JEE Main 2025 — 22 Jan Shift 1 (Previous Year Paper)

The area of the region, inside the circle $(x-2\sqrt{3})^2+y^2=12$ and outside the parabola $y^2=2\sqrt{3}x$ is :

1. A.$6\pi-16$✓
2. B.$3\pi-8$
3. C.$3\pi+8$
4. D.$6\pi-8$

Correct answer: A

Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive terms. If $a_1a_5=28$ and $a_2+a_4=29$, then $a_6$ is equal to :

1. A.526
2. B.812
3. C.628
4. D.784✓

Correct answer: D

If $\sum_{r=1}^{n} T_r=\frac{(2n-1)(2n+1)(2n+3)(2n+5)}{64}$, then $\lim_{n\to\infty}\sum_{r=1}^{n}\left(\frac{1}{T_r}\right)$ is equal to :

1. A.1
2. B.$\frac{1}{3}$
3. C.0
4. D.$\frac{2}{3}$✓

Correct answer: D

A coin is tossed three times. Let X denote the number of times a tail follows a head. If $\mu$ and $\sigma^2$ denote the mean and variance of X, then the value of $64(\mu+\sigma^2)$ is :

1. A.32
2. B.64
3. C.51
4. D.48✓

Correct answer: D

The number of non-empty equivalence relations on the set $\{1, 2, 3\}$ is :

1. A.6
2. B.7
3. C.5✓
4. D.4

Correct answer: C

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point (2, 5) and intersects the circle C at exactly two points. If the set of all possible values of r is the interval $(\alpha, \beta)$, then $3\beta-2\alpha$ is equal to :

1. A.14
2. B.15✓
3. C.12
4. D.10

Correct answer: B

Let $z_1, z_2$ and $z_3$ be three complex numbers on the circle $|z|=1$ with $\arg(z_1)=\frac{-\pi}{4}$, $\arg(z_2)=0$ and $\arg(z_3)=\frac{\pi}{4}$. If $|z_1\bar{z}_2+z_2\bar{z}_3+z_3\bar{z}_1|^2=\alpha+\beta\sqrt{2}$, $\alpha,\beta\in\mathbf{Z}$, then the value of $\alpha^2+\beta^2$ is :

1. A.24
2. B.29✓
3. C.31
4. D.41

Correct answer: B

Let $L_1:\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $L_2:\frac{x-2}{3}=\frac{y-4}{4}=\frac{z-5}{5}$ be two lines. Then which of the following points lies on the line of the shortest distance between $L_1$ and $L_2$ ?

1. A.$\left(2, 3, \frac{1}{3}\right)$
2. B.$\left(-\frac{5}{3}, -7, 1\right)$
3. C.$\left(\frac{14}{3}, -3, \frac{22}{3}\right)$✓
4. D.$\left(\frac{8}{3}, -1, \frac{1}{3}\right)$

Correct answer: C

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is 'M', is :

1. A.4356
2. B.14950
3. C.5148✓
4. D.6084

Correct answer: C

Let $A=\{1, 2, 3, \ldots, 10\}$ and $B=\left\{\frac{m}{n}: m, n\in A, m<n \text{ and } \gcd(m, n)=1\right\}$. Then $n(B)$ is equal to :

1. A.29
2. B.36
3. C.31✓
4. D.37

Correct answer: C

The product of all solutions of the equation $e^{5(\log_e x)^2+3}=x^8$, $x>0$, is :

1. A.$e$
2. B.$e^2$
3. C.$e^{8/5}$✓
4. D.$e^{6/5}$

Correct answer: C

Let $f(x)$ be a real differentiable function such that $f(0)=1$ and $f(x+y)=f(x)f'(y)+f'(x)f(y)$ for all $x, y\in\mathbf{R}$. Then $\sum_{n=1}^{100}\log_e f(n)$ is equal to :

1. A.2525✓
2. B.2406
3. C.5220
4. D.2384

Correct answer: A

Let for $f(x)=7\tan^8x+7\tan^6x-3\tan^4x-3\tan^2x$, $I_1=\int_0^{\pi/4}f(x)\,dx$ and $I_2=\int_0^{\pi/4}x f(x)\,dx$. Then $7I_1+12I_2$ is equal to :

1. A.2
2. B.$\pi$
3. C.1✓
4. D.$2\pi$

Correct answer: C

Let $f:\mathbf{R}\to\mathbf{R}$ be a twice differentiable function such that $f(x+y)=f(x)f(y)$ for all $x, y\in\mathbf{R}$. If $f'(0)=4a$ and $f$ satisfies $f''(x)-3af'(x)-f(x)=0$, $a>0$, then the area of the region $R=\{(x, y)\,|\,0\le y\le f(ax), 0\le x\le 2\}$ is :

1. A.$e^4-1$
2. B.$e^4+1$
3. C.$e^2+1$
4. D.$e^2-1$✓

Correct answer: D

Let $x=x(y)$ be the solution of the differential equation $y^2dx+\left(x-\frac{1}{y}\right)dy=0$. If $x(1)=1$, then $x\left(\frac{1}{2}\right)$ is :

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

Correct answer: B

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is $\frac{m}{n}$, where $\gcd(m, n)=1$, then $m+n$ is equal to :

1. A.14✓
2. B.4
3. C.13
4. D.11

Correct answer: A

Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of $16\left((\sec^{-1}x)^2+(\mathrm{cosec}^{-1}x)^2\right)$ is :

1. A.$31\pi^2$
2. B.$24\pi^2$
3. C.$22\pi^2$✓
4. D.$18\pi^2$

Correct answer: C

Let the parabola $y=x^2+px-3$, meet the coordinate axes at the points P, Q and R. If the circle C with centre at $(-1, -1)$ passes through the points P, Q and R, then the area of $\triangle PQR$ is :

1. A.7
2. B.6✓
3. C.5
4. D.4

Correct answer: B

Let the triangle PQR be the image of the triangle with vertices (1, 3), (3, 1) and (2, 4) in the line $x+2y=2$. If the centroid of $\triangle PQR$ is the point $(\alpha, \beta)$, then $15(\alpha-\beta)$ is equal to :

1. A.19
2. B.21
3. C.22✓
4. D.24

Correct answer: C

Let the foci of a hyperbola be (1, 14) and (1, $-12$). If it passes through the point (1, 6), then the length of its latus-rectum is :

1. A.$\frac{144}{5}$
2. B.$\frac{24}{5}$
3. C.$\frac{25}{6}$
4. D.$\frac{288}{5}$✓

Correct answer: D

Let the function, $f(x)=\begin{cases}-3ax^2-2, & x<1\\ a^2+bx, & x\ge1\end{cases}$ be differentiable for all $x\in\mathbf{R}$, where $a>1$, $b\in\mathbf{R}$. If the area of the region enclosed by $y=f(x)$ and the line $y=-20$ is $\alpha+\beta\sqrt{3}$, $\alpha, \beta\in\mathbf{Z}$, then the value of $\alpha+\beta$ is ______.

Correct answer: 34

If $\sum_{r=0}^{5}\frac{{}^{11}C_{2r+1}}{2r+2}=\frac{m}{n}$, $\gcd(m, n)=1$, then $m-n$ is equal to ______.

Correct answer: 2035

Let $\vec{c}$ be the projection vector of $\vec{b}=\lambda\hat{i}+4\hat{k}$, $\lambda>0$, on the vector $\vec{a}=\hat{i}+2\hat{j}+2\hat{k}$. If $|\vec{a}+\vec{c}|=7$, then the area of the parallelogram formed by the vectors $\vec{b}$ and $\vec{c}$ is ______.

Correct answer: 16

Let A be a square matrix of order 3 such that $\det(A)=-2$ and $\det(3\,\mathrm{adj}(-6\,\mathrm{adj}(3A)))=2^{m+n}\cdot3^{mn}$, $m>n$. Then $4m+2n$ is equal to ______.

Correct answer: 34

Let $L_1:\frac{x-1}{3}=\frac{y-1}{-1}=\frac{z+1}{0}$ and $L_2:\frac{x-2}{2}=\frac{y}{0}=\frac{z+4}{\alpha}$, $\alpha\in\mathbf{R}$, be two lines, which intersect at the point B. If P is the foot of perpendicular from the point A(1, 1, $-1$) on $L_2$, then the value of $26\alpha(PB)^2$ is ______.

Correct answer: 216

A line charge of length $\frac{a}{2}$ is kept at the center of an edge BC of a cube ABCDEFGH having edge length 'a' as shown in the figure. If the density of line charge is $\lambda$ C per unit length, then the total electric flux through all the faces of the cube will be ______. (Take, $\epsilon_0$ as the free space permittivity)

1. A.$\frac{\lambda a}{16\epsilon_0}$
2. B.$\frac{\lambda a}{8\epsilon_0}$✓
3. C.$\frac{\lambda a}{4\epsilon_0}$
4. D.$\frac{\lambda a}{2\epsilon_0}$

Correct answer: B

An amount of ice of mass $10^{-3}$ kg and temperature $-10^\circ$C is transformed to vapour of temperature $110^\circ$C by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice $=2100\ \mathrm{J\,kg^{-1}K^{-1}}$, specific heat of water $=4180\ \mathrm{J\,kg^{-1}K^{-1}}$, specific heat of steam $=1920\ \mathrm{J\,kg^{-1}K^{-1}}$, Latent heat of ice $=3.35\times10^5\ \mathrm{J\,kg^{-1}}$ and Latent heat of steam $=2.25\times10^6\ \mathrm{J\,kg^{-1}}$)

1. A.3043 J✓
2. B.3022 J
3. C.3024 J
4. D.3003 J

Correct answer: A

Given below are two statements : Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. 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 false
2. B.Both Statement I and Statement II are true
3. C.Statement I is false but Statement II is true
4. D.Statement I is true but Statement II is false✓

Correct answer: D

A parallel-plate capacitor of capacitance $40\,\mu$F is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K = 2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are

1. A.4 mC and 0.2 J✓
2. B.2 mC and 0.4 J
3. C.2 mC and 0.2 J
4. D.8 mC and 2.0 J

Correct answer: A

Which of the following circuits represents a forward biased diode ? (A)–(E) as shown in the figure. Choose the correct answer from the options given below :

1. A.(A) and (D) only
2. B.(B), (D) and (E) only
3. C.(C) and (E) only
4. D.(B), (C) and (E) only✓

Correct answer: D

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer. Reason (R) : The speed of light reduces in an optically denser medium than air while its frequency does not change. In the light of the above statements, choose the most appropriate 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.(A) is false but (R) is true
4. D.Both (A) and (R) are true and (R) is the correct explanation of (A)✓

Correct answer: D

If B is magnetic field and $\mu_0$ is permeability of free space, then the dimensions of $(B/\mu_0)$ is

1. A.$LT^{-2}A^{-1}$
2. B.$ML^2T^{-2}A^{-1}$
3. C.$MT^{-2}A^{-1}$
4. D.$L^{-1}A$✓

Correct answer: D

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance $R_p=1\,\Omega$ as shown in the figure. An external resistance of $R_e=2\,\Omega$ is connected via the sliding contact. The electric current in the circuit is :

1. A.1.35 A
2. B.0.9 A
3. C.0.3 A
4. D.1.0 A✓

Correct answer: D

The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV, respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of

1. A.Cs only✓
2. B.Both Cs and Li
3. C.Neither Cs nor Li
4. D.Li only

Correct answer: A

An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity $10^6$ m/s. If the magnitude of the electric field between the plates is 9.1 V/cm, then the vertical component of velocity of electron is (mass of electron $=9.1\times10^{-31}$ kg and charge of electron $=1.6\times10^{-19}$ C)

1. A.$1\times10^6$ m/s
2. B.$16\times10^4$ m/s
3. C.$16\times10^6$ m/s✓
4. D.0

Correct answer: C

A bob of mass m is suspended at a point O by a light string of length $l$ and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity $v_0$ at the point 'A', the string becomes slack when, the bob reaches at the point 'D'. The ratio of the kinetic energy of the bob at the points B and C is ______.

1. A.3
2. B.4
3. C.1
4. D.2✓

Correct answer: D

In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to $|R_1|$ and $|R_2|$, i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is

1. A.$\frac{1}{6}\left(\frac{1}{|R_1|}+\frac{1}{|R_2|}\right)$
2. B.$-\frac{1}{6}\left(\frac{1}{|R_1|}+\frac{1}{|R_2|}\right)$
3. C.$\frac{1}{6}\left(\frac{1}{|R_1|}-\frac{1}{|R_2|}\right)$
4. D.$-\frac{1}{6}\left(\frac{1}{|R_1|}-\frac{1}{|R_2|}\right)$✓

Correct answer: D

A small point of mass m is placed at a distance 2R from the centre 'O' of a big uniform solid sphere of mass M and radius R. The gravitational force on 'm' due to M is $F_1$. A spherical part of radius R/3 is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be $F_2$. The value of ratio $F_1:F_2$ is

1. A.12 : 11✓
2. B.16 : 9
3. C.11 : 10
4. D.12 : 9

Correct answer: A

Given below are two statements : Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs. Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries. In the light of the above statements, choose the correct answer from the options given below.

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

Correct answer: A

Which of the following resistivity ($\rho$) v/s temperature (T) curves is most suitable to be used in wire bound standard resistors ?

1. A.Graph: $\rho$ starts near zero and rises steeply (upward-curving) with T
2. B.Graph: $\rho$ decreases linearly with T
3. C.Graph: $\rho$ is large and almost constant, rising only very slightly with T✓
4. D.Graph: $\rho$ falls steeply and then flattens (decreasing curve) with T

Correct answer: C

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities $\rho_1$ and $\rho_2$, respectively. The frequency of $9^{th}$ harmonic of closed tube is identical with $4^{th}$ harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is $\rho_1:\rho_2=1:16$, then the length of the open tube is :

1. A.$\frac{20}{7}$ cm
2. B.$\frac{15}{7}$ cm
3. C.$\frac{20}{9}$ cm✓
4. D.$\frac{15}{9}$ cm

Correct answer: C

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K. If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

1. A.64 E
2. B.E✓
3. C.256 E
4. D.16 E

Correct answer: B

An electron in the ground state of the hydrogen atom has the orbital radius of $5.3\times10^{-11}$ m while that for the electron in third excited state is $8.48\times10^{-10}$ m. The ratio of the de Broglie wavelengths of electron in the ground state to that in the excited state is

1. A.16
2. B.3
3. C.4✓
4. D.9

Correct answer: C

A uniform circular disc of radius 'R' and mass 'M' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2 is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.

1. A.$\frac{9}{32}MR^2$
2. B.$\frac{17}{32}MR^2$
3. C.$\frac{13}{32}MR^2$✓
4. D.$\frac{7}{32}MR^2$

Correct answer: C

Given is a thin convex lens of glass (refractive index $\mu$) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself ?

1. A.$R/\mu$
2. B.$\mu R$
3. C.$R/(2\mu-3)$
4. D.$R/(2\mu-1)$✓

Correct answer: D

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature R = 2 m. Another car approaches him from behind with a uniform speed of 90 km/hr. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is 'a'. The value of 100a is ______ $m/s^2$.

Correct answer: 8

Two soap bubbles of radius 2 cm and 4 cm, respectively, are in contact with each other. The radius of curvature of the common surface, in cm, is ______.

Correct answer: 4

A particle is projected at an angle of 30° from horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is $h_0$ and height traversed in the last second, before it reaches the maximum height, is $h_1$. The ratio $h_0:h_1$ is ______. [Take, g = 10 $m/s^2$]

Correct answer: 5

The position vectors of two 1 kg particles, (A) and (B), are given by $\vec{r}_A=(\alpha_1t^2\hat{i}+\alpha_2t\hat{j}+\alpha_3t\hat{k})$ m and $\vec{r}_B=(\beta_1t\hat{i}+\beta_2t^2\hat{j}+\beta_3t\hat{k})$ m, respectively; ($\alpha_1=1\ m/s^2$, $\alpha_2=3n$ m/s, $\alpha_3=2$ m/s, $\beta_1=2$ m/s, $\beta_2=-1\ m/s^2$, $\beta_3=4p$ m/s), where t is time, n and p are constants. At t = 1 s, $|\vec{V}_A|=|\vec{V}_B|$ and velocities $\vec{V}_A$ and $\vec{V}_B$ of the particles are orthogonal to each other. At t = 1 s, the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is $\sqrt{L}$ $kgm^2s^{-1}$. The value of L is ______.

Correct answer: 90

Three conductors of same length having thermal conductivity $k_1$, $k_2$ and $k_3$ are connected as shown in figure. Area of cross sections of $1^{st}$ and $2^{nd}$ conductor are same and for $3^{rd}$ conductor it is double of the $1^{st}$ conductor. The temperatures are given in the figure. In steady state condition, the value of $\theta$ is ______ °C. (Given : $k_1=60\ Js^{-1}m^{-1}K^{-1}$, $k_2=120\ Js^{-1}m^{-1}K^{-1}$, $k_3=135\ Js^{-1}m^{-1}K^{-1}$)

Correct answer: 40

Match List-I with List-II. List-I: (A) $Al^{3+}<Mg^{2+}<Na^{+}<F^{-}$ (B) $B<C<O<N$ (C) $B<Al<Mg<K$ (D) $Si<P<S<Cl$. List-II: (I) Ionisation Enthalpy (II) Metallic character (III) Electronegativity (IV) Ionic radii. Choose the correct answer from the options given below :

1. A.(A)-(IV), (B)-(I), (C)-(III), (D)-(II)
2. B.(A)-(II), (B)-(III), (C)-(IV), (D)-(I)
3. C.(A)-(III), (B)-(IV), (C)-(II), (D)-(I)
4. D.(A)-(IV), (B)-(I), (C)-(II), (D)-(III)✓

Correct answer: D

The incorrect statements regarding geometrical isomerism are : (A) Propene shows geometrical isomerism. (B) Trans isomer has identical atoms/groups on the opposite sides of the double bond. (C) Cis-but-2-ene has higher dipole moment than trans-but-2-ene. (D) 2-methylbut-2-ene shows two geometrical isomers. (E) Trans-isomer has lower melting point than cis isomer. Choose the correct answer from the options given below :

1. A.(C), (D) and (E) Only
2. B.(B) and (C) Only
3. C.(A), (D) and (E) Only✓
4. D.(A) and (E) Only

Correct answer: C

Which of the following statement is not true for radioactive decay ?

1. A.Half life is $\ln 2$ times of $\frac{1}{\text{rate constant}}$.
2. B.Amount of radioactive substance remained after three half lives is $\frac{1}{8}$th of original amount.
3. C.Decay constant increases with increase in temperature.✓
4. D.Decay constant does not depend upon temperature.

Correct answer: C

Which of the following electronegativity order is incorrect ?

1. A.Al < Mg < B < N✓
2. B.Mg < Be < B < N
3. C.Al < Si < C < N
4. D.S < Cl < O < F

Correct answer: A

The IUPAC name of the following compound is : $CH_3-CH(COOH)-CH_2-CH_2-CH(COOCH_3)-CH_3$

1. A.Methyl-6-carboxy-2,5-dimethylhexanoate.
2. B.6-Methoxycarbonyl-2,5-dimethylhexanoic acid.✓
3. C.Methyl-5-carboxy-2-methylhexanoate.
4. D.2-Carboxy-5-methoxycarbonylhexane.

Correct answer: B

Arrange the following solutions in order of their increasing boiling points. (i) $10^{-4}$ M NaCl (ii) $10^{-4}$ M Urea (iii) $10^{-3}$ M NaCl (iv) $10^{-2}$ M NaCl

1. A.(i) < (ii) < (iii) < (iv)
2. B.(ii) < (i) < (iii) < (iv)✓
3. C.(iv) < (iii) < (i) < (ii)
4. D.(ii) < (i) $\equiv$ (iii) < (iv)

Correct answer: B

Lanthanoid ions with $4f^7$ configuration are : (A) $Eu^{2+}$ (B) $Gd^{3+}$ (C) $Eu^{3+}$ (D) $Tb^{3+}$ (E) $Sm^{2+}$. Choose the correct answer from the options given below :

1. A.(A) and (B) only✓
2. B.(B) and (E) only
3. C.(A) and (D) only
4. D.(B) and (C) only

Correct answer: A

From the magnetic behaviour of $[NiCl_4]^{2-}$ (paramagnetic) and $[Ni(CO)_4]$ (diamagnetic), choose the correct geometry and oxidation state.

1. A.$[NiCl_4]^{2-}$ : $Ni^{II}$, square planar; $[Ni(CO)_4]$ : Ni(0), square planar
2. B.$[NiCl_4]^{2-}$ : $Ni^{II}$, tetrahedral; $[Ni(CO)_4]$ : Ni(0), tetrahedral✓
3. C.$[NiCl_4]^{2-}$ : Ni(0), tetrahedral; $[Ni(CO)_4]$ : Ni(0), square planar
4. D.$[NiCl_4]^{2-}$ : $Ni^{II}$, tetrahedral; $[Ni(CO)_4]$ : $Ni^{II}$, square planar

Correct answer: B

A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2A. The amount of the aluminium deposited at the cathode is ______. [Given : molar mass of aluminium and chlorine are 27 g $mol^{-1}$ and 35.5 g $mol^{-1}$ respectively. Faraday constant = 96500 C $mol^{-1}$]

1. A.0.441 g
2. B.1.660 g
3. C.0.336 g✓
4. D.1.007 g

Correct answer: C

The products formed in the following reaction sequence are : Nitrobenzene $\xrightarrow{\text{(i) } Br_2, AcOH;\ \text{(ii) } Sn, HCl;\ \text{(iii) } NaNO_2, HCl, 273 K;\ \text{(iv) } C_2H_5OH}$ A + B

1. A.m-Bromophenetole (1-bromo-3-ethoxybenzene), $CH_3-COOH$
2. B.Bromobenzene, $CH_3-CHO$✓
3. C.m-Bromophenol, $CH_3-CHO$
4. D.m-Bromophenol, m-bromophenetole (1-bromo-3-ethoxybenzene)

Correct answer: B

A liquid when kept inside a thermally insulated closed vessel at 25°C was mechanically stirred from outside. What will be the correct option for the following thermodynamic parameters ?

1. A.$\Delta U=0, q<0, w>0$
2. B.$\Delta U=0, q=0, w=0$
3. C.$\Delta U>0, q=0, w>0$✓
4. D.$\Delta U<0, q=0, w>0$

Correct answer: C

Given below are two statements : Statement I : $CH_3-O-CH_2-Cl$ will undergo $S_N1$ reaction though it is a primary halide. Statement II : $CH_3-C(CH_3)_2-CH_2-Cl$ will not undergo $S_N2$ reaction very easily though it is a primary halide. In the light of the above statements, choose the most appropriate answer from the options given below :

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

Correct answer: B

How many different stereoisomers are possible for the given molecule ? $CH_3-CH(OH)-CH=CH-CH_3$

1. A.3
2. B.1
3. C.4✓
4. D.2

Correct answer: C

Which of the following electrolyte can be used to obtain $H_2S_2O_8$ by the process of electrolysis ?

1. A.Concentrated solution of sulphuric acid✓
2. B.Acidified dilute solution of sodium sulphate.
3. C.Dilute solution of sodium sulphate.
4. D.Dilute solution of sulphuric acid

Correct answer: A

A vessel at 1000 K contains $CO_2$ with a pressure of 0.5 atm. Some of $CO_2$ is converted into CO on addition of graphite. If total pressure at equilibrium is 0.8 atm, then Kp is :

1. A.0.18 atm
2. B.1.8 atm✓
3. C.0.3 atm
4. D.3 atm

Correct answer: B

The compounds which give positive Fehling's test are : (A) Benzaldehyde ($C_6H_5CHO$) (B) Acetophenone ($C_6H_5COCH_3$) (C) $HOCH_2-CO-(CHOH)_3-CH_2-OH$ (D) $CH_3-CHO$ (E) Phenylacetaldehyde ($C_6H_5CH_2CHO$). Choose the correct answer from the options given below :

1. A.(A), (C) and (D) Only
2. B.(C), (D) and (E) Only✓
3. C.(A), (D) and (E) Only
4. D.(A), (B) and (C) Only

Correct answer: B

In which of the following complexes the CFSE, $\Delta_o$ will be equal to zero ?

1. A.$K_4[Fe(CN)_6]$
2. B.$K_3[Fe(SCN)_6]$✓
3. C.$[Fe(NH_3)_6]Br_2$
4. D.$[Fe(en)_3]Cl_3$