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JEE-MAIN EXAMINATION – JANUARY 2025

JEE-MAIN TEST PAPER WITH SOLUTION

Held on Wednesday 22nd January 2025, Time: 3:00 PM to 6:00 PM

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JEE Main
Mathematics, Physics, Chemistry
Evening Session
3 hours

Paper Overview

75
Total Questions
0
Correct
0
Incorrect
75
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Complete Solutions

Q#ExplanationQuestionCorrectSolutionStatus
1Explain
Let α,β,γ\alpha, \beta, \gamma and δ\delta be the coefficients of x7,x5,x3x^{7}, x^{5}, x^{3} and xx respectively in the expansion of (x+x3−1)5+(x−x3−1)5,x>1\left(x+\sqrt{x^{3}-1}\right)^{5}+\left(x-\sqrt{x^{3}-1}\right)^{5}, x>1. If uu and vv satisfy the equations αu+βv=18\alpha u+\beta v=18, γu+δv=20\gamma u+\delta v=20, then u+v\mathrm{u}+\mathrm{v} equals :
(A) 5
(B) 4
(C) 3
(D) 8
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2Explain
In a group of 3 girls and 4 boys, there are two boys B1\mathrm{B}_{1} and B2\mathrm{B}_{2}. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but B1\mathrm{B}_{1} and B2\mathrm{B}_{2} are not adjacent to each other, is :
(A) 144
(B) 72
(C) 96
(D) 120
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3Explain
Let P(4,43)\mathrm{P}(4,4 \sqrt{3}) be a point on the parabola y2=4ax\mathrm{y}^{2}=4 \mathrm{ax} and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to:
(A) 26338\frac{263 \sqrt{3}}{8}
(B) 17317 \sqrt{3}
(C) 34338\frac{343 \sqrt{3}}{8}
(D) 3433\frac{34 \sqrt{3}}{3}
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4Explain
For a 3×33 \times 3 matrix M , let trace (M)(\mathrm{M}) denote the sum of all the diagonal elements of M . Let A be a 3×33 \times 3 matrix such that ∣A∣=12|\mathrm{A}|=\frac{1}{2} and trace (A)=3(\mathrm{A})=3. If B=adj⁡(adj⁡(2A))B=\operatorname{adj}(\operatorname{adj}(2 A)), then the value of ∣B∣+|B|+ trace (B) equals:
(A) 56
(B) 132
(C) 174
(D) 280
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5Explain
Suppose that the number of terms in an A.P. is 2 k , k∈N\mathrm{k} \in \mathrm{N}. If the sum of all odd terms of the A.P. is 40 , the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27 , then k is equal to
(A) 5
(B) 8
(C) 6
(D) 4
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6Explain
Let a line pass through two distinct points P(−2,−1,3)\mathrm{P}(-2,-1,3) and Q , and be parallel to the vector 3i^+2j^+2k3 \hat{i}+2 \hat{j}+2 \mathrm{k}. If the distance of the point Q from the point R(1,3,3)\mathrm{R}(1,3,3) is 5 , then the square of the area of △PQR\triangle \mathrm{PQR} is equal to:
(A) 136
(B) 140
(C) 144
(D) 148
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7Explain
If lim⁡x→∞((e1−e)(1e−x1+x))x=α\lim _{\mathrm{x} \rightarrow \infty}\left(\left(\frac{\mathrm{e}}{1-\mathrm{e}}\right)\left(\frac{1}{\mathrm{e}}-\frac{\mathrm{x}}{1+\mathrm{x}}\right)\right)^{\mathrm{x}}=\alpha, then the value of log⁡eα1+log⁡eα\frac{\log _{\mathrm{e}} \alpha}{1+\log _{\mathrm{e}} \alpha} equals :
(A) e
(B) e−2e^{-2}
(C) e2\mathrm{e}^{2}
(D) e−1\mathrm{e}^{-1}
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8Explain
Let f(x)=∫0x2t2−8t+15etdt,x∈Rf(x)=\int_{0}^{x^{2}} \frac{t^{2}-8 t+15}{e^{t}} d t, x \in \mathbf{R}. Then the numbers of local maximum and local minimum points of ff, respectively, are :
(A) 2 and 3
(B) 3 and 2
(C) 1 and 3
(D) 2 and 2
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9Explain
The perpendicular distance, of the line x−12=y+2−1=z+32\frac{x-1}{2}=\frac{y+2}{-1}=\frac{z+3}{2} from the point P(2,−10,1)P(2,-10,1), is:
(A) 6
(B) 525 \sqrt{2}
(C) 353 \sqrt{5}
(D) 434 \sqrt{3}
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10Explain
If x=f(y)\mathrm{x}=\mathrm{f}(\mathrm{y}) is the solution of the differential equation (1+y2)+(x−2etan⁡−1y)dydx=0,y∈(−π2,π2)\left(1+y^{2}\right)+\left(x-2 e^{\tan ^{-1} y}\right) \frac{d y}{d x}=0, y \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) with f(0)=1f(0)=1, then f(13)f\left(\frac{1}{\sqrt{3}}\right) is equal to :
(A) eπ/4\mathrm{e}^{\pi / 4}
(B) eπ/12e^{\pi / 12}
(C) eπ/3e^{\pi / 3}
(D) eπ/6\mathrm{e}^{\pi / 6}
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11Explain
If ∫ex(xsin⁡−1x1−x2+sin⁡−1x(1−x2)3/2+x1−x2)dx=g(x)+C\int \mathrm{e}^{\mathrm{x}}\left(\frac{\mathrm{x} \sin ^{-1} \mathrm{x}}{\sqrt{1-\mathrm{x}^{2}}}+\frac{\sin ^{-1} \mathrm{x}}{\left(1-\mathrm{x}^{2}\right)^{3 / 2}}+\frac{\mathrm{x}}{1-\mathrm{x}^{2}}\right) \mathrm{dx}=\mathrm{g}(\mathrm{x})+\mathrm{C}, where CC is the constant of integration, then g(12)g\left(\frac{1}{2}\right) equals :
(A) π6e2\frac{\pi}{6} \sqrt{\frac{e}{2}}
(B) π4e2\frac{\pi}{4} \sqrt{\frac{e}{2}}
(C) π6e3\frac{\pi}{6} \sqrt{\frac{e}{3}}
(D) π4e3\frac{\pi}{4} \sqrt{\frac{\mathrm{e}}{3}}
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12Explain
Let αθ\alpha_{\theta} and βθ\beta_{\theta} be the distinct roots of 2x2+(cos⁡θ)x−1=0,θ∈(0,2π)2 \mathrm{x}^{2}+(\cos \theta) \mathrm{x}-1=0, \theta \in(0,2 \pi). If m and M are the minimum and the maximum values of αθ4+βθ4\alpha_{\theta}^{4}+\beta_{\theta}^{4}, then 16(M+m)16(M+m) equals :
(A) 24
(B) 25
(C) 27
(D) 17
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13Explain
Let A={1,2,3,4}A=\{1,2,3,4\} and B={1,4,9,16}B=\{1,4,9,16\}. Then the number of many-one functions f:A→B\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B} such that 1∈f(A)1 \in f(A) is equal to :
(A) 127
(B) 151
(C) 163
(D) 139
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14Explain
If the system of linear equations : x+y+2z=6x+y+2 z=6, 2x+3y+az=a+12 \mathrm{x}+3 \mathrm{y}+\mathrm{az}=\mathrm{a}+1, −x−3y+bz=2 b-\mathrm{x}-3 \mathrm{y}+\mathrm{bz}=2 \mathrm{~b}, where a,b∈R\mathrm{a}, \mathrm{b} \in \mathbf{R}, has infinitely many solutions, then 7a+3b7 a+3 b is equal to:
(A) 9
(B) 12
(C) 16
(D) 22
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15Explain
Let a⃗\vec{a} and b⃗\vec{b} be two unit vectors such that the angle between them is π3\frac{\pi}{3}. If λa⃗+2b⃗\lambda \vec{a}+2 \vec{b} and 3a⃗−λb⃗3 \vec{a}-\lambda \vec{b} are perpendicular to each other, then the number of values of λ\lambda in [−1,3][-1,3] is :
(A) 3
(B) 2
(C) 1
(D) 0
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16Explain
Let E:x2a2+y2 b2=1,a>b\mathrm{E}: \frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=1, \mathrm{a}>\mathrm{b} and H:x2 A2−y2 B2=1\mathrm{H}: \frac{\mathrm{x}^{2}}{\mathrm{~A}^{2}}-\frac{\mathrm{y}^{2}}{\mathrm{~B}^{2}}=1. Let the distance between the foci of E and the foci of H be 232 \sqrt{3}. If a−A=2\mathrm{a}-\mathrm{A}=2, and the ratio of the eccentricities of E and H is 13\frac{1}{3}, then the sum of the lengths of their latus rectums is equal to:
(A) 10
(B) 7
(C) 8
(D) 9
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17Explain
If A and B are two events such that P(A∩B)=0.1\mathrm{P}(\mathrm{A} \cap \mathrm{B})=0.1, and P(A∣B)\mathrm{P}(\mathrm{A} \mid \mathrm{B}) and P(B∣A)\mathrm{P}(\mathrm{B} \mid \mathrm{A}) are the roots of the equation 12x2−7x+1=012 x^{2}-7 x+1=0, then the value of P(Aˉ∪Bˉ)P(Aˉ∩Bˉ)\frac{P(\bar{A} \cup \bar{B})}{P(\bar{A} \cap \bar{B})} is:
(A) 53\frac{5}{3}
(B) 43\frac{4}{3}
(C) 94\frac{9}{4}
(D) 74\frac{7}{4}
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18Explain
The sum of all values of θ∈[0,2π]\theta \in[0,2 \pi] satisfying 2sin⁡2θ=cos⁡2θ2 \sin ^{2} \theta=\cos 2 \theta and 2cos⁡2θ=3sin⁡θ2 \cos ^{2} \theta=3 \sin \theta is
(A) π2\frac{\pi}{2}
(B) 4π4 \pi
(C) 5π6\frac{5 \pi}{6}
(D) π\pi
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19Explain
Let the curve z(1+i)+zˉ(1−i)=4,z∈Cz(1+i)+\bar{z}(1-i)=4, z \in C, divide the region ∣z−3∣≤1|z-3| \leq 1 into two parts of areas α\alpha and β\beta. Then ∣α−β∣|\alpha-\beta| equals :
(A) 1+π21+\frac{\pi}{2}
(B) 1+π31+\frac{\pi}{3}
(C) 1+π41+\frac{\pi}{4}
(D) 1+π61+\frac{\pi}{6}
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20Explain
The area of the region enclosed by the curves y=x2−4x+4y=x^{2}-4 x+4 and y2=16−8xy^{2}=16-8 x is :
(A) 83\frac{8}{3}
(B) 43\frac{4}{3}
(C) 5
(D) 8
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21Explain
Let y=f(x)y=f(x) be the solution of the differential equation dydx+xyx2−1=x6+4x1−x2,−1<x<1\frac{d y}{d x}+\frac{x y}{x^{2}-1}=\frac{x^{6}+4 x}{\sqrt{1-x^{2}}},-1<x<1 such that f(0)=0f(0)=0. If 6∫−1/21/2f(x)dx=2π−α6 \int_{-1 / 2}^{1 / 2} f(x) d x=2 \pi-\alpha then α2\alpha^{2} is equal to ____\_\_\_\_ .
(27)
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22Explain
Let A(6,8),B(10cos⁡α,−10sin⁡α)\mathrm{A}(6,8), \mathrm{B}(10 \quad \cos \alpha,-10 \quad \sin \alpha) and C ( −10sin⁡α,10cos⁡α-10 \sin \alpha, 10 \cos \alpha ), be the vertices of a triangle. If L(a,9)\mathrm{L}(\mathrm{a}, 9) and G(h,k)\mathrm{G}(\mathrm{h}, \mathrm{k}) be its orthocenter and centroid respectively, then (5a−3h+6k+100sin⁡2α)(5 a-3 h+6 k+100 \sin 2 \alpha) is equal to ____\_\_\_\_
(145)
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23Explain
Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the parallel lines, while R lies on the other. Then (QR)2(\mathrm{QR})^{2} is equal to ____\_\_\_\_ .
(28)
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24Explain
If ∑r=130r2(30Cr)230Cr−1=α×229\sum_{\mathrm{r}=1}^{30} \frac{\mathrm{r}^{2}\left({ }^{30} \mathrm{C}_{\mathrm{r}}\right)^{2}}{{ }^{30} \mathrm{C}_{\mathrm{r}-1}}=\alpha \times 2^{29}, then α\alpha is equal to ____\_\_\_\_ .
(465)
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25Explain
Let A={1,2,3}\mathrm{A}=\{1,2,3\}. The number of relations on A , containing ( 1,2 ) and ( 2,3 ), which are reflexive and transitive but not symmetric, is ____\_\_\_\_ .
(3)
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26Explain
A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is 4D then the power of a part of the divided lens is
(A) 8 D
(B) 4 D
(C) D
(D) 2 D
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27Explain
A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)
(A) 32Mg\frac{3}{2} \mathrm{Mg}
(B) Mg2\frac{M g}{2}
(C) Mg
(D) 2 Mg
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28Explain
The maximum percentage error in the measurment of density of a wire is [Given, mass of wire =(0.60±0.003)g=(0.60 \pm 0.003) \mathrm{g} radius of wire =(0.50±0.01)cm=(0.50 \pm 0.01) \mathrm{cm} length of wire (10.00±0.05)cm(10.00 \pm 0.05) \mathrm{cm} ]
(A) 4
(B) 5
(C) 8
(D) 7
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29Explain
A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is I0\mathrm{I}_{0}. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be
(A) I0I_{0}
(B) I02\frac{\mathrm{I}_{0}}{2}
(C) I02\frac{I_{0}}{\sqrt{2}}
(D) 2I02 \mathrm{I}_{0}
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30Explain
For a short dipole placed at origin O , the dipole moment P is along x -axis, as shown in the figure. If the electric potential and electric field at A are V0\mathrm{V}_{0} and E0\mathrm{E}_{0}, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y -axis is given by:
(A) V02\frac{V_{0}}{2} and E016\frac{E_{0}}{16}
(B) zero and E08\frac{\mathrm{E}_{0}}{8}
(C) zero and E016\frac{\mathrm{E}_{0}}{16}
(D) V0V_{0} and E04\frac{E_{0}}{4}
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31Explain
Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge,
(A) [F]=[C2M−2 L2 T2][\mathrm{F}]=\left[\mathrm{C}^{2} \mathrm{M}^{-2} \mathrm{~L}^{2} \mathrm{~T}^{2}\right]
(B) [F]=[CM−2 L−2 T−2][\mathrm{F}]=\left[\mathrm{CM}^{-2} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right]
(C) [F]=[CM−1 L−2 T2][\mathrm{F}]=\left[\mathrm{CM}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{2}\right]
(D) [F]=[C2M−1 L−2 T2][\mathrm{F}]=\left[\mathrm{C}^{2} \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{2}\right]
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32Explain
An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :
(A) 2hπeB\sqrt{\frac{2 h}{\pi e B}}
(B) 4hπeB\sqrt{\frac{4 h}{\pi e B}}
(C) h2πeB\sqrt{\frac{h}{2 \pi e B}}
(D) hπeB\sqrt{\frac{h}{\pi e B}}
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33Explain
For a diatomic gas, if γ1=(CpCv)\gamma_{1}=\left(\frac{\mathrm{Cp}}{\mathrm{Cv}}\right) for rigid molecules and γ2=(CpCv)\gamma_{2}=\left(\frac{\mathrm{Cp}}{\mathrm{Cv}}\right) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? ( Cp and Cv are specific heats of the gas at constant pressure and volume)
(A) γ2>γ1\gamma_{2}>\gamma_{1}
(B) γ2=γ1\gamma_{2}=\gamma_{1}
(C) 2γ2=γ12 \gamma_{2}=\gamma_{1}
(D) γ2<γ1\gamma_{2}<\gamma_{1}
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34Explain
A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf ( ε\varepsilon ) with time ( t ) is given by
(4)
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35Explain
A light source of wavelength λ\lambda illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength λ2\frac{\lambda}{2}, then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV )
(A) 2 eV
(B) 6 eV
(C) 5 eV
(D) 3 eV
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36Explain
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet. Reason (R) : The mass of the pendulum remains unchanged at Earth and the other planet. In the light of the above statements, choose the correct answer from the options given below :
(A) Both (A) and (R) are true but (R) is NOT 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 and (R) is the correct explanation of (A)
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37Explain
The torque due to the force (2i^+j^+2k^)(2 \hat{i}+\hat{j}+2 \hat{k}) about the origin, acting on a particle whose position vector is (i^+j^+k^)(\hat{i}+\hat{j}+\hat{k}), would be
(A) i^−j^+k^\hat{i}-\hat{j}+\hat{k}
(B) i^+k^\hat{\mathrm{i}}+\hat{\mathrm{k}}
(C) i^−k^\hat{i}-\hat{k}
(D) j^−k^\hat{j}-\hat{k}
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38Explain
To obtain the given truth table, following logic gate should be placed at G :
(A) NOR Gate
(B) AND Gate
(C) NAND Gate
(D) OR Gate
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39Explain
A force F⃗=2i^+bj^+k^\vec{F}=2 \hat{i}+b \hat{j}+\hat{k} is applied on a particle and it undergoes a displacement i^−2j^−k^\hat{i}-2 \hat{j}-\hat{k}. What will be the value of bb, if work done on the particle is zero.
(A) 0
(B) 12\frac{1}{2}
(C) 13\frac{1}{3}
(D) 2
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40Explain
Given below are two statements. On is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light. Reason (R) : The fringe width is directly proportional to the wavelength of light. In the light of above statements, 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 false but (R) is true.
(C) Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
(D) (A) is true but (R) is false.
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41Explain
A ball of mass 100 g is projected with velocity 20 m/s20 \mathrm{~m} / \mathrm{s} at 60∘60^{\circ} with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is :
(A) 20 J
(B) 15 J
(C) zero
(D) 5 J
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42Explain
A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45 . What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.]
(A) 94.8 nm
(B) 68.7 nm
(C) 137.5 nm
(D) 275 nm
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43Explain
The tube of length LL is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s2 \mathrm{~m} / \mathrm{s}, then velocity of water leaving the point (2) will be :
(A) 2 m/s2 \mathrm{~m} / \mathrm{s}
(B) 4 m/s4 \mathrm{~m} / \mathrm{s}
(C) 6 m/s6 \mathrm{~m} / \mathrm{s}
(D) 8 m/s8 \mathrm{~m} / \mathrm{s}
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44Explain
Given are statements for certain thermodynamic variables, Internal energy, volume (V) and mass (M) are extensive variables. Pressure (P), temperature (T) and density ( ρ\rho ) are intensive variables. Volume (V), temperature (T) and density ( ρ\rho ) are intensive variables. Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the points given below :
(A) (C) and (D) only
(B) (D) and (A) only
(C) (A) and (B) only
(D) (B) and (C) only
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45Explain
A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m/s10 \mathrm{~m} / \mathrm{s}. The ratio of its kinetic energies at point B and C is : (Take acceleration due to gravity as 10 m/s210 \mathrm{~m} / \mathrm{s}^{2} )
(A) 2+33\frac{2+\sqrt{3}}{3}
(B) 2+23\frac{2+\sqrt{2}}{3}
(C) 3+32\frac{3+\sqrt{3}}{2}
(D) 3−22\frac{3-\sqrt{2}}{2}
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46Explain
A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of 2×105 ms−12 \times 10^{5} \mathrm{~ms}^{-1}. When the electric field is switched off, the proton moves along a circular path of radius 2 cm . The magnitude of electric field is x×104 N/Cx \times 10^{4} \mathrm{~N} / \mathrm{C}. the value of xx is ____\_\_\_\_ . Take the mass of the proton =1.6×10−27 kg=1.6 \times 10^{-27} \mathrm{~kg}.
(2)
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47Explain
Two long parallel wires X and Y , separated by a distance of 6 cm , carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point PP at a distance of 4 cm from wire YY is x×10−5Tx \times 10^{-5} T. The value of xx is ____\_\_\_\_ . Take permeability of free space as μ0=4π×10−7\mu_{0}=4 \pi \times 10^{-7} SI units.
(1)
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48Explain
A parallel plate capacitor of area A=16 cm2\mathrm{A}=16 \mathrm{~cm}^{2} and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area A0=3.2 cm2\mathrm{A}_{0}=3.2 \mathrm{~cm}^{2} inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through A0\mathrm{A}_{0} is ____\_\_\_\_ mA .
(1200)
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49Explain
A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is FαM\sqrt{\frac{F}{\alpha M}} in SI unit. The value of α\alpha is ____\_\_\_\_ .
(1)
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50Explain
The net current flowing in the given circuit is ____\_\_\_\_ A.
(1)
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51Explain
Arrange the following compounds in increasing order of their dipole moment : HBr,H2 S,NF3\mathrm{HBr}, \mathrm{H}_{2} \mathrm{~S}, \mathrm{NF}_{3} and CHCl3\mathrm{CHCl}_{3}
(A) NF3<HBr<H2 S<CHCl3\mathrm{NF}_{3}<\mathrm{HBr}<\mathrm{H}_{2} \mathrm{~S}<\mathrm{CHCl}_{3}
(B) HBr<H2 S<NF3<CHCl3\mathrm{HBr}<\mathrm{H}_{2} \mathrm{~S}<\mathrm{NF}_{3}<\mathrm{CHCl}_{3}
(C) H2 S<HBr<NF3<CHCl3\mathrm{H}_{2} \mathrm{~S}<\mathrm{HBr}<\mathrm{NF}_{3}<\mathrm{CHCl}_{3}
(D) CHCl3<NF3<HBr<H2 S\mathrm{CHCl}_{3}<\mathrm{NF}_{3}<\mathrm{HBr}<\mathrm{H}_{2} \mathrm{~S}
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52Explain
Identify the number of structure/s from the following which can be correlated to D-glyceraldehyde.
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53Explain
The maximum covalency of a non-metallic group 15 element ' E ' with weakest E−E\mathrm{E}-\mathrm{E} bond is :
(A) 5
(B) 3
(C) 6
(D) 4
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54Explain
Consider the given figure and choose the correct option :
(A) Activation energy of backward reaction is E1E_{1} and product is more stable than reactant.
(B) Activation energy of forward reaction is E1+E2\mathrm{E}_{1}+\mathrm{E}_{2} and product is more stable than reactant.
(C) Activation energy of forward reaction is E1+E2\mathrm{E}_{1}+\mathrm{E}_{2} and product is less stable than reactant.
(D) Activation energy of both forward and backward reaction is E1+E2\mathrm{E}_{1}+\mathrm{E}_{2} and reactant is more stable than product.
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55Explain
When sec-butylcyclohexane reacts with bromine in the presence of sunlight, the major product is :
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56Explain
The species which does not undergo disproportionation reaction is :
(A) ClO2−\mathrm{ClO}_{2}^{-}
(B) ClO4−\mathrm{ClO}_{4}^{-}
(C) ClO−\mathrm{ClO}^{-}
(D) ClO3−\mathrm{ClO}_{3}^{-}
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57Explain
Match the Compounds (List-I) with the appropriate Catalyst/Reagents (List-II) for their reduction into corresponding amines. List-I (Compounds)
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58Explain
The maximum number of RBr producing 2-methylbutane by above sequence of reactions is ____\_\_\_\_ . (Consider the structural isomers only)
(A) 4
(B) 5
(C) 3
(D) 1
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59Explain
Match List-I with List-II. Choose the correct answer from the options given below :
(A) (A)-(II), (B)-(I), (C)-(III), (D)-(IV)
(B) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(C) (A)-(I), (B)-(II), (C)-(IV), (D)-(III)
(D) (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
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60Explain
The correct order of the following complexes in terms of their crystal field stabilization energies is :
(A) [Co(NH3)4]2+<[Co(NH3)6]2+<[Co(en)3]3+<[Co(NH3)6]3+\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}<\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}<\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}<\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}
(B) [Co(NH3)4]2+<[Co(NH3)6]2+<[Co(NH3)6]3+<[Co(en)3]3+\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}<\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}<\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}<\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}
(C) [Co(NH3)6]2+<[Co(NH3)6]3+<[Co(NH3)4]2+<[Co(en)3]3+\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}<\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}<\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}<\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}
(D) [Co(en)3]3+<[Co(NH3)6]3+<[Co(NH3)6]2+<[Co(NH3)4]2+\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}<\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}<\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}<\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}
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61Explain
Density of 3 M NaCl solution is 1.25 g/mL1.25 \mathrm{~g} / \mathrm{mL}. The molality of the solution is :
(A) 1.79 m
(B) 2 m
(C) 3 m
(D) 2.79 m
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62Explain
The molar solubility(s) of zirconium phosphate with molecular formula (Zr4+)3(PO43−)4\left(\mathrm{Zr}^{4+}\right)_{3}\left(\mathrm{PO}_{4}^{3-}\right)_{4} is given by relation :
(A) (Ksp6912)17\left(\frac{\mathrm{K}_{\mathrm{sp}}}{6912}\right)^{\frac{1}{7}}
(B) (Ksp5348)16\left(\frac{\mathrm{K}_{\mathrm{sp}}}{5348}\right)^{\frac{1}{6}}
(C) (Ksp8435)17\left(\frac{\mathrm{K}_{\mathrm{sp}}}{8435}\right)^{\frac{1}{7}}
(D) (Ksp9612)13\left(\frac{\mathrm{K}_{\mathrm{sp}}}{9612}\right)^{\frac{1}{3}}
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63Explain
The most stable carbocation from the following is :
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64Explain
Given below are two statements : Statement (I) : An element in the extreme left of the periodic table forms acidic oxides. Statement (II): Acid is formed during the reaction between water and oxide of a reactive element present in the extreme right of the periodic table. In the light of the above statements, choose the correct answer from the options given below :
(A) Statement-I is false but Statement-II is true.
(B) Both Statement-I and Statement-II are false.
(C) Statement-I is true but Statement-II is false.
(D) Both Statement-I and Statement-II are true.
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65Explain
Given below are two statements : Statement (I) : A spectral line will be observed for a 2px→2py2 \mathrm{p}_{\mathrm{x}} \rightarrow 2 \mathrm{p}_{\mathrm{y}} transition. Statement (II): 2px2 \mathrm{p}_{\mathrm{x}} and 2py2 \mathrm{p}_{\mathrm{y}} are degenerate orbitals. In the light of the above statements, choose the correct answer from the options given below :
(A) Both Statement-I and Statement-II are true.
(B) Both Statement-I and Statement-II are false.
(C) Statement-I is true but Statement-II is false.
(D) Statement-I is false but Statement-II is true.
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66Explain
Given below are two statement : Statement (I) : Nitrogen, sulphur, halogen and phosphorus present in an organic compound are detected by Lassaigne's Test. Statement (II) : The elements present in the compound are converted from covalent form into ionic form by fusing the compound with Magnesium in Lassaigne's test. In the light of the above statements, choose the correct answer from the options given below :
(A) Both Statement I and Statement II are true
(B) Both Statement I and Statement II are false
(C) Statement I is true but Statement II is false
(D) Statement I is false but Statement II is true
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67Explain
Identify the homoleptic complex(es) that is/are low spin. [Fe(CN)5NO]2−\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NO}\right]^{2-}, [CoF6]3−\left[\mathrm{CoF}_{6}\right]^{3-}, [Fe(CN)6]4−\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}, [Co(NH3)6]3+\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}, [Cr(H2O)6]2+\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} Choose the correct answer from the options given below:
(A) (B) and (E) only
(B) (A) and (C) only
(C) (C) and (D) only
(D) (C) only
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68Explain
Residue (A) +HCl (dil.) →\rightarrow Compound (B) Structure of residue (A) and compound (B) Formed respectively is :
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69Explain
Given below are two statements : Statement (I) : Corrosion is an electrochemical phenomenon in which pure metal acts as an anode and impure metal as a cathode. Statement (II) : The rate of corrosion is more in alkaline medium than in acidic medium. 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
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70Explain
The alkane from below having two secondary hydrogens is :
(A) 4-Ethyl-3,4-dimethyloctane
(B) 2,2,4,4-Tetramethylhexane
(C) 2,2,3,3-Tetramethylpentane
(D) 2,2,4,5-Tetramethylheptane
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71Explain
The compound with molecular formula C6H6\mathrm{C}_{6} \mathrm{H}_{6}, which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has ____\_\_\_\_ π\pi electrons.
(8)
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72Explain
Niobium (Nb) and ruthenium (Ru) have "x" and " y " number of electrons in their respective 4 d orbitals. The value of x+yx+y is ____\_\_\_\_
(11)
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73Explain
The complex of Ni2+\mathrm{Ni}^{2+} ion and dimethyl glyoxime contains ____\_\_\_\_ number of Hydrogen (H)(\mathrm{H}) atoms.
(14)
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74Explain
Consider the following cases of standard enthalpy of reaction ( ΔHro\Delta \mathrm{H}_{\mathrm{r}}^{\mathrm{o}} in kJmol−1\mathrm{kJ} \mathrm{mol}^{-1} ) C2H6( g)+72O2( g)→2CO2( g)+3H2O(ℓ)ΔH1o=−1550\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})+\frac{7}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) \Delta \mathrm{H}_{1}^{\mathrm{o}}=-1550 C (graphite) +O2( g)→CO2( g)ΔH2o=−393.5+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g}) \Delta \mathrm{H}_{2}^{\mathrm{o}}=-393.5 H2( g)+12O2( g)→H2O(ℓ)ΔH3o=−286\mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\ell) \Delta \mathrm{H}_{3}^{\mathrm{o}}=-286 The magnitude of ΔHf2H6( g)o\Delta \mathrm{H}_{\mathrm{f}_{2} \mathrm{H}_{6}(\mathrm{~g})}^{\mathrm{o}} is ____\_\_\_\_ kJmol−1\mathrm{kJ} \mathrm{mol}^{-1} (Nearest integer).
(95)
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75Explain
20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is ____\_\_\_\_ ×10−2M\times 10^{-2} \mathrm{M}. (Nearest integer).
(57)
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