JEE Main 2025 — 4 Apr Shift 1 (Previous Year Paper)

$1+3+5^2+7+9^2+\ldots$ upto 40 terms is equal to

1. A.40870
2. B.43890
3. C.41880✓
4. D.33980

Correct answer: C

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is

1. A.$\frac{3}{5}$
2. B.$\frac{2}{15}$
3. C.$\frac{11}{15}$
4. D.$\frac{28}{75}$✓

Correct answer: D

The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is

1. A.$\frac{103}{182}$
2. B.$\frac{129}{182}$✓
3. C.$\frac{19}{26}$
4. D.$\frac{17}{26}$

Correct answer: B

Consider the equation $x^2+4x-n=0$, where $n\in[20, 100]$ is a natural number. Then the number of all distinct values of n, for which the given equation has integral roots, is equal to

1. A.6✓
2. B.5
3. C.8
4. D.7

Correct answer: A

Consider two vectors $\vec{u}=3\hat{i}-\hat{j}$ and $\vec{v}=2\hat{i}+\hat{j}-\lambda\hat{k}$, $\lambda>0$. The angle between them is given by $\cos^{-1}\left(\frac{\sqrt{5}}{2\sqrt{7}}\right)$. Let $\vec{v}=\vec{v}_1+\vec{v}_2$, where $\vec{v}_1$ is parallel to $\vec{u}$ and $\vec{v}_2$ is perpendicular to $\vec{u}$. Then the value $|\vec{v}_1|^2+|\vec{v}_2|^2$ is equal to

1. A.$\frac{25}{2}$
2. B.$\frac{23}{2}$
3. C.14✓
4. D.10

Correct answer: C

Let $A=\{1, 6, 11, 16, \ldots\}$ and $B=\{9, 16, 23, 30, \ldots\}$ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then $n(A\cup B)$ is

1. A.3814
2. B.4027
3. C.3761✓
4. D.4003

Correct answer: C

For an integer $n\ge2$, if the arithmetic mean of all coefficients in the binomial expansion of $(x+y)^{2n-3}$ is 16, then the distance of the point P$(2n-1, n^2-4n)$ from the line $x+y=8$ is

1. A.$2\sqrt{2}$
2. B.$3\sqrt{2}$✓
3. C.$\sqrt{2}$
4. D.$5\sqrt{2}$

Correct answer: B

In the expansion of $\left(\sqrt[3]{2}+\frac{1}{\sqrt[3]{3}}\right)^n$, $n\in\mathbf{N}$, if the ratio of $15^{th}$ term from the beginning to the $15^{th}$ term from the end is $\frac{1}{6}$, then the value of ${}^nC_3$ is

1. A.2300✓
2. B.4960
3. C.4060
4. D.1040

Correct answer: A

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

1. A.$\frac{6}{5}$
2. B.$\frac{50}{3}$
3. C.$\frac{10}{3}$
4. D.$\frac{18}{5}$✓

Correct answer: D

Let the three sides of a triangle are on the lines $4x-7y+10=0$, $x+y=5$ and $7x+4y=15$. Then the distance of its orthocentre from the orthocentre of the tringle formed by the lines $x=0$, $y=0$ and $x+y=1$ is

1. A.$\sqrt{5}$✓
2. B.$\sqrt{20}$
3. C.5
4. D.20

Correct answer: A

If $\lim_{x\to1^+}\frac{(x-1)(6+\lambda\cos(x-1))+\mu\sin(1-x)}{(x-1)^3}=-1$, where $\lambda, \mu\in\mathbf{R}$, then $\lambda+\mu$ is equal to

1. A.19
2. B.17
3. C.20
4. D.18✓

Correct answer: D

Let A and B be two distinct points on the line L: $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$. Both A and B are at a distance $2\sqrt{17}$ from the foot of perpendicular drawn from the point (1, 2, 3) on the line L. If O is the origin, then $\vec{OA}\cdot\vec{OB}$ is equal to

1. A.47✓
2. B.49
3. C.21
4. D.62

Correct answer: A

Let the shortest distance between the lines $\frac{x-3}{3}=\frac{y-\alpha}{-1}=\frac{z-3}{1}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-\beta}{4}$ be $3\sqrt{30}$. Then the positive value of $5\alpha+\beta$ is

1. A.40
2. B.46✓
3. C.48
4. D.42

Correct answer: B

Considering the principal values of the inverse trigonometric functions, $\sin^{-1}\left(\frac{\sqrt{3}}{2}x+\frac{1}{2}\sqrt{1-x^2}\right)$, $-\frac{1}{2}<x<\frac{1}{\sqrt{2}}$, is equal to

1. A.$\frac{\pi}{4}+\sin^{-1}x$
2. B.$\frac{\pi}{6}+\sin^{-1}x$✓
3. C.$\frac{5\pi}{6}-\sin^{-1}x$
4. D.$\frac{-5\pi}{6}-\sin^{-1}x$

Correct answer: B

If $10\sin^4\theta+15\cos^4\theta=6$, then the value of $\frac{27\,\mathrm{cosec}^6\theta+8\sec^6\theta}{16\sec^8\theta}$ is

1. A.$\frac{1}{5}$
2. B.$\frac{3}{5}$
3. C.$\frac{2}{5}$✓
4. D.$\frac{3}{4}$

Correct answer: C

Consider the sets $A=\{(x, y)\in\mathbf{R}\times\mathbf{R}: x^2+y^2=25\}$, $B=\{(x, y)\in\mathbf{R}\times\mathbf{R}: x^2+9y^2=144\}$, $C=\{(x, y)\in\mathbf{Z}\times\mathbf{Z}: x^2+y^2\le4\}$ and $D=A\cap B$. The total number of one-one functions from the set D to the set C is:

1. A.15120
2. B.18290
3. C.19320
4. D.17160✓

Correct answer: D

Let $f:[0, \infty)\to\mathbf{R}$ be a differentiable function such that $f(x)=1-2x+\int_0^xe^{x-t}f(t)\,dt$ for all $x\in[0, \infty)$. Then the area of the region bounded by $y=f(x)$ and the coordinate axes is

1. A.2
2. B.$\frac{1}{2}$✓
3. C.$\sqrt{2}$
4. D.$\sqrt{5}$

Correct answer: B

Let $f:\mathbf{R}\to\mathbf{R}$ be a continuous function satisfying $f(0)=1$ and $f(2x)-f(x)=x$ for all $x\in\mathbf{R}$. If $\lim_{n\to\infty}\left\{f(x)-f\left(\frac{x}{2^n}\right)\right\}=G(x)$, then $\sum_{r=1}^{10}G(r^2)$ is equal to

1. A.420
2. B.215
3. C.385✓
4. D.540

Correct answer: C

The value of $\int_{-1}^{1}\frac{\left(1+\sqrt{|x|-x}\right)e^x+\left(\sqrt{|x|-x}\right)e^{-x}}{e^x+e^{-x}}dx$ is equal to

1. A.$1-\frac{2\sqrt{2}}{3}$
2. B.$1+\frac{2\sqrt{2}}{3}$✓
3. C.$2+\frac{2\sqrt{2}}{3}$
4. D.$3-\frac{2\sqrt{2}}{3}$

Correct answer: B

Let $f, g:(1, \infty)\to\mathbf{R}$ be defined as $f(x)=\frac{2x+3}{5x+2}$ and $g(x)=\frac{2-3x}{1-x}$. If the range of the function $f\circ g:[2, 4]\to\mathbf{R}$ is $[\alpha, \beta]$, then $\frac{1}{\beta-\alpha}$ is equal to

1. A.68
2. B.56✓
3. C.29
4. D.2

Correct answer: B

Let $A=\{z\in\mathbf{C}: |z-2-i|=3\}$, $B=\{z\in\mathbf{C}: \mathrm{Re}(z-iz)=2\}$ and $S=A\cap B$. Then $\sum_{z\in S}|z|^2$ is equal to ______.

Correct answer: 22

Let m and n be the number of points at which the function $f(x)=\max\{x, x^3, x^5, \ldots, x^{21}\}$, $x\in\mathbf{R}$, is not differentiable and not continuous, respectively. Then m + n is equal to ______.

Correct answer: 3

If the area of the region $\{(x, y): |x-5|\le y\le4\sqrt{x}\}$ is A, then 3A is equal to ______.

Correct answer: 368

Let C be the circle $x^2+(y-1)^2=2$, $E_1$ and $E_2$ be two ellipses whose centres lie at the origin and major axes lie on x-axis and y-axis respectively. Let the straight line $x+y=3$ touch the curves C, $E_1$ and $E_2$ at P($x_1$, $y_1$), Q($x_2$, $y_2$) and R($x_3$, $y_3$) respectively. Given that P is the mid point of the line segment QR and $PQ=\frac{2\sqrt{2}}{3}$, the value of $9(x_1y_1+x_2y_2+x_3y_3)$ is equal to ______.

Correct answer: 46

Let $A=\begin{bmatrix}\cos\theta & 0 & -\sin\theta\\ 0 & 1 & 0\\ \sin\theta & 0 & \cos\theta\end{bmatrix}$. If for some $\theta\in(0, \pi)$, $A^2=A^T$, then the sum of the diagonal elements of the matrix $(A+I)^3+(A-I)^3-6A$ is equal to ______.

Correct answer: 6

In an experiment with a closed organ pipe, it is filled with water by $\left(\frac{1}{5}\right)$th of its volume. The frequency of the fundamental note will change by

1. A.25%✓
2. B.−20%
3. C.−25%
4. D.20%

Correct answer: A

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: In photoelectric effect, on increasing the intensity of incident light the stopping potential increases. Reason R: Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than threshold frequency. In the light of the above statements, choose the correct answer from the options given below

1. A.A is true but R is false
2. B.Both A and R are true but R is NOT the correct explanation of A
3. C.Both A and R are true and R is the correct explanation of A
4. D.A is false but R is true✓

Correct answer: D

Two infinite identical charged sheets and a charged spherical body of charge density '$\rho$' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is:

1. A.$\vec{E}_A>\vec{E}_B$; $\vec{E}_C=\vec{E}_D$
2. B.$\vec{E}_C\neq\vec{E}_D$; $\vec{E}_A>\vec{E}_B$✓
3. C.$|\vec{E}_A|=|\vec{E}_B|$; $\vec{E}_C>\vec{E}_D$
4. D.$\vec{E}_A=\vec{E}_B$; $\vec{E}_C=\vec{E}_D$

Correct answer: B

The Boolean expression $Y=A\bar{B}C+\bar{A}\bar{C}$ can be realised with which of the following gate configurations. A. One 3-input AND gate, 3 NOT gates and one 2-input OR gate, One 2-input AND gate, B. One 3-input AND gate, 1 NOT gate, One 2-input NOR gate and one 2-input OR gate C. 3-input OR gate, 3 NOT gates and one 2-input AND gate. Choose the correct answer from the options given below:

1. A.A, C Only
2. B.A, B Only✓
3. C.A, B, C Only
4. D.B, C Only

Correct answer: B

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

1. A.$\frac{100}{\sqrt{2}}$A, 100 Hz
2. B.$100\sqrt{2}$A, 100 Hz
3. C.100 A, 50 Hz✓
4. D.$50\sqrt{2}$A, 50 Hz

Correct answer: C

When an object is placed 40 cm away from a spherical mirror an image of magnification $\frac{1}{2}$ is produced. To obtain an image with magnification of $\frac{1}{3}$, the object is to be moved :

1. A.80 cm away from the mirror.
2. B.20 cm towards the mirror.
3. C.20 cm away from the mirror.
4. D.40 cm away from the mirror.✓

Correct answer: D

Current passing through a wire as function of time is given as $I(t)=0.02t+0.01$ A. The charge that will flow through the wire from t = 1 s to t = 2 s is

1. A.0.06 C
2. B.0.04 C✓
3. C.0.02 C
4. D.0.07 C

Correct answer: B

A body of mass m is suspended by two strings making angles $\theta_1$ and $\theta_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ simultaneously. $T_1$ and $T_2$ are related by $T_1=\sqrt{3}T_2$, the angles $\theta_1$ and $\theta_2$ are

1. A.$\theta_1=30^\circ$ $\theta_2=60^\circ$ with $T_2=\frac{4mg}{5}$
2. B.$\theta_1=60^\circ$ $\theta_2=30^\circ$ with $T_2=\frac{mg}{2}$✓
3. C.$\theta_1=45^\circ$ $\theta_2=45^\circ$ with $T_2=\frac{3mg}{4}$
4. D.$\theta_1=30^\circ$ $\theta_2=60^\circ$ with $T_2=\frac{3mg}{4}$

Correct answer: B

The mean free path and the average speed of oxygen molecules at 300K and 1 atm are $3\times10^{-7}$ m and 600 m/s, respectively. Find the frequency of its collisions.

1. A.$2\times10^{10}$ /s
2. B.$9\times10^5$ /s
3. C.$2\times10^9$ /s✓
4. D.$5\times10^8$ /s

Correct answer: C

A small mirror of mass m is suspended by a massless thread of length $l$. Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror (c = speed of light in vacuum and g = acceleration due to gravity)

1. A.$\theta=\frac{E}{mc\sqrt{gl}}$
2. B.$\theta=\frac{E}{2mc\sqrt{gl}}$
3. C.$\theta=\frac{3E}{4mc\sqrt{gl}}$
4. D.$\theta=\frac{2E}{mc\sqrt{gl}}$✓

Correct answer: D

Two small spherical balls of mass 10g each with charges $-2\mu C$ and $2\mu C$, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charge sheet with uniform charge density of $100\mu C/m^2$ such that length of rod makes an angle of 30° with electric field generated by charge sheet. Net torque acting on the rod is: (Take $\epsilon_0$ : $8.85\times10^{-12}\ C^2/Nm^2$)

1. A.11.2 Nm
2. B.1.12 Nm✓
3. C.112 Nm
4. D.2.24 Nm

Correct answer: B

Consider the sound wave travelling in ideal gases of He, $CH_4$, and $CO_2$. All the gases have the same ratio $\frac{P}{\rho}$, where P is the pressure and $\rho$ is the density. The ratio of the speed of sound through the gases $v_{He}:v_{CH_4}:v_{CO_2}$ is given by

1. A.$\sqrt{\frac{4}{3}}:\sqrt{\frac{5}{3}}:\sqrt{\frac{7}{5}}$
2. B.$\sqrt{\frac{5}{3}}:\sqrt{\frac{4}{3}}:\sqrt{\frac{4}{3}}$✓
3. C.$\sqrt{\frac{5}{3}}:\sqrt{\frac{4}{3}}:\sqrt{\frac{7}{5}}$
4. D.$\sqrt{\frac{7}{5}}:\sqrt{\frac{5}{3}}:\sqrt{\frac{4}{3}}$

Correct answer: B

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $\theta_1$ and $\theta_2$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

1. A.$\theta_1l_2^2=\theta_2l_1^2$
2. B.$\theta_1l_2=\theta_2l_1$✓
3. C.$\theta_1l_1=\theta_2l_2$
4. D.$\theta_1l_1^2=\theta_2l_2^2$

Correct answer: B

Two liquids A and B have $\theta_A$ and $\theta_B$ as contact angles in a capillary tube. If $K=\cos\theta_A/\cos\theta_B$, then identify the correct statement:

1. A.K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.
2. B.K is negative, then liquid A has concave meniscus and liquid B has convex meniscus.✓
3. C.K is negative, then liquid A and liquid B have convex meniscus.
4. D.K is negative, then liquid A and liquid B have concave meniscus.

Correct answer: B

Considering the Bohr model of hydrogen like atoms, the ratio of the radius of $5^{th}$ orbit of the electron in $Li^{2+}$ and $He^+$ is

1. A.$\frac{4}{9}$
2. B.$\frac{9}{4}$
3. C.$\frac{2}{3}$✓
4. D.$\frac{3}{2}$

Correct answer: C

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The kinetic energy needed to project a body of mass m from earth surface to infinity is $\frac{1}{2}$mgR, where R is the radius of earth. Reason R: The maximum potential energy of a body is zero when it is projected to infinity from earth surface. In the light of the above statements, choose the correct answer from the options given below

1. A.Both A and R are true but R is NOT the correct explanation of A
2. B.Both A and R are true and R is the correct explanation of A
3. C.A is true but R is false
4. D.A is false but R is true✓

Correct answer: D

In a Young's double slit experiment, the slits are separated by 0.2 mm. If the slits separation is increased to 0.4 mm, the percentage change of the fringe width is :

1. A.25%
2. B.0%
3. C.100%
4. D.50%✓

Correct answer: D

If $\vec{L}$ and $\vec{P}$ represent the angular momentum and linear momentum respectively of a particle of mass 'm' having position vector as $\vec{r}=a(\hat{i}\cos\omega t+\hat{j}\sin\omega t)$. The direction of force is

1. A.Opposite to the direction of $\vec{r}$✓
2. B.Opposite to the direction of $\vec{L}$
3. C.Opposite to the direction of $\vec{P}$
4. D.Opposite to the direction of $\vec{L}\times\vec{P}$

Correct answer: A

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^PL^QT^RA^S$, where value of 'Q' and 'R' are

1. A.(−2, 2)
2. B.(3, −5)
3. C.(1, −1)✓
4. D.(−2, 1)

Correct answer: C

Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of $\frac{1}{\sqrt{2}}$ Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm/s, induced emf between points A and E is ______ mV.

Correct answer: 10

Four capacitors each of capacitance 16$\mu F$ are connected as shown in the figure. The capacitance between points A and B is : ______ (in $\mu F$).

Correct answer: 64

Two slabs with square cross section of different materials (1, 2) with equal sides ($l$) and thickness $d_1$ and $d_2$ such that $d_2=2d_1$ and $l>d_2$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is $\theta_2=2\theta_1$. If the shear moduli of material 1 is $4\times10^9\ N/m^2$, then shear moduli of material 2 is $x\times10^9\ N/m^2$, where value of x is ______.

Correct answer: 1

Distance between object and its image (magnified by $-\frac{1}{3}$) is 30 cm. The focal length of the mirror used is $\left(\frac{x}{4}\right)$ cm, where magnitude of value of x is ______

Correct answer: 45

The major product (A) formed in the following reaction sequence is Nitrobenzene $\xrightarrow{\text{(i) Sn, HCl; (ii) } Ac_2O, \text{Pyridine; (iii) } Br_2, \text{AcOH; (iv) NaOH (aq)}}$ A

1. A.2,4-Dibromoaniline
2. B.3-Bromoaniline
3. C.4-Bromoaniline✓
4. D.2,4,6-Tribromoaniline

Correct answer: C

Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect? (Bohr\'s radius is represented by $a_0$)

1. A.The electron can be found at a distance $2a_0$ from the nucleus
2. B.The probability density of finding the electron is maximum at the nucleus
3. C.The total energy of the electron is maximum when it is at a distance $a_0$ from the nucleus✓
4. D.The 1s orbital is spherically symmetrical

Correct answer: C

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

1. A.$NH_2-CH_2-COOH$ and $NH_2-CH(CH_3)-COCl$
2. B.$NH_2-CH_2-COCl$ and $\overset{+}{N}H_3-CH(CH_3)-COCl$
3. C.$NH_2-CH_2-COOH$ and $NH_2-CH(CH_3)-COOH$
4. D.$NH_2-CH_2-COCl$ and $NH_2-CH(CH_3)-COOH$✓

Correct answer: D

XY is the membrane/partition between two chambers 1 and 2 containing sugar solutions of concentration $c_1$ and $c_2$ ($c_1>c_2$) mol $L^{-1}$. For the reverse osmosis to take place identify the correct condition. (Here $p_1$ and $p_2$ are pressures applied on chamber 1 and 2). A. Membrane/Partition : Cellophane, $p_1>\pi$ B. Membrane/Partition : Porous, $p_2>\pi$ C. Membrane/Partition : Parchment paper, $p_1>\pi$ D. Membrane/Partition : Cellophane, $p_2>\pi$. Choose the correct answer from the option given below:

1. A.C Only
2. B.A and C Only✓
3. C.B and D Only
4. D.A and D Only

Correct answer: B

Given below are the pairs of group 13 elements showing their relation in terms of atomic radius. (B < Al), (Al < Ga), (Ga < In) and (In < Tl). Identify the elements present in the incorrect pair and in that pair find out the element (X) that has higher ionic radius ($M^{3+}$) than the other one. The atomic number of the element (X) is

1. A.81
2. B.49
3. C.13
4. D.31✓

Correct answer: D

Benzene is treated with oleum to produce compound (X) which when further heated with molten sodium hydroxide followed by acidification produces compound (Y). The compound Y is treated with zinc metal to produce compound (Z). Identify the structure of compound (Z) from the following option.

1. A.Hydroquinone (1,4-dihydroxybenzene)
2. B.Catechol (1,2-dihydroxybenzene)
3. C.Phenol
4. D.Benzene✓

Correct answer: D

Given below are two statements. Statement I: The dipole moment of $\overset{4}{C}H_3-\overset{3}{C}H=\overset{2}{C}H-\overset{1}{C}H=O$ is greater than $\overset{4}{C}H_3-\overset{3}{C}H_2-\overset{2}{C}H_2-\overset{1}{C}H=O$. Statement II: $C_1-C_2$ bond length of $CH_3-CH=CH-CH=O$ is greater than $C_1-C_2$ bond length of $CH_3-CH_2-CH_2-CH=O$. In the light of the above statements, choose the correct answer from the options given below:

1. A.Both Statement I and Statement II are true
2. B.Statement I is false but Statement II is true
3. C.Both Statement I and Statement II are false
4. D.Statement I is true but Statement II is false✓

Correct answer: D

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

1. A.$Ti^{2+}$, $Co^{2+}$
2. B.$Ti^{3+}$, $Mn^{2+}$
3. C.$V^{2+}$, $Co^{2+}$✓
4. D.$Fe^{3+}$, $Cr^{2+}$

Correct answer: C

Given below are two statements: Statement I: Nitrogen forms oxides with +1 to +5 oxidation states due to the formation of p$\pi$ - p$\pi$ bond with oxygen. Statement II: Nitrogen does not form halides with +5 oxidation state due to the absence of d-orbital in it. In the light of given statements, choose the correct answer from the options given below.

1. A.Both Statement I and Statement II are False
2. B.Statement I is true but Statement II is false
3. C.Statement I is false but Statement II are true
4. D.Both Statement I and Statement II are true✓

Correct answer: D

Number of stereoisomers possible for the complexes, $[CrCl_3(py)_3]$ and $[CrCl_2(ox)_2]^{3-}$ are respectively (py = pyridine, ox = oxalate)

1. A.2 & 2
2. B.1 & 2
3. C.2 & 3✓
4. D.3 & 3

Correct answer: C

Which of the following molecule(s) show/s paramagnetic behavior? A. $O_2$ B. $N_2$ C. $F_2$ D. $S_2$ E. $Cl_2$. Choose the correct answer from the options given below:

1. A.A & E Only
2. B.A & C only
3. C.B Only
4. D.A & D Only✓

Correct answer: D

One mole of an ideal gas expands isothermally and reversibly from 10 $dm^3$ to 20 $dm^3$ at 300 K. ΔU, q and work done in the process respectively are Given: R = 8.3 J $K^{-1}$ $mol^{-1}$, ln 10 = 2.3, log 2 = 0.30, log 3 = 0.48

1. A.0, 1.718 kJ, −1.718 kJ✓
2. B.0, −17.18 kJ, 1.718 J
3. C.0, 21.84 kJ, 21.84 kJ
4. D.0, 21.84 kJ, −1.726 J

Correct answer: A

Let us consider a reversible reaction at temperature, T. In this reaction, both ΔH and ΔS were observed to have positive values. If the equilibrium temperature is Te, then the reaction becomes spontaneous at:

1. A.T = Te
2. B.Te = 5T
3. C.Te > T
4. D.T > Te✓

Correct answer: D

For $A_2+B_2\rightleftharpoons2AB$, $E_a$ for forward and backward reaction are 180 and 200 kJ $mol^{-1}$ respectively. If catalyst lowers $E_a$ for both reaction by 100 kJ $mol^{-1}$. Which of the following statement is correct?

1. A.The enthalpy change for the catalysed reaction is different from that of uncatalysed reaction.
2. B.The enthalpy change for the reaction is +20 kJ $mol^{-1}$.
3. C.Catalyst does not alter the Gibbs energy change of a reaction.✓
4. D.Catalyst can cause non-spontaneous reactions to occur.

Correct answer: C

Predict the major product of the following reaction sequence:- Methylcyclohexane $\xrightarrow{\text{(1) } Br_2/h\nu;\ \text{(2) Alcoholic KOH, }\Delta;\ \text{(3) H–Br/R–O–O–R, }h\nu}$ ?

1. A.Bromocycloheptane
2. B.1-Bromo-2-methylcyclohexane✓
3. C.(Bromomethyl)cyclohexane
4. D.1-Bromo-1-methylcyclohexane

Correct answer: B

On charging the lead storage battery, the oxidation state of lead changes from $x_1$ to $y_1$ at the anode and from $x_2$ to $y_2$ at the cathode. The values of $x_1, y_1, x_2, y_2$ are respectively :

1. A.0, +2, +4, +2
2. B.+4, +2, 0, +2
3. C.+2, 0, +2, +4✓
4. D.+2, 0, 0, +4

Correct answer: C

An organic compound (X) with molecular formula $C_3H_6O$ is not readily oxidised. On reduction it gives $C_3H_8O$(Y) which reacts with HBr to give a bromide (Z) which is converted to Grignard reagent. This Grignard reagent on reaction with (X) followed by hydrolysis give 2, 3-dimethylbutan-2-ol. Compounds (X), (Y) and (Z) respectively are:

1. A.$CH_3COCH_3$, $CH_3CH(OH)CH_3$, $CH_3CH(Br)CH_3$✓
2. B.$CH_3CH_2CHO$, $CH_3CH_2CH_2OH$, $CH_3CH_2CH_2Br$
3. C.$CH_3CH_2CHO$, $CH_3CH=CH_2$, $CH_3CH(Br)CH_3$
4. D.$CH_3COCH_3$, $CH_3CH_2CH_2OH$, $CH_3CH(Br)CH_3$

Correct answer: A

Aldol condensation is a popular and classical method to prepare $\alpha,\beta$-unsaturated carbonyl compounds. This reaction can be both intermolecular and intramolecular. Predict which one of the following is not a product of intramolecular aldol condensation?

1. A.2-Methylene-1-tetralone (exocyclic C=CH2 alpha to the ketone of 1-tetralone)✓
2. B.Cyclohex-2-en-1-one
3. C.Bicyclic enone: octahydronaphthalenone with the C=C at the ring fusion (Δ1,9-octalin-2-one type)
4. D.Inden-1-one (benzo-fused cyclopentenone)

Correct answer: A

Which one of the following complexes will have $\Delta_o=0$ and $\mu$ = 5.96 B.M?

1. A.$[FeF_6]^{4-}$
2. B.$[Fe(CN)_6]^{4-}$
3. C.$[Mn(SCN)_6]^{4-}$✓
4. D.$[Co(NH_3)_6]^{3+}$

Correct answer: C

Rate law for a reaction between A and B is given by $r=k[A]^n[B]^m$. If concentration of A is doubled and concentration of B is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction $\left(\frac{r_2}{r_1}\right)$ is

1. A.$\frac{1}{2^{m+n}}$
2. B.(n − m)
3. C.$2^{(n-m)}$✓
4. D.(m + n)