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JEE-MAIN EXAMINATION – JANUARY 2025

JEE-MAIN TEST PAPER WITH SOLUTION

Held on Friday 24th January 2025, Time: 3:00 PM to 6:00 PM

JEE Main

Mathematics, Physics, Chemistry

Evening Session

3 hours

Paper Overview

Total Questions

Correct

Incorrect

N/A

iExplain doesn't support the question format

Complete Solutions

Q#	Explanation	Question	Correct	Solution	Status
1	View ExplanationExplain	The equation of the chord, of the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{16}=1$ , whose mid-point is $(3,1)$ is : (A) $48 x+25 y=169$ (B) $4 x+122 y=134$ (C) $25 x+101 y=176$ (D) $5 x+16 y=31$	1	Available	Available
2	View ExplanationExplain	The function $f:(-\infty, \infty) \rightarrow(-\infty, 1)$ , defined by $f(x)=\frac{2^{x}-2^{-x}}{2^{x}+2^{-x}}$ is : (A) One-one but not onto (B) Onto but not one-one (C) Both one-one and onto (D) Neither one-one nor onto	1	Available	Available
3	View ExplanationExplain	If $\alpha>\beta>\gamma>0$ , then the expression $\cot ^{-1}\left\{\beta+\frac{\left(1+\beta^{2}\right)}{(\alpha-\beta)}\right\}+\cot ^{-1}\left\{\gamma+\frac{\left(1+\gamma^{2}\right)}{(\beta-\gamma)}\right\}$ $+\cot ^{-1}\left\{\alpha+\frac{\left(1+\alpha^{2}\right)}{(\gamma-\alpha)}\right\}$ is equal to: (A) $\frac{\pi}{2}-(\alpha+\beta+\gamma)$ (B) $3 \pi$ (C) 0 (D) $\pi$	4	Available	Available
4	View ExplanationExplain	Let $\mathrm{f}:(0, \infty) \rightarrow \mathbf{R}$ be a function which is differentiable at all points of its domain and satisfies the condition $x^{2} f^{\prime}(x)=2 x f(x)+3$ , with $f(1)=4$ . Then $2 f(2)$ is equal to: (A) 29 (B) 19 (C) 39 (D) 23	3	Available	Available
5	View ExplanationExplain	Let $A=\left\{x \in(0, \pi)-\left\{\frac{\pi}{2}\right\}: \log _{(2 / \pi)}\|\sin x\|+\log _{(2 / \pi)}\|\cos x\|=2\right\}$ and $B=\{x \geq 0: \sqrt{x}(\sqrt{x}-4)-3\|\sqrt{x}-2\|+6=0\}$ . Then $\mathrm{n}(\mathrm{A} \cup \mathrm{B})$ is equal to: (A) 4 (B) 2 (C) 8 (D) 6	3	Available	Available
6	View ExplanationExplain	Let the position vectors of three vertices of a triangle be $4 \vec{p}+\vec{q}-3 \vec{r},-5 \vec{p}+\vec{q}+2 \vec{r} \quad$ and $2 \vec{p}-\vec{q}+2 \vec{r}$ . If the position vectors of the orthocenter and the circumcenter of the triangle are $\frac{\overrightarrow{\mathrm{p}}+\overrightarrow{\mathrm{q}}+\overrightarrow{\mathrm{r}}}{4}$ and $\alpha \overrightarrow{\mathrm{p}}+\beta \overrightarrow{\mathrm{q}}+\gamma \overrightarrow{\mathrm{r}}$ respectively, then $\alpha+2 \beta+5 \gamma$ is equal to: (A) 3 (B) 1 (C) 6 (D) 4	1	Available	Available
7	View ExplanationExplain	Let $[x]$ denote the gereatest integer function, and let $m$ and $n$ respectively be the numbers of the points, where the function $\mathrm{f}(\mathrm{x})=[\mathrm{x}]+\|\mathrm{x}-2\|$ , $-2<\mathrm{x}<3$ , is not continuous and not differentiable. Then $\mathrm{m}+\mathrm{n}$ is equal to: (A) 6 (B) 9 (C) 8 (D) 7	3	Available	Available
8	View ExplanationExplain	Let the points $\left(\frac{11}{2}, \alpha\right)$ lie on or inside the triangle with sides $x+y=11, x+2 y=16$ and $2 x+3 y=29$ . Then the product of the smallest and the largest values of $\alpha$ is equal to : (A) 22 (B) 44 (C) 33 (D) 55	3	Available	Available
9	View ExplanationExplain	In an arithmetic progression, if $\mathrm{S}_{40}=1030$ and $\mathrm{S}_{12}=57$ , then $\mathrm{S}_{30}-\mathrm{S}_{10}$ is equal to: (A) 510 (B) 515 (C) 525 (D) 505	2	Available	Available
10	View ExplanationExplain	If $7=5+\frac{1}{7}(5+\alpha)+\frac{1}{7^{2}}(5+2 \alpha)+\frac{1}{7^{3}}(5+3 \alpha)+$ $\_\_\_\_$ $\infty$ , then the value of $\alpha$ is: (A) 1 (B) $\frac{6}{7}$ (C) 6 (D) $\frac{1}{7}$	3	Available	Available
11	View ExplanationExplain	If the system of equations $x+2 y-3 z=2$ $2 x+\lambda y+5 z=5$ $14 x+3 y+\mu z=33$ has infinitely many solutions, then $\lambda+\mu$ is equal to: (A) 13 (B) 10 (C) 11 (D) 12	4	Available	Available
12	View ExplanationExplain	Let $(2,3)$ be the largest open interval in which the function $\mathrm{f}(\mathrm{x})=2 \log _{\mathrm{e}}(\mathrm{x}-2)-\mathrm{x}^{2}+$ ax +1 is strictly increasing and ( $\mathrm{b}, \mathrm{c}$ ) be the largest open interval, in which the function $\mathrm{g}(\mathrm{x})=(\mathrm{x}-1)^{3}(\mathrm{x}+2-\mathrm{a})^{2}$ is strictly decreasing. Then $100(\mathrm{a}+\mathrm{b}-\mathrm{c})$ is equal to: (A) 280 (B) 360 (C) 420 (D) 160	2	Available	Available
13	View ExplanationExplain	Suppose $A$ and $B$ are the coefficients of $30^{\text {th }}$ and $12^{\text {th }}$ terms respectively in the binomial expansion of $(1+x)^{2 n-1}$ . If $2 A=5 B$ , then $n$ is equal to: (A) 22 (B) 21 (C) 20 (D) 19	2	Available	Available
14	View ExplanationExplain	Let $\vec{a}=3 \hat{i}-\hat{j}+2 \hat{k}, \vec{b}=\vec{a} \times(\hat{i}-2 \hat{k})$ and $\vec{c}=\vec{b} \times \hat{k}$ . Then the projection of $\vec{c}-2 \hat{j}$ on $\vec{a}$ is: (A) $3 \sqrt{7}$ (B) $\sqrt{14}$ (C) $2 \sqrt{14}$ (D) $2 \sqrt{7}$	3	Available	Available
15	View ExplanationExplain	For some $a, b$ , let $f(x)=\left\|\begin{array}{ccc}a+\frac{\sin x}{x} & 1 & b \\ a & 1+\frac{\sin x}{x} & b \\ a & 1 & b+\frac{\sin x}{x}\end{array}\right\|, \quad x \quad \neq 0$ , $\lim _{x \rightarrow 0} f(x)=\lambda+\mu a+v b$ . Then $(\lambda+\mu+v)^{2}$ is equal to: (A) 25 (B) 9 (C) 36 (D) 16	4	Available	Available
16	View ExplanationExplain	Group A consists of 7 boys and 3 girls, while group $B$ consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B , is equal to: (A) 8575 (B) 9100 (C) 8925 (D) 8750	3	Available	Available
17	View ExplanationExplain	The area of the region enclosed by the curves $y=e^{x}, y=\left\|e^{x}-1\right\|$ and $y$ -axis is: (A) $1+\log _{\mathrm{e}} 2$ (B) $\log _{e} 2$ (C) $2 \log _{\mathrm{e}} 2-1$ (D) $1-\log _{\mathrm{e}} 2$	4	Available	Available
18	View ExplanationExplain	The number of real solution(s) of the equation $\mathrm{x}^{2}+3 \mathrm{x}+2=\min \{\|\mathrm{x}-3\|,\|\mathrm{x}+2\|\}$ is : (A) 2 (B) 0 (C) 3 (D) 1	1	Available	Available
19	View ExplanationExplain	Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]$ be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability $\mathrm{P}(\mathrm{E})$ is : (A) $\frac{5}{8}$ (B) $\frac{3}{16}$ (C) $\frac{1}{8}$ (D) $\frac{3}{8}$	4	Available	Available
20	View ExplanationExplain	If the equation of the parabola with vertex $\mathrm{V}\left(\frac{3}{2}, 3\right)$ and the directrix $\mathrm{x}+2 \mathrm{y}=0$ is $\alpha x^{2}+\beta y^{2}-\gamma x y-30 x-60 y+225=0$ , then $\alpha+\beta+\gamma$ is equal to: (A) 6 (B) 8 (C) 7 (D) 9	4	Available	Available
21	View ExplanationExplain	Number of functions $f:\{1,2, \ldots, 100\} \rightarrow\{0,1\}$ , that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to $\_\_\_\_$ .	(392)	Available	Available
22	View ExplanationExplain	Let P be the image of the point $\mathrm{Q}(7,-2,5)$ in the line $\mathrm{L}: \frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}+1}{3}=\frac{\mathrm{z}}{4}$ and $\mathrm{R}(5, \mathrm{p}, \mathrm{q})$ be a point on L . Then the square of the area of $\triangle \mathrm{PQR}$ is $\_\_\_\_$	(957)	Available	Available
23	View ExplanationExplain	Let $y=y(x)$ be the solution of the differential equation $2 \cos x \frac{d y}{d x}=\sin 2 x-4 y \sin x, x \in\left(0, \frac{\pi}{2}\right)$ . If $y\left(\frac{\pi}{3}\right)=0$ , then $y^{\prime}\left(\frac{\pi}{4}\right)+y\left(\frac{\pi}{4}\right)$ is equal to $\_\_\_\_$ .	(1)	Available	Available
24	View ExplanationExplain	Let $\mathrm{H}_{1}: \frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}-\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=1$ and $\mathrm{H}_{2}:-\frac{\mathrm{x}^{2}}{\mathrm{~A}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{~B}^{2}}=1$ be two hyperbolas having length of latus rectums $15 \sqrt{2}$ and $12 \sqrt{5}$ respectively. Let their eccentricities be $\mathrm{e}_{1}=\sqrt{\frac{5}{2}}$ and $\mathrm{e}_{2}$ respectively. If the product of the lengths of their transverse axes is $100 \sqrt{10}$ , then $25 \mathrm{e}_{2}^{2}$ is equal to $\_\_\_\_$	(55)	Available	Available
25	View ExplanationExplain	If $\int \frac{2 x^{2}+5 x+9}{\sqrt{x^{2}+x+1}} d x=x \sqrt{x^{2}+x+1}+\alpha \sqrt{x^{2}+x+1}+ \beta \log _{\mathrm{e}}\left\|\mathrm{x}+\frac{1}{2}+\sqrt{\mathrm{x}^{2}+\mathrm{x}+1}\right\|+\mathrm{C}$ , where C is the constant of integration, then $\alpha+2 \beta$ is equal to $\_\_\_\_$	(16)	Available	Available
26	View ExplanationExplain	Young's double slit interference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm . The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm . The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m , will be : (A) 0.23 mm (B) 0.33 mm (C) 0.63 mm (D) 0.46 mm	1	Available	Available
27	View ExplanationExplain	Arrange the following in the ascending order of wavelength ( $\lambda$ ) : Microwaves ( $\lambda_{1}$ ), Ultraviolet rays ( $\lambda_{2}$ ), Infrared rays ( $\lambda_{3}$ ), X-rays ( $\lambda_{4}$ ) Choose the most appropriate answer from the options given below :- (A) $\lambda_{4}<\lambda_{3}<\lambda_{2}<\lambda_{1}$ (B) $ $\lambda_{3}<\lambda_{4}<\lambda_{2}<\lambda_{1}$ (C) $ $\lambda_{4}<\lambda_{2}<\lambda_{3}<\lambda_{1}$ (D) $ $\lambda_{4}<\lambda_{3}<\lambda_{1}<\lambda_{2}$	3	Available	Available
28	View ExplanationExplain	Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason(R). Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path. Reason (A) : The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below : (A) (A) is false but (R) is true (B) Both (A) and (R) are true and (R) is the correct explanation of (A) (C) Both (A) and (R) are true but (R) is NOT the correct explanation of (A) (D) (A) is true but (R) is false	2	Available	Available
29	View ExplanationExplain	A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is : (A) $\frac{2}{5}$ (B) $\frac{5}{2}$ (C) $\frac{3}{4}$ (D) $\frac{4}{3}$	2	Available	Available
30	View ExplanationExplain	A long straight wire of a circular cross-section with radius ' $a$ ' carries a steady current $I$ . The current $I$ is a uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance $r$ from the centre of the wire is given by	1	Diagram Question	Available
31	View ExplanationExplain	Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason(R). Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases. Reason (R) : Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statement, choose the correct answer from the options given below : (A) Both (A) and (R) are true and (R) is the correct explanation of (A) (B) (A) is true but (R) is false (C) (A) is false but (R) is true (D) Both (A) and (R) are true but (R) is NOT the correct explanation of (A)	3	Available	Available
32	View ExplanationExplain	In the first configuration (1) as shown in the figure, four identical charges $\left(\mathrm{q}_{0}\right)$ are kept at the corners $A, B, C$ and $D$ of square of side length ' $a$ '. In the second configuration (2), the same charges are shifted to mid points $\mathrm{G}, \mathrm{E}, \mathrm{H}$ and F , of the square, If $\mathrm{K}=\frac{1}{4 \pi \varepsilon_{0}}$ , the difference between the potential energies of configuration (2) and (1) is given by : (A) $\frac{K q_{0}^{2}}{a}(4 \sqrt{2}-2)$ (B) $\frac{K q_{0}^{2}}{a}(3-\sqrt{2})$ (C) $\frac{\mathrm{Kq}_{0}^{2}}{\mathrm{a}}(4-2 \sqrt{2})$ (D) $\frac{\mathrm{Kq}_{0}^{2}}{\mathrm{a}}(3 \sqrt{2}-2)$	4	Diagram Question	Available
33	View ExplanationExplain	The position vector of a moving body at any instant of time is given as $\vec{r}=\left(5 t^{2} \hat{i}-5 t \hat{j}\right) \mathrm{m}$ . The magnitude and direction of velocity at $\mathrm{t}=2 \mathrm{~s}$ is, (A) $5 \sqrt{15} \mathrm{~m} / \mathrm{s}$ , making an angle of $\tan ^{-1} 4$ with -ve Y axis (B) $5 \sqrt{15} \mathrm{~m} / \mathrm{s}$ , making an angle of $\tan ^{-1} 4$ with +ve X axis (C) $5 \sqrt{17} \mathrm{~m} / \mathrm{s}$ , making an angle of $\tan ^{-1} 4$ with -ve Y axis (D) $5 \sqrt{17} \mathrm{~m} / \mathrm{s}$ , making an angle of $\tan ^{-1} 4$ with +ve X axis	3	Available	Available
34	View ExplanationExplain	A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_{1}$ and $t_{2}$ , respectively, then (A) $t_{1}<t_{2}$ (B) $t_{1}=t_{2}$ (C) $\mathrm{t}_{1}=2 \mathrm{t}_{2}$ (D) $t_{1}>t_{2}$	1	Available	Available
35	View ExplanationExplain	Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?	2	Diagram Question	Available
36	View ExplanationExplain	N equally spaced charges each of value q , are placed on a circle of radius $R$ . The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, $I_{A}-I_{B}$ , for the given Amperian loops is (A) $\frac{\mathrm{N}^{2}}{2 \pi} \mathrm{q} \omega$ (B) $\frac{2 \pi}{N} q \omega$ (C) $\frac{\mathrm{N}}{2 \pi} \mathrm{q} \omega$ (D) $\frac{\mathrm{N}}{\pi} \mathrm{q} \omega$	3	Diagram Question	Available
37	View ExplanationExplain	In photoelectric effect, the stopping potential ( $\mathrm{V}_{0}$ ) $\mathrm{v} / \mathrm{s}$ frequency (v) curve is plotted. ( h is the Planck's constant and $\phi_{0}$ is work function of metal) A. $\mathrm{V}_{0} \mathrm{v} / \mathrm{s} v$ is linear B. The slope of $\mathrm{V}_{0} \mathrm{v} / \mathrm{s}$ v curve $=\frac{\phi_{0}}{\mathrm{~h}}$ C. h constant is related to the slope of $\mathrm{V}_{0} \mathrm{v} / \mathrm{s} v$ line D. The value of electric charge of electron is not required to determine $h$ using the $V_{0} v / s v$ curve. E. The work function can be estimated without knowing the value of h . Choose the correct answer from the options given below : (A) (A), (B) and (C) only (B) (C) and (D) only (C) (A),(C) and (E) only (D) (D) and (E) only	3	Available	Available
38	View ExplanationExplain	The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) (A) $10 \pi$ (B) $5 \pi$ (C) zero (D) $40 \pi$	2	Diagram Question	Available
39	View ExplanationExplain	A photograph of a landscape is captured by a drone camera at a height of 18 km . The size of the camera film is $2 \mathrm{~cm} \times 2 \mathrm{~cm}$ and the area of the landscape photographed is $400 \mathrm{~km}^{2}$ . The focal length of the lens in the drone camera is : (A) 1.8 cm (B) 2.8 cm (C) 2.5 cm (D) 0.9 cm	1	Available	Available
40	View ExplanationExplain	The output of the circuit is low (zero) for : $\mathrm{X}=0, \mathrm{Y}=0$ , $X=0, Y=1$ , $X=1, Y=0$ , $X=1, Y=1$ Choose the correct answer from the options given below : (A) (A), (C) and (D) only (B) (A), (B) and (C) only (C) (B), (C) and (D) only (D) (A), (B) and (D) only	3	Diagram Question	Available
41	View ExplanationExplain	The temperature of a body in air falls from $40^{\circ} \mathrm{C}$ to $24^{\circ} \mathrm{C}$ in 4 minutes. The temperature of the air is $16^{\circ} \mathrm{C}$ . The temperature of the body in the next 4 minutes will be : (A) $\frac{14}{3}^{\circ} \mathrm{C}$ (B) $\frac{28}{3}{ }^{\circ} \mathrm{C}$ (C) $\frac{56}{3}^{\circ} \mathrm{C}$ (D) $\frac{42}{3}^{\circ} \mathrm{C}$	3	Available	Available
42	View ExplanationExplain	The energy $E$ and momentum $p$ of a moving body of mass $m$ are related by some equation. Given that c represents the speed of light, identify the correct equation. (A) $\mathrm{E}^{2}=\mathrm{pc}^{2}+\mathrm{m}^{2} \mathrm{c}^{4}$ (B) $\mathrm{E}^{2}=\mathrm{pc}^{2}+\mathrm{m}^{2} \mathrm{c}^{2}$ (C) $E^{2}=p^{2} c^{2}+m^{2} c^{2}$ (D) $E^{2}=p^{2} c^{2}+m^{2} c^{4}$	4	Available	Available
43	View ExplanationExplain	A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 \times 10^{-8}$ C charge and then removed to a distance such that the force of repulsion between them is $9 \times 10^{-3} \mathrm{~N}$ . The distance between them is (Take $\frac{1}{4 \pi \varepsilon_{0}}$ as $9 \times 10^{9}$ in SI units) (A) 2 cm (B) 3 cm (C) 4 cm (D) 1 cm	1	Available	Available
44	View ExplanationExplain	A particle oscillates along the x -axis according to the law, $x(t)=x_{0} \sin ^{2}\left(\frac{t}{2}\right)$ where $x_{0}=1 \mathrm{~m}$ . The kinetic energy ( K ) of the particle as a function of x is correctly represented by the graph.	1	Diagram Question	Available
45	View ExplanationExplain	In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ are orthogonal to each other. The polarizer $P_{3}$ covers both the slits with its transmission axis at $45^{\circ}$ to those of $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ . An unpolarized light of wavelength $\lambda$ and intensity $\mathrm{I}_{0}$ is incident on $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ . The intensity at a point after $P_{3}$ where the path difference between the light waves from $\mathrm{s}_{1}$ and $\mathrm{s}_{2}$ is $\frac{\lambda}{3}$ , is (A) $\frac{I_{0}}{2}$ (B) $\frac{\mathrm{I}_{0}}{4}$ (C) $\mathrm{I}_{0}$ (D) $\frac{\mathrm{I}_{0}}{3}$	3	Diagram Question	Available
46	View ExplanationExplain	A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75ns. The number of turns per metre in the solenoid is $\_\_\_\_$ . [Take mass of electron $\mathrm{m}_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg}$ , charge of electron $\left\|\mathrm{q}_{\mathrm{e}}\right\|=1.6 \times 10^{-19} \mathrm{C}$ , $\left.\mu_{0}=4 \pi \times 10^{-7} \frac{\mathrm{~N}}{\mathrm{~A}^{2}}, 1 \mathrm{~ns}=10^{-9} \mathrm{~s}\right]$	(250)	Available	Available
47	View ExplanationExplain	A string of length $L$ is fixed at one end and carries a mass of $M$ at the other end. The mass makes $\left(\frac{3}{\pi}\right)$ rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is $\_\_\_\_$ ML.	(36)	Diagram Question	Available
48	View ExplanationExplain	The ratio of the power of a light source $S_{1}$ to that the light source $\mathrm{S}_{2}$ is $2 . \mathrm{S}_{1}$ is emitting $2 \times 10^{15}$ photons per second at 600 nm . If the wavelength of the source $\mathrm{S}_{2}$ is 300 nm , then the number of photons per second emitted by $S_{2}$ is $\_\_\_\_$ $\times 10^{14}$ .	(5)	Available	Available
49	View ExplanationExplain	The increase in pressure required to decrease the volume of a water sample by $0.2 \%$ is $\mathrm{P} \times 10^{5} \mathrm{Nm}^{-2}$ . Bulk modulus of water is $2.15 \times 10^{9} \mathrm{Nm}^{-2}$ . The value of $P$ is $\_\_\_\_$ .	(43)	Available	Available
50	View ExplanationExplain	Acceleration due to gravity on the surface of earth is ' g '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is $\_\_\_\_$ g.	(9)	Available	Available
51	View ExplanationExplain	Based on the data given below: $\mathrm{E}_{\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} / \mathrm{Cr}^{3+}}^{0}=1.33 \mathrm{~V} \quad \mathrm{E}_{\mathrm{Cl}_{2} / \mathrm{Cl}^{(-)}}^{0}=1.36 \mathrm{~V}$ $\mathrm{E}_{\mathrm{MnO}_{4}^{-} / \mathrm{Mn}^{2+}}^{0}=1.51 \mathrm{~V} \quad \mathrm{E}_{\mathrm{Cr}^{3+} / \mathrm{Cr}}^{0}=-0.74 \mathrm{~V}$ the strongest reducing agent is : (A) $\mathrm{Mn}^{2+}$ (B) Cr (C) $\mathrm{MnO}_{4}^{-}$ (D) $\mathrm{Cl}^{-}$	2	Available	Available
52	View ExplanationExplain	Given below are two statements : {Statement(I) :} {Statement(II) :} In the light of the above statements, choose the correct answer from the options given below : (A) Both Statement I and Statement II are false (B) Statement I is false but Statement II is true (C) Both Statement I and Statement II are true (D) Statement I is true but Statement II is false	4	Diagram Question	Available
53	View ExplanationExplain	For reaction The correct order of set of reagents for the above conversion is : (A) $\mathrm{Br}_{2} \mid \mathrm{FeBr}_{3}, \mathrm{H}_{2} \mathrm{O}(\Delta), \mathrm{NaOH}$ (B) $\mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm{Ac}_{2} \mathrm{O}, \mathrm{Br}_{2}, \mathrm{H}_{2} \mathrm{O}(\Delta), \mathrm{NaOH}$ (C) $\mathrm{Ac}_{2} \mathrm{O}, \mathrm{Br}_{2}, \mathrm{H}_{2} \mathrm{O}(\Delta), \mathrm{NaOH}$ (D) $\mathrm{Ac}_{2} \mathrm{O}, \mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm{Br}_{2}, \mathrm{NaOH}$	2	Diagram Question	Available
54	View ExplanationExplain	For hydrogen atom, the orbital/s with lowest energy is/are : A. 4 s, B. $3 \mathrm{p}_{\mathrm{x}}$ , C. $3 d_{x^{2}-y^{2}}$ , D. $3 d_{z^{2}}$ , E. $4 \mathrm{p}_{\mathrm{z}}$ Choose the correct answer from the options given below : (A) (A) and (E) only (B) (B) only (C) (A) only (D) (B), (C) and (D) only	4	Available	Available
55	View ExplanationExplain	In the given structure, number of sp and $\mathrm{sp}^{2}$ hybridized carbon atoms present respectively are : (A) 3 and 6 (B) 3 and 5 (C) 4 and 6 (D) 4 and 5	2	Diagram Question	Available
56	View ExplanationExplain	Which of the following mixing of 1 M base and 1 M acid leads to the largest increase in temperature? (A) 30 mL HCl and 30 mL NaOH (B) $30 \mathrm{~mL} \mathrm{CH}_{3} \mathrm{COOH}$ and 30 mL NaOH (C) 50 mL HCl and 20 mL NaOH (D) $45 \mathrm{~mL} \mathrm{CH}_{3} \mathrm{COOH}$ and 25 mL NaOH	1	Available	Available
57	View ExplanationExplain	Given below are two statements : Statement(I) : Experimentally determined oxygen-oxygen bond lengths in the $\mathrm{O}_{3}$ are found to be same and the bond length is greater than that of a $\mathrm{O}=\mathrm{O}$ (double bond) but less than that of a single $(\mathrm{O}-\mathrm{O})$ bond. Statement (II) : The strong lone pair-lone pair repulsion between oxygen atoms is solely responsible for the fact that the bond length in ozone is smaller than that of a double bond $(\mathrm{O}=\mathrm{O})$ but more than that of a single bond $(\mathrm{O}-\mathrm{O})$ . In the light of the above statements, choose the correct answer from the options given below: (A) Statement I is true but Statement II is false (B) Both Statement I and Statement II are true (C) Both Statement I and Statement II are false (D) Statement I is false but Statement II is true	1	Available	Available
58	View ExplanationExplain	Find the compound 'A' from the following reaction sequences. \[ \mathrm{A} \xrightarrow{\text { aqua-regia }} \mathrm{B} \xrightarrow[\text { (2)AcOH }]{\text { (1) } \mathrm{KNO}_{2} \mid \mathrm{NH}_{4} \mathrm{OH}} \text { yellow ppt } \] (A) ZnS (B) CoS (C) MnS (D) Nis	2	Diagram Question	Available
59	View ExplanationExplain	For the reaction, $\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})$ Attainment of equilibrium is predicted correctly by:	2	Diagram Question	Available
60	View ExplanationExplain	Match List-I with List-II. Choose the correct answer from the options given below : (A) (A)-(III), (B)-(I), (C)-(II), (D)-(IV) (B) (A)-(III), (B)-(I), (C)-(IV), (D)-(II) (C) (A)-(IV), (B)-(II), (C)-(III), (D)-(I) (D) (A)-(II), (B)-(IV), (C)-(I), (D)-(III)	2	Diagram Question	Available
61	View ExplanationExplain	The elemental composition of a compound is $54.2 \%, \mathrm{C}, 9.2 \% \mathrm{H}$ and $36.6 \% \mathrm{O}$ . If the molar mass of the compound is $132 \mathrm{~g} \mathrm{~mol}^{-1}$ , the molecular formula of the compound is : [Given : The relative atomic mass of $\mathrm{C}: \mathrm{H}: \mathrm{O}=$ 12:1:16] (A) $\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{O}_{3}$ (B) $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$ (C) $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{3}$ (D) $\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}$	3	Available	Available
62	View ExplanationExplain	When Ethane-1,2-diamine is added progressively to an aqueous solution of Nickel (II) chloride, the sequence of colour change observed will be : (A) Pale Blue $\rightarrow$ Blue $\rightarrow$ Green $\rightarrow$ Violet (B) Pale Blue $\rightarrow$ Blue $\rightarrow$ Violet $\rightarrow$ Green (C) Green $\rightarrow$ Pale Blue $\rightarrow$ Blue $\rightarrow$ Violet (D) Violet $\rightarrow$ Blue $\rightarrow$ Pale Blue $\rightarrow$ Green	3	Available	Available
63	View ExplanationExplain	The conditions and consequence that favours the $\mathrm{t}_{2 \mathrm{~g}}{ }^{3}, \mathrm{e}_{\mathrm{g}}{ }^{1}$ configuration in a metal complex are : (A) weak field ligand, high spin complex (B) strong field ligand, high spin complex (C) strong field ligand, low spin complex (D) weak field ligand, low spin complex	1	Available	Available
64	View ExplanationExplain	Identify correct statement/s : A. $-\mathrm{OCH}_{3}$ and $-\mathrm{NHCOCH}_{3}$ are activating group, B. -CN and -OH are meta directing group, C. -CN and $-\mathrm{SO}_{3} \mathrm{H}$ are meta directing group, D. Activating groups act as ortho - and para directing groups, E. Halides are activating groups Choose the correct answer from the options given below : (A) (A), (C) and (D) only (B) (A), (B) and (E) only (C) (A) only (D) (A) and (C) only	1	Available	Available
65	View ExplanationExplain	Given below are two statements : Statement (I): The first ionization energy of Pb is greater than that of Sn Statement(II) : The first ionization energy of Ge is greater than that of Si . In the light of the above statements, choose the correct answer from the options given below : (A) Statement I is true but Statement II is false (B) Both Statement I and Statement II are false (C) Statement I is false but Statement II is true (D) Both Statement I and Statement II are true	1	Available	Available
66	View ExplanationExplain	$\mathrm{S}(\mathrm{g})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{SO}_{3}(\mathrm{~g})+2 \mathrm{x} \mathrm{kcal}$ $\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{SO}_{3}(\mathrm{~g})+\mathrm{y} \mathrm{kcal}$ The heat of formation of $\mathrm{SO}_{2}(\mathrm{~g})$ is given by : (A) $\frac{2 x}{y} \mathrm{kcal}$ (B) $y-2 x \mathrm{kcal}$ (C) $2 x+y$ kcal (D) $x+y$ kcal	2	Available	Available
67	View ExplanationExplain	Match List-I with List-II Choose the correct answer from the options given below : (A) (A)-(IV), (B)-(III), (C)-(I), (D)-(II) (B) (A)-(III), (B)-(IV), (C)-(II), (D)-(I) (C) (A)-(I), (B)-(III), (C)-(II), (D)-(IV) (D) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)	1	Diagram Question	Available
68	View ExplanationExplain	The structure of the major product formed in the following reaction is :	2	Diagram Question	Available
69	View ExplanationExplain	Match List-I with List-II. Choose the correct answer from the options given below : (A) (A)-(III), (B)-(IV), (C)-(II), (D)-(I) (B) (A)-(III), (B)-(I), (C)-(IV), (D)-(II) (C) (A)-(IV), (B)-(III), (C)-(II), (D)-(I) (D) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)	1	Diagram Question	Available
70	View ExplanationExplain	The successive 5 ionisation energies of an element are $800,2427,3658,25024$ and $32824 \mathrm{~kJ} / \mathrm{mol}$ , respectively. By using the above values predict the group in which the above element is present : (A) Group 2 (B) Group 13 (C) Group 4 (D) Group 14	2	Available	Available
71	View ExplanationExplain	The observed and normal masses of compound $\mathrm{MX}_{2}$ are 65.6 and 164 respectively. The percent degree of ionisation of $\mathrm{MX}_{2}$ is $\_\_\_\_$ \%. (Nearest integer)	(75)	Available	Available
72	View ExplanationExplain	The possible number of stereoisomers for 5-phenylpent-4-en-2-ol is $\_\_\_\_$ .	(4)	Available	Available
73	View ExplanationExplain	Consider a complex reaction taking place in three steps with rate constants $\mathrm{k}_{1}, \mathrm{k}_{2}$ and $\mathrm{k}_{3}$ respectively. The overall rate constant k is given by the expression $\mathrm{k}=\sqrt{\frac{\mathrm{k}_{1} \mathrm{k}_{3}}{\mathrm{k}_{2}}}$ . If the activation energies of the three steps are 60,30 and $10 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively, then the overall energy of activation in $\mathrm{kJ} \mathrm{mol}^{-1}$ is $\_\_\_\_$ . (Nearest integer)	(20)	Available	Available
74	View ExplanationExplain	The hydrocarbon ( X ) with molar mass $80 \mathrm{~g} \mathrm{~mol}^{-1}$ and $90 \%$ carbon has $\_\_\_\_$ degree of unsaturation.	(3)	Available	Available
75	View ExplanationExplain	In Carius method of estimation of halogen, 0.25 g of an organic compound gave 0.15 g of silver bromide (AgBr). The percentage of Bromine in the organic compound is $\_\_\_\_$ $\times 10^{-1} \%$ (Nearest integer). (Given : Molar mass of Ag is 108 and Br is $80 \mathrm{~g} \mathrm{~mol}^{-1}$ )	(255)	Available	Available