $27^{\circ} \mathrm{C}$ and 1 atm pressure. The $\mathrm{K}_{\mathrm{c}}$ for...

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Certain galvanometers have a fixed core made of non-magnetic metallic material. The function of this metallic material is

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If compound A reacts with B following first order kinetics with rate constant 2.011 × $10(–3)s(–1)$. The time taken by...

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The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is

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Two projectiles A and B are thrown with initial velocities of $40 \mathrm{~m} / \mathrm{s}$ and $60 \mathrm{~m} / \mathrm{s}$...

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'A' and 'B' formed in the following set of reactions are :

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A solution containing 2 g of a non-volatile solute in 20 g of water boils at 373.52 K. The molecular...

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By what percentage will the transmission range of a TV tower be affected when the height of the tower is...

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Zinc reacts with hydrochloric acid to give hydrogen and zinc chloride. The volume of hydrogen gas produced at STP from...

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Reaction of BeQ with ammonia and hydrogen fluoride gives 'A' which on thermal decomposition gives $\mathrm{BeF}_2$ and $\mathrm{NH}_4 \mathrm{~F}$. What...

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The kinetic energy of an electron, $\alpha$-particle and a proton are given as 4K, 2K and K respectively. The de-Broglie...

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A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to...

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The electric field in an electromagnetic wave is given as $\vec{E}=20 \sin \omega\left(t-\frac{x}{c}\right) \vec{j} N C^{-1}$ Where $\omega$ and c...

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A 300 mL bottle of soft drink has 0.2 M $CO_2$ dissolved in it. Assuming $CO_2$ behaves as an ideal...

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At $27^{\circ} \mathrm{C}$, a solution containing 2.5 g of solute in 250.0 mL of solution exerts an osmotic pressure of...

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The range of the projectile projected at an angle of 15° with horizontal is 50 m. If the projectile is...

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Statement I: For colloidal particles, the values of colligative properties are of small order as compared to values shown by...

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The resistivity $(\rho)$ of semiconductor varies with temperature. Which of the following curve represents the correct behaviour

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On complete combustion, 0.492 g of an organic compound gave 0.792 g of $CO2$. The % of carbon in the...

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The enthalpy change for the conversion of $\frac{1}{2} \mathrm{Cl}_2(\mathrm{~g})$ to $\mathrm{Cl}^{-}(\mathrm{aq})$ is (-) $\_\_\_\_$ $\mathrm{kJ} \mathrm{mol}^{-1}$ (Nearest integer) Given: $...

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For a uniformly charged thin spherical shell, the electric potential (V) radially away from the center (O) of shell can...

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$$ A \rightarrow B $$ The rate constants of the above reaction at 200 K and 300 K are $...

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

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The logarithm of equilibrium constant for the reaction $\mathrm{Pd}^{2+}+4 \mathrm{Cl} \rightleftharpoons \mathrm{PdCl}_4^{2-}$ is $\_\_\_\_$ (Nearest integer) Given: $...

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

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A planet has double the mass of the earth. Its average density is equal to the that of the earth....

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Which one of the following statements is correct for electrolysis of brine solution?

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25 mL of an aqueous solution of KCl was found to require 20 mL of $1 \mathrm{M} \mathrm{AgNO}_3$ solution when...

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Two resistances are given as $\mathrm{R}_1=(10 \pm 0.5) \Omega$ and $\mathrm{R}_2=(10 \pm 0.5) \Omega$. The percentage error in the measurement...

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An organic compound 'A' with empirical formula $\mathrm{C}_6 \mathrm{H}_6 \mathrm{O}$ gives sooty flame on burning. Its reaction with bromine solution...

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

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At 25°C, the enthalpy of the following processes are given: $...

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Adding surfactants in non polar solvent, the micelles structure will look like

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A zener diode of power rating 1.6 W is to be used as voltage regulator. If the zener diode has...

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A monochromatic light wave with wavelength $\lambda_1$ and frequency $V_1$ in air enters another medium. If the angle of incidence...

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A and B are two substances undergoing radioactive decay in a container. The half life of A is 15 min...

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'R' formed in the following sequence of reaction is:

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Choose the correct set of reagents for the following conversion trans $\left(\mathrm{Ph}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_3\right) \rightarrow$ cis $\left(\mathrm{Ph}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_3\right)$

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A physical quantity P is given as The percentage error in the measurement of a, b, c and d are...

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Number of isomeric compounds with molecular formula$\mathrm{C}_9 \mathrm{H}_{10} \mathrm{O}$ which (i) do not dissolve in NaOH (ii) do not dissolve...

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A small block of mass 100 g is tied to a spring of spring constant 7.5 N/m and length 20...

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An ammoniacal metal salt solution gives a brilliant red precipitate on addition of dimethylglyoxime. The metal ion is :

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

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A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ}$,the ratio...

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At what pH, given half cell $\mathrm{MnO}_4^{-}(0.1 \mathrm{M}) \mid \mathrm{Mn}^{2+}(0.001 \mathrm{M})$ will have electrode potential of 1.282 V? _______ (Nearest...

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A source supplies heat to a system at the rate of 1000 W. If the system performs work at a...

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Sum of oxidation states of bromine in bromic acid and perbromic acid is _______.

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Consider the cell $$ \mathrm{Pt}_{(\mathrm{s})}\left|\mathrm{H}_2(\mathrm{~g}, 1 \mathrm{~atm})\right| \mathrm{H}^{+}(\mathrm{aq}, 1 \mathrm{M})| | \mathrm{Fe}^{3+}(\mathrm{aq}), \mathrm{Fe}^{2+}(\mathrm{aq}) \mid \mathrm{Pt}(\mathrm{~s}) $$ When the potential of...

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17 mg of a hydrocarbon (M.F. C10H16) takes up 8.40 mL of the H2 gas measured at 0ºC and 760...

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The number of air molecules per $\mathrm{cm}^3$ increased from $3 \times 10^{19}$ to $12 \times 10^{19}$. The ratio of collision...

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Which of the following artificial sweeteners has the highest sweetness value in comparison to cane sugar?

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Electrons in a cathode ray tube have been emitted with a velocity of $1000 \mathrm{~ms}^{-1}$. The number of following statements...

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Following chromatogram was developed by adsorption of compound ‘A’ on a 6 cm TLC glass plate. Retardation factor of the...

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Consider the cell $ \operatorname{Pt}(\mathrm{s})|\mathrm{H}(\mathrm{~s})(1 \mathrm{~atm})| \mathrm{H}^{+}\left(\mathrm{aq},\left[\mathrm{H}^{+}\right]=1\right) \| \mathrm{Fe}^{3+}(\mathrm{aq}), \mathrm{Fe}^{2+}(\mathrm{aq}) \mid \operatorname{Pt}(\mathrm{s}) $ Given: $\mathrm{E}_{\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}}^{\infty}=0.771 \mathrm{~V}$ and $...

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A small ball of mass M and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After some...

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The sum of bridging carbonyls in W(CO)6 and Mn2 (CO)10 is ________ .

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It is observed that characteristic X-ray spectra of elements show regularity. When frequency to the power ' $n$ ' i.e....

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

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$\mathrm{H}_2 \mathrm{O}_2$ acts as a reducing agent in

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The number of paramagnetic species from the following is_____.

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For certain chemical reaction X Y, the rate of formation of product is plotted against the time as shown in...

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Name the logic gate equivalent to the diagram attached

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The density of 3 M solution of NaCl is $1.0 \mathrm{~g} \mathrm{~mL}^{-1}$. Molality of the solution is __________ $...

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Lithium aluminium hydride can be prepared from the reaction of

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In sulphur estimation. 0.471 g of an organic compound gave 1.4439 g of barium sulphate. The percentage of sulphur in...

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The correct increasing order of the ionic radii is

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Following figure shows dependence of molar conductance of two electrolytes on concentration. is the limiting molar conductivity.

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For the plane electromagnetic wave given by $E=E_0 \sin (\omega t-k x)$ and $B=B_0 \sin (\omega t-k x)$, ), the...

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The total number of lone pairs of electrons on oxygen atoms of ozone is_____

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Water decomposes at 2300 K $\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g})$ The percent of water decomposing at 2300 K and 1...

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Match items of column I and IICorrect match is :

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For the first order reaction $\mathrm{A} \rightarrow \mathrm{B} \mathrm{Br}$ the half life is 30 mm . The time taken for...

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For $OF_2$ molecule consider the following: (A) Number of lone pairs on oxygen is 2. (B) FOF angle is less...

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

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Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at 100.15ºC. When 0.2...

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Number of moles of AgCl formed in the following reaction is _____.

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The density of a monobasic strong acid (Molar mass 24.2 g mol ) is 1.21 kg L . The volume...

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The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is

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Consider the following reaction approaching equilibrium at 27ºC and 1 atm pressure The standard Gibb’s energy change (rG°) at 27ºC...

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

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Uracil is base present in RNA with the following structure. % of N in uracil is ______. Given : Molar...

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How many of the following metal ions have similar value of spin only magnetic moment in gaseous state? $\_\_\_\_$ (Given:...

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The number of molecules or ions from the following, which do not have odd number of electrons are ______.

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

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Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from n = 4...

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For independent process at 300 K. The number of non-spontaneous process from the following is ______.

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Millimoles of calcium hydroxyide required to produce 100 mL of the aqueous solution of pH 12 is x × 10–1....

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In the wet tests for identification of various cations by precipitation, which transition element cation doesn't belong to group IV...

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The osmotic pressure of solutions of PVC in cyclohexanone at 300 K are plotted on the graph. The molar mass...

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But-2-yne is reacted separately with one mole of Hydrogen as shown $...

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Compound that will give positive Lassaigne’s test for both nitrogen and halogen is

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A protein 'X' with molecular weight of 70,000 u, on hydrolysis gives amino acids. One of these amino acid is

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The d-electronic configuration of $\left[\mathrm{CoCl}_4\right]^{2-}$ in tetrahedral crystal field is $\mathrm{e}^{\mathrm{m}} t 2^{\mathrm{n}}$. Sum of 'm' and 'number of unpaired...

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

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A litre of buffer solution contains 0.1 mole of each of $\mathrm{NH}_3$ and $\mathrm{NH}_4 \mathrm{Cl}$. On the addition of 0.02...

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To inhibit the growth of tumours, identify the compounds used from the following: (A) EDTA (B) Coordination Compounds of Pt...

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Number of cyclic tripeptides formed with 2 amino acids A and B is:

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Increasing order of stability of the resonance structure is :

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During the qualitative analysis of $\mathrm{SO}_3^{2-}$ using dilute $\mathrm{H}_2 \mathrm{SO}_4, \mathrm{SO}_2$ gas is evolved which turns $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ solution...

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An athlete is given 100 g of glucose $\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6\right)$ for energy. This is equivalent to 1800 kJ of...

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The correct order of melting point of dichlorobenzenes is

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Match List I with List II

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Choose the correct statement(s): A. Beryllium oxide is purely acidic in nature. B. Beryllium carbonate is kept in the atmosphere...

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Formation of photochemical smog involves the following reaction in which A, B and C are respectively. (i) $\mathrm{NO}_2 \xrightarrow{\mathrm{hv}} \mathrm{A}+\mathrm{B}$...

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In the cumene to phenol preparation in presence of air, the intermediate is

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During the borax bead test with CuSO4, a blue green colour of the bead was observed in oxidising flame due...

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When $\mathrm{Fe}_{0.93} \mathrm{O}$ is heated in presence of oxygen, it converts to $\mathrm{Fe}_2 \mathrm{O}_3$. The number of correct statement/s from...

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Identify $\mathrm{X}, \mathrm{Y}$ and Z in the following reaction. (Equation not balanced) $$ \mathrm{ClO}+\mathrm{NO}_2 \underline{X} \xrightarrow{\mathrm{H}_2 \mathrm{O}} \underline{\mathrm{Y}}+\underline{\mathrm{Z}} $$

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Match the List–I with List–II :

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

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Match List I with List II

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The major product ‘P’ for the following sequence of reactions is: 1) $\mathrm{Zn} / \mathrm{Hg}$ HCI major product 2) $\mathrm{LiAlH}_4$...

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Which of the following is correct order of ligand field strength?

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Order of Covalent bond;

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Cobalt chloride when dissolved in water forms pink colored complex X which has octahedral geometry. This solution on treating with...

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How can photochemical smog be controlled?

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15. Match List I with List II.

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At 298 K, a 1 litre solution containing 10 mmol of $\mathrm{Cr}_2 \mathrm{O}_7^{2-}$ and 100 mmol of $\mathrm{Cr}^{3+}$ shows a...

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The alkaline earth metal sulphate(s) which are readily soluble in water is/are:

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Some reactions of NO2 relevant to photochemical smog formation are Identify A, B, X and Y

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Which of the following complex will show largest splitting of d–orbitals?

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Assertion A : Hydrolysis of an alkyl chloride is a slow reaction but in the presence of NaI, the rate...

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The increasing order of pKa for the following phenols is

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The number of correct statement/s from the following is _______. A. Larger the activation energy, smaller is the value of...

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Identify the correct order for the given property for following compounds

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Which of the following are the example of double salt? Choose the correct answer.

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A solution of $\mathrm{FeCl}_3$ when treated with $\mathrm{K}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ gives a prussiun blue precipitate due to the formation of

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Identify the incorrect option from the following:

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Resonance in carbonate ion $\left(\mathrm{CO}_3^{2-}\right)$ is Which of the following is true?

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Given below are two statements: Statement I: Chlorine can easily combine with oxygen to from oxides: and the product has...

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Chiral complex from the following is : Here en = ethylene diamine

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Match List I with List II

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Compound A reacts with $\mathrm{NH}_4 \mathrm{Cl}$ and forms a compound B . Compound B reacts with $\mathrm{H}_2 \mathrm{O}$ and excess...

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If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of...

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Caprolactam when heated at high temperature in presence of water, gives

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Correct statement about smog is

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Which of the following statements is incorrect for antibiotics?

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5 g of NaOH was dissolved in deionized water to prepare a 450 mL stock solution. What volume (in mL)...

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The standard electrode potential (M3+/M2+) for V, Cr, Mn and Co are –0.26 V, –0.41 V, +1.57 V and +1.97...

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When $\mathrm{Cu}^{2+}$ ion is treated with KI , a white precipitate, X appears in solution. The solution is titrated with...

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'25 volume' hydrogen peroxide means

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

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The dissociation constant of acetic is $\mathrm{x} \times 10^{-5}$. When 25 mL of $0.2 \mathrm{M} \mathrm{CH}_3 \mathrm{COONa}$ solution is mixed...

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A obtained by Ostwald‟s method involving air oxidation of NH3, upon further air oxidation produces “B”. “B” on hydration forms...

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Compound (X) undergoes following sequence of reactions to give the Lactone (Y).

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The correct order of basicity of oxides of vanadium is

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Which of the following is true about freons ?

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The magnetic behaviour of Li2O, Na2O2 and KO2, respectively, are

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In the depression of freezing point experiment A. Vapour pressure of the solution is less than that of pure solvent...

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Decreasing order of dehydration of the following alcohols is

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The major products 'A' and 'B', respectively, are

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Consider the following reaction $$ \text { Propanal }+ \text { Methanal }=\xrightarrow[\substack{\text { (iii)s } \\ \text { (ii)...

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The correct sequence of reagents for the preparation of Q and R is :

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The correct order of hydration enthalpies is (A) K+ (B) Rb+ (C) Mg2+ (D) Cs+ (E) Ca2+ Choose the correct...

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Given below are two statements : Statement I : Noradrenaline is a neurotransmitter. Statement II : Low level of noradrenaline...

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Highest oxidation state of Mn is exhibited in Mn2O7. The correct statements about Mn2O7 are (A) Mn is tetrahedrally surrounded...

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Decreasing order of the hydrogen bonding in following forms of water is correctly represented by A. Liquid water B. Ice...

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Which of the given compounds can enhance the efficiency of hydrogen storage tank?

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Amongst the following compounds, which one is an antacid ?

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Which one of the following reactions does not occur during extraction of copper ?

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The reaction representing the Mond process for metal refining is ______ [

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In the extraction of copper, its sulphide ore is heated in a reverberatory furnace after mixing with silica to :

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A thin uniform rod of length 2 m . cross sectional area ' $A$ ' and density ' d '...

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The correct representation in six membered pyranose form for the following sugar [X] is

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The methods NOT involved in concentration of ore are (A) Liquation (B) Leaching (C) Electrolysis (D) Hydraulic washing (E) Froth...

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The bond dissociation energy is highest for

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In the following given reaction ‘A’ is

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

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In an experiment for estimating the value of focal length of converging mirror, image of an object placed at 40...

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Which of the following salt solutions would coagulate the colloid solution formed when FeCl3 is added to NaOH solution, at...

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$\mathrm{Nd}^{2+}=$

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Which of the following represents the lattice structure of$\mathrm{A}_{0.95} \mathrm{O}$ containing $\mathrm{A}^{2+} \mathrm{A}^{3+}$ and $\mathrm{O}^2$ions?

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'A' and 'B' formed in the following set of reactions are :

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In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by 0.5 mm...

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

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The shortest wavelength of hydrogen atom in Lyman series is . The longest wavelength in Balmer series of He+ is

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Reaction of BeO with ammonia and hydrogen fluoride gives 'A' which on thermal decomposition gives $\mathrm{BeF}_2$ and $\mathrm{NH}_4 \mathrm{~F}$. What...

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Match items of Row I with those of Row II.

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Which of the following compounds would give the following set of qualitative analysis ? (i) Fehling's Test: Positive (ii) Na...

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For 1 mol of gas, the plot of pV vs p is shown below. p is the pressure and V...

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Match List I with List II.

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Statement I : For colloidal particles, the values of colligative properties are of small order as compared to values shown...

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If and then, The unit vector in the direction of is . The value of x is

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

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Which of the following conformations will be the most stable ?

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An LCR series circuit of capacitance 62.5 nF and resistance of 50. is connected to an A.C. source of frequency...

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As shown in figures, three identical polaroids $P_1, P_2$ and $P_3$ are placed one after another. The pass axis of...

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'R' formed in the following sequence of reaction is:

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A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron...

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The radius of the $2^{\text {nd }}$ orbit of $\mathrm{Li}^{2+}$ is x . The expected radius of the $...

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A point source of light is placed at the center of curvature of a hemispherical surface. The source emits a...

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A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a...

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The distance between two consecutive points with phase difference of 60° in a wave of frequency 500 Hz is 6.0...

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An ammoniacal metal salt solution gives a brilliant red precipitate on addition of dimethylglyoxime. The metal ion is :

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ICM is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to...

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The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25%...

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In a metre bridge experiment the balance point in obtained if the gaps are closed by $2 \Omega$ and $...

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A horse rider covers half the distance with $5 \mathrm{~m} / \mathrm{s}$ speed. The remaining part of the distance was...

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A cubic solid is made up of two elements $X$ and $Y$. Atoms of $X$ are present on every alternate...

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The primary and secondary valencies of cobalt respectively in $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}\right] \mathrm{Cl}_2$ are :

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A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60...

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The wavelength of the radiation emitted is 0 when an electron jumps from the second excited state to the first...

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A point charge q1 = 4q0 is placed at origin. Another point charge q2 = –q0 is placed at x...

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Reaction of thionyl chloride with white phosphorus forms a compound [A], which on hydrolysis gives [B], a dibasic acid. [A]...

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In the following circuit, the magnitude of current $l_1$, is $\_\_\_\_$ A.

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An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force...

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Which of the Phosphorus oxoacid can create silver mirror from $\mathrm{AgNO}_3$ solution ?

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A thin cylindrical rod of length 10 cm is placed horizontally on the principle axis of a concave mirror of...

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As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted....

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

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In Young's double slit experiment, two slits $\mathrm{S}_1$ and $\mathrm{S}_2$ are 'd' distance apart and the separation from slits to...

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In the given circuit, the equivalent resistance between the terminal A and B is _____ .

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It is observed that characteristic X-ray spectra of elements show regularity. When frequency to the power 'n' i.e. $v^n$ of...

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A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height...

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A certain pressure 'P' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets...

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A ray of light is incident from air on a glass plate having thickness $\sqrt{3} \mathrm{~cm}$ and refractive index $\sqrt{2}$....

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A 0.4 kg mass takes 8s to reach ground when dropped from a certain height ‘P’ above surface of earth....

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A light of energy 12.75 eV is incident on a hydrogen atom in its ground state. The atom absorbs the...

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A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m....

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The variation of the rate of an enzyme catalyzed reaction with substrate concentration is correctly represented by graph

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A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J...

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A bowl filled with very hot soup cools from 98°C to 86°C in 2 minutes when the room temperature is...

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A small particle moves to position $5 \hat{i}-2 \hat{j}+\hat{k}$ from its initial position $2 \hat{i}+3 \hat{j}-4 \hat{k}$ under the action...

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The compound which will have the lowest rate towards nucleophilic aromatic substitution on treatment with OH– is

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The general displacement of a simple harmonic oscillator is $x=A \sin \omega t$. Let $J$ be its time period. The...

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A body cools from 60ºC to 40ºC in 6 minutes. If, temperature of surroundings is 10ºC. Then, after the next...

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A uniform metallic wire carries a current 2 A. when 3.4 V battery is connected across it. The mass of...

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In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of...

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Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the...

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A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and...

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The figure represents the momentum time ( $p-t$ ) curve for a particle moving along an axis under the influence...

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The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is

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

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A radioactive element ${ }_{92}^{242} \mathrm{X}$ emits two $\alpha$-particles, one electron and two positrons. The product nucleus is represented by...

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Two identical cells, when connected either in parallel or in series gives same current in an external resistance $5 \Omega$....

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A block of mass 5 kg is placed at rest on a table of rough surface. Now, if a force...

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

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For hydrogen atom, $\lambda_i$ and $\lambda_2$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in...

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Increasing order of stability of the resonance structure is :

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Which of the following statement is not correct in the case of light emitting diodes? A. It is a heavily...

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Math List I with List II

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The average kinetic energy of a molecule of the gas is

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A lift of mass $M=500 \mathrm{~kg}$ is descending with speed of $2 \mathrm{~ms}^{-1}$. Its supporting cable begins to slip thus...

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$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where P is the pressure, V is the volume, T...

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Order of Covalent bond;

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A ball of mass 200 g rests on a vertical post of height 20 m . A bullet of mass...

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Expression for an electric field is given by $\overrightarrow{\mathrm{E}}=4000 \mathrm{x}^2 \hat{\mathrm{i}} \frac{\mathrm{V}}{\mathrm{m}}$. The electric flux through the cube of side...

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The mass of proton, neutron and helium nucleus are respectively 1.0073 u, 1.0087 u and 4.0015u. The binding energy of...

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If the gravitational field in the space is given as $\left(-\frac{\mathrm{K}}{\mathrm{r}^2}\right)$. Taking the reference point to be at $\mathrm{r}=2 \mathrm{~cm}$...

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An inductor of 0.5 mH , a capacitor of $20 \mu \mathrm{~F}$ and resistance of $20 \Omega$ are connected in...

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A mercury drop of radius $10^(–3)$ m is broken into 125 equal size droplets. Surface tension of mercury is 0.45...

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Assertion A : Hydrolysis of an alkyl chloride is a slow reaction but in the presence of NaI, the rate...

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In a series $L R$ circuit with $X_L=R$. power factor is $P_1$. If a capacitor of capacitance $C$ with $X_C=X_L$...

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A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is $...

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A sinusoidal carrier voltage is amplitude modulated. The resultant amplitude modulated wave has maximum and minimum amplitude of 120 V...

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Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric...

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In a medium the speed of light wave decreases to 0.2 times to its speed in free space The ratio...

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Compound (X) undergoes following sequence of reactions to give the Lactone (Y).

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In the figure given below, a block of mass $\mathrm{M}=490 \mathrm{~g}$ placed on a frictionless table is connected with two...

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The equivalent resistance between A and B of the network shown in figure:

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The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is,...

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The speed of a swimmer is $4 \mathrm{~km} \mathrm{~h}^{-1}$ in still water. If the swimmer makes his strokes normal to...

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A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas...

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A thin rod having a length of 1 m and area of cross-section $3 \times 10^{-6} \mathrm{~m}^2$ is suspended vertically...

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100 balls each of mass m moving with speed v simultaneously strike a wall normally and reflected back with same...

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A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda$ . An...

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If $R, X_L$. and $X_c$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

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A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with...

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Two polaroide A and B are placed in such a way that the pass-axis of polaroids are perpendicular to each...

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A steel wire with mass per unit length 7.0 × $10^(–3)$ kg m$^(–1)$ is under tension of 70 N. The...

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The amplitude of $15 \sin (1000 \pi \mathrm{t})$ is modulated by $10 \sin (4 \pi \mathrm{t})$ signal. The amplitude modulated...

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Which of the following frequencies does not belong to FM broadcast.

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If a radioactive element having half-life of 30 min is undergoing beta decay, the fraction of radioactive element remains undecayed...

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As per given figure, a weightless pulley P is attached on a double inclined frictionless surface. The tension in the...

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The threshold wavelength for photoelectric emission from a material is 5500Ǻ. Photoelectrons will be emitted, when this material is illuminated...

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If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be...

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A person observes two moving trains, ‘A’ reaching the station and ‘B’ leaving the station with equal speed of 30...

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The output waveform of the given logical circuit for the following inputs A and B as shown below, is

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A bicycle tyre is filled with air having pressure of 270 kPa at 27ºC. The approximate pressure of the air...

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The correct relation between $\mu=\frac{C_p}{C_v}$ and temperature $T$ is :

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

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A rod with circular cross-section area $2 \mathrm{~cm}^2$ and length 40 cm is wound uniformly with 400 turns of an...

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'n' polarizing sheets are arranged such that each makes an angle 45° with the proceeding sheet. An unpolarized light of...

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Electric field in a certain region is given by $\vec{E}=\left(\frac{A}{x^2} \hat{i}+\frac{B}{y^3} \hat{j}\right)$. The $S I$ unit of $A$ and $B$...

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If 1000 droplets of water of surface tension $0.07 \mathrm{~N} / \mathrm{m}$. having same radius 1 mm each, combine to...

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Surface tension of a soap bubble is $2.0 \times 10^{-2} \mathrm{Nm}^{-1}$. Work done to increase the radius of soap bubble...

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If earth has a mass nine times and radius twice to the of a planet $P$. Then $\frac{v_e}{3} \sqrt{x} \mathrm{~ms}^{-1}$...

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At a certain depth "d" below surface of earth, value of acceleration due to gravity becomes four times that of...

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Heat is given to an ideal gas in an isothermal process. A. Internal energy of the gas will decrease. B....

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

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Two particles of equal mass ‘m’ move in a circle of radius ‘r’ under the action of their mutual gravitational...

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The drift velocity of electrons for a conductor connected in an electrical circuit is Vd . The conductor in now...

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Given below are two statements : Statement I: Acceleration due to gravity is different at different places on the surface...

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

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A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will...

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Two isolated metallic solid spheres of radii $R$ and $2 R$ are charged such that both have same charge density...

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Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R)...

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An object moves with speed $v_1, v_2$ and $v_3$ along a line segment $\mathrm{AB}, \mathrm{BC}$ and CD respectively as shown...

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The pressure of a gas changes linearly with volume from A to B as shown in figure. If no heat...

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A block of mass m slides down the plane inclined at angle 30º with an acceleration g/4 . The value...

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A massless square loop, of wire of resistance 10 D . supporting a mass of I g . hangs vertically...

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

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The maximum potential energy of a block executing simple harmonic motion is 25 J .A is amplitude of oscillation. At...

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A stone is projected at angle 30º to the horizontal. The ratio of kinetic energy of the stone at point...

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The effect of increase in temperature on the number of electrons in conduction band (ne) and resistance of a semiconductor...

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Speed of an electron in Bohr's $7^{\text {th }}$ orbit for Hydrogen atom is $3.6 \times 10^6 \mathrm{~m} / \mathrm{s}$....

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A free neutron decays into a proton but a free proton does not decay into neutron. This is because

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In a Young's double slit experiment, two slits are illuminated with a light of wavelength 800 nm . The line...

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A small object at rest, absorbs a light pulse of power 20 mWX and duration 300 ns . Assuming speed...

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Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose...

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Which of the following are true? A. Speed of light in vacuum is dependent on the direction of propagation. B....

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The initial speed of a projectile fired from ground is $u$. At the highest point during its motion, the speed...

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As shown in figure, a 70 kg garden roller is pushed with a force of $\vec{F}=200 \mathrm{~N}$ at an angle...

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Choose the correct relationship between Poisson ratio $(\sigma)$, bulk modulus $(\mathrm{K})$ and modulus of rigidity $(\eta)$ of a given solid...

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Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ‘R’ is placed inside...

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As per the given figure, a small ball $P$ slides down the quadrant of a circle and hits the other...

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The magnitude of magnetic induction at mid-point O due to current arrangement as shown in Fig will be :

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A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve z direction and...

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The charge flowing in a conductor changes with time as $\mathrm{Q}(\mathrm{t})=\alpha \mathrm{t}-\beta \mathrm{t}^2+\gamma \mathrm{t}^3$. Where $\alpha, \beta$ and $\gamma$ are...

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Ratio of thermal energy released in two resistor R and 3R connected in parallel in an electric circuit is

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If a source of electromagnetic radiation having power 15 kW produces $10^{16}$ photons per second, the radiation belongs to a...

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In a cuboid of dimension 2L × 2L × L, a charge q is placed at the centre of the...

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The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation PT2 = constant. The volume expansion...

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A bar magnet with a magnetic moment $5.0 \mathrm{Am}^2$ is placed in parallel position relative to a magnetic field of...

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

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Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5...

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