JEE Main 2025 — 2 Apr Shift 2 (Previous Year Paper)

Given three indentical bags each containing 10 balls, whose colours are as follows : Bag I: Red 3, Blue 2, Green 5; Bag II: Red 4, Blue 3, Green 3; Bag III: Red 5, Blue 1, Green 4. A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is q, then the value of $\left(\frac{1}{p}+\frac{1}{q}\right)$ is :

1. A.7✓
2. B.6
3. C.9
4. D.8

Correct answer: A

Let (a, b) be the point of intersection of the curve $x^2=2y$ and the straight line $y-2x-6=0$ in the second quadrant. Then the integral $I=\int_a^b\frac{9x^2}{1+5^x}dx$ is equal to :

1. A.24✓
2. B.18
3. C.21
4. D.27

Correct answer: A

If the image of the point P(1, 0, 3) in the line joining the points A(4, 7, 1) and B(3, 5, 3) is Q($\alpha, \beta, \gamma$), then $\alpha+\beta+\gamma$ is equal to :

1. A.$\frac{46}{3}$✓
2. B.18
3. C.$\frac{47}{3}$
4. D.13

Correct answer: A

If $\theta\in\left[-\frac{7\pi}{6}, \frac{4\pi}{3}\right]$, then the number of solutions of $\sqrt{3}\,\mathrm{cosec}^2\theta-2(\sqrt{3}-1)\mathrm{cosec}\,\theta-4=0$, is equal to :

1. A.8
2. B.7
3. C.6✓
4. D.10

Correct answer: C

Let the point P of the focal chord PQ of the parabola $y^2=16x$ be $(1, -4)$. If the focus of the parabola divides the chord PQ in the ratio m : n, $\gcd(m, n)=1$, then $m^2+n^2$ is equal to :

1. A.10
2. B.37
3. C.17✓
4. D.26

Correct answer: C

If the system of equations $2x+\lambda y+3z=5$, $3x+2y-z=7$, $4x+5y+\mu z=9$ has infinitely many solutions, then $(\lambda^2+\mu^2)$ is equal to :

1. A.18
2. B.22
3. C.30
4. D.26✓

Correct answer: D

If the domain of the function $f(x)=\frac{1}{\sqrt{10+3x-x^2}}+\frac{1}{\sqrt{x+|x|}}$ is (a, b), then $(1+a)^2+b^2$ is equal to :

1. A.25
2. B.30
3. C.26✓
4. D.29

Correct answer: C

$4\int_0^1\left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right)dx-3\log_e(\sqrt{3})$ is equal to :

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

Correct answer: C

The line $L_1$ is parallel to the vector $\vec{a}=-3\hat{i}+2\hat{j}+4\hat{k}$ and passes through the point (7, 6, 2) and the line $L_2$ is parallel to the vector $\vec{b}=2\hat{i}+\hat{j}+3\hat{k}$ and passes through the point (5, 3, 4). The shortest distance between the lines $L_1$ and $L_2$ is :

1. A.$\frac{21}{\sqrt{38}}$
2. B.$\frac{21}{\sqrt{57}}$
3. C.$\frac{23}{\sqrt{57}}$
4. D.$\frac{23}{\sqrt{38}}$✓

Correct answer: D

The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$. Then the number of terms which are integers in the A.P. is :

1. A.4✓
2. B.8
3. C.10
4. D.6

Correct answer: A

Let $\vec{a}=2\hat{i}-3\hat{j}+\hat{k}$, $\vec{b}=3\hat{i}+2\hat{j}+5\hat{k}$ and a vector $\vec{c}$ be such that $(\vec{a}-\vec{c})\times\vec{b}=-18\hat{i}-3\hat{j}+12\hat{k}$ and $\vec{a}\cdot\vec{c}=3$. If $\vec{b}\times\vec{c}=\vec{d}$, then $|\vec{a}\cdot\vec{d}|$ is equal to :

1. A.18
2. B.15✓
3. C.12
4. D.9

Correct answer: B

Let $f:[1, \infty)\to[2, \infty)$ be a differentiable function. If $10\int_1^x f(t)dt=5xf(x)-x^5-9$ for all $x\ge1$, then the value of $f(3)$ is :

1. A.18
2. B.26
3. C.32✓
4. D.22

Correct answer: C

If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :

1. A.$\frac{3}{\sqrt{19}}$
2. B.$\frac{\sqrt{3}}{16}$
3. C.$\frac{\sqrt{5}}{7}$
4. D.$\frac{4}{\sqrt{17}}$✓

Correct answer: D

If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then $a+b+ab$ is equal to :

1. A.103✓
2. B.105
3. C.106
4. D.100

Correct answer: A

If $\lim_{x\to0}\frac{\cos(2x)+a\cos(4x)-b}{x^4}$ is finite, then (a + b) is equal to :

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

Correct answer: D

Let $A=\{1, 2, 3, \ldots, 100\}$ and R be a relation on A such that $R=\{(a, b): a=2b+1\}$. Let $(a_1, a_2), (a_2, a_3), (a_3, a_4), \ldots, (a_k, a_{k+1})$ be a sequence of k elements of R such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k, for which such a sequence exists, is equal to :

1. A.6
2. B.7
3. C.8
4. D.5✓

Correct answer: D

If $\sum_{r=0}^{10}\left(\frac{10^{r+1}-1}{10^r}\right)\cdot{}^{11}C_{r+1}=\frac{\alpha^{11}-11^{11}}{10^{10}}$, then $\alpha$ is equal to :

1. A.15
2. B.24
3. C.11
4. D.20✓

Correct answer: D

The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is :

1. A.840
2. B.5880
3. C.5760✓
4. D.960

Correct answer: C

Let the area of the triangle formed by a straight line L : $x+by+c=0$ with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of 45° with the positive x-axis, then the value of $b^2+c^2$ is :

1. A.90
2. B.97✓
3. C.93
4. D.83

Correct answer: B

Let A be a $3\times3$ real matrix such that $A^2(A-2I)-4(A-I)=O$, where I and O are the identity and null matrices, respectively. If $A^5=\alpha A^2+\beta A+\gamma I$, where $\alpha$, $\beta$, and $\gamma$ are real constants, then $\alpha+\beta+\gamma$ is equal to :

1. A.20
2. B.76
3. C.12✓
4. D.4

Correct answer: C

If the set of all $a\in\mathbf{R}-\{1\}$, for which the roots of the equation $(1-a)x^2+2(a-3)x+9=0$ are positive is $(-\infty, -\alpha]\cup[\beta, \gamma)$, then $2\alpha+\beta+\gamma$ is equal to ______.

Correct answer: 7

Let A(4, $-2$), B(1, 1) and C(9, $-3$) be the vertices of a triangle ABC. Then the maximum area of the parallelogram AFDE, formed with vertices D, E and F on the sides BC, CA and AB of the triangle ABC respectively, is ______.

Correct answer: 3

Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}+2y\sec^2x=2\sec^2x+3\tan x\cdot\sec^2x$ such that $y(0)=\frac{5}{4}$. Then $12\left(y\left(\frac{\pi}{4}\right)-e^{-2}\right)$ is equal to ______.

Correct answer: 21

If the sum of the first 10 terms of the series $\frac{4\cdot1}{1+4\cdot1^4}+\frac{4\cdot2}{1+4\cdot2^4}+\frac{4\cdot3}{1+4\cdot3^4}+\ldots$ is $\frac{m}{n}$, where $\gcd(m, n)=1$, then m + n is equal to ______.

Correct answer: 441

If $y=\cos\left(\frac{\pi}{3}+\cos^{-1}\frac{x}{2}\right)$, then $(x-y)^2+3y^2$ is equal to ______.

Correct answer: 3

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field. Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions. In the light of the above statements, choose the most appropriate answer from the options given below :

1. A.(A) is correct but (R) is not correct
2. B.Both (A) and (R) are correct and (R) is the correct explanation of (A)
3. C.(A) is not correct but (R) is correct✓
4. D.Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Correct answer: C

A solenoid having area A and length '$l$' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

1. A.$B^2Al$
2. B.$\frac{B^2Al}{2\mu_0}$
3. C.$\frac{B^2Al}{\mu_0}$
4. D.$\frac{B^2Al}{4\mu_0}$✓

Correct answer: D

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at x = 0 at t = 0 sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave ?

1. A.$y=2\sin(0.83x-3.5t)$ cm
2. B.$y=2\cos(3.35x-0.83t)$ cm
3. C.$y=2\cos(0.13x-0.5t)$ cm
4. D.$y=2\cos(0.83x-3.35t)$ cm✓

Correct answer: D

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions $T_1$ and $T_2$, respectively, are (in N) : (Take acceleration due to gravity 10 $m/s^2$)

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

Correct answer: D

An electron with mass 'm' with an initial velocity (t=0) $\vec{v}=v_0\hat{i}$ ($v_0>0$) enters a magnetic field $\vec{B}=B_0\hat{j}$. If the initial de-Broglie wavelength at t = 0 is $\lambda_0$ then its value after time 't' would be :

1. A.$\lambda_0\sqrt{1+\frac{e^2B_0^2t^2}{m^2}}$
2. B.$\lambda_0$✓
3. C.$\frac{\lambda_0}{\sqrt{1+\frac{e^2B_0^2t^2}{m^2}}}$
4. D.$\frac{\lambda_0}{\sqrt{1-\frac{e^2B_0^2t^2}{m^2}}}$

Correct answer: B

Energy released when two deuterons (${}_1H^2$) fuse to form a helium nucleus (${}_2He^4$) is : (Given : Binding energy per nucleon of ${}_1H^2$ = 1.1 MeV and binding energy per nucleon of ${}_2He^4$ = 7.0 MeV)

1. A.23.6 MeV✓
2. B.26.8 MeV
3. C.8.1 MeV
4. D.5.9 MeV

Correct answer: A

Consider a circular loop that is uniformly charged and has a radius $a\sqrt{2}$. Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy plane at the origin :

1. A.0
2. B.$a/\sqrt{2}$
3. C.$a/2$
4. D.a✓

Correct answer: D

Match List - I with List - II. List - I: (A) Heat capacity of body (B) Specific heat capacity of body (C) Latent heat (D) Thermal conductivity. List - II: (I) $J\,kg^{-1}$ (II) $J\,K^{-1}$ (III) $J\,kg^{-1}K^{-1}$ (IV) $J\,m^{-1}K^{-1}s^{-1}$. Choose the correct answer from the options given below :

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

Correct answer: D

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V. The potential difference between the points A and B (shown in the figure) is :

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

Correct answer: C

In the digital circuit shown in the figure, for the given inputs the P and Q values are :

1. A.P = 0, Q = 0✓
2. B.P = 0, Q = 1
3. C.P = 1, Q = 1
4. D.P = 1, Q = 0

Correct answer: A

Two water drops each of radius 'r' coalesce to form a bigger drop. If 'T' is the surface tension, the surface energy released in this process is :

1. A.$4\pi r^2T\left[2-2^{2/3}\right]$✓
2. B.$4\pi r^2T\left[2-2^{1/3}\right]$
3. C.$4\pi r^2T\left[\sqrt{2}-1\right]$
4. D.$4\pi r^2T\left[1+\sqrt{2}\right]$

Correct answer: A

The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in the plane of the ring is :

1. A.$\frac{3}{2}Mr^2$
2. B.$\frac{1}{2}Mr^2$
3. C.$\frac{3}{8}Mr^2$✓
4. D.$2Mr^2$

Correct answer: C

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $Li^{++}$ ion in its ground state is given by $\frac{1}{X}a_0$, where X = ______. (Where $a_0$ is the first Bohr's radius.)

1. A.9
2. B.2
3. C.3✓
4. D.1

Correct answer: C

A bi-convex lens has radius of curvature of both the surfaces same as 1/6 cm. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides ($R_1\neq R_2$), without any change in lens power then possible combination of $R_1$ and $R_2$ is :

1. A.$\frac{1}{3}$ cm and $\frac{1}{3}$ cm
2. B.$\frac{1}{6}$ cm and $\frac{1}{9}$ cm
3. C.$\frac{1}{5}$ cm and $\frac{1}{7}$ cm✓
4. D.$\frac{1}{3}$ cm and $\frac{1}{7}$ cm

Correct answer: C

Given a charge q, current I and permeability of vacuum $\mu_0$. Which of the following quantity has the dimension of momentum ?

1. A.$q^2\mu_0I$
2. B.$qI/\mu_0$
3. C.$q\mu_0/I$
4. D.$q\mu_0I$✓

Correct answer: D

If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0\epsilon_0}\right)$ is :

1. A.$L/T^2$
2. B.$T^2/L$
3. C.$L^2/T^2$✓
4. D.$T^2/L^2$

Correct answer: C

Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from $T_1$ to $T_2$ is proportional to $(T_2-T_1)$. Choose the correct answer from the options given below :

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

Correct answer: C

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm, at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :

1. A.1/3
2. B.3
3. C.2
4. D.1/2✓

Correct answer: D

A sportsman runs around a circular track of radius r such that he traverses the path ABAB. The distance travelled and displacement, respectively, are

1. A.$3\pi r$, $\pi r$
2. B.$2r$, $3\pi r$
3. C.$3\pi r$, $2r$✓
4. D.$\pi r$, $3r$

Correct answer: C

In a moving coil galvanometer, two moving coils $M_1$ and $M_2$ have the following particulars : $R_1=5\,\Omega$, $N_1=15$, $A_1=3.6\times10^{-3}\ m^2$, $B_1=0.25$ T; $R_2=7\,\Omega$, $N_2=21$, $A_2=1.8\times10^{-3}\ m^2$, $B_2=0.50$ T. Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of $M_1$ and $M_2$ ?

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

Correct answer: C

The internal energy of air in 4 m × 4 m × 3 m sized room at 1 atmospheric pressure will be ______ $\times10^6$ J. (Consider air as diatomic molecule)

Correct answer: 12

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N, the length of the string is 1.56 m. The original length of the string is ______ m.

Correct answer: 1

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of 2 $rad/s^2$. Moment of intertia of the wheel is ______ kg $m^2$. (Acceleration due to gravity = 10 $m/s^2$)

Correct answer: 1

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to 60°. The refractive index of the prism material is $\sqrt{2}$. The angle of incidence (in degrees) is ______.

Correct answer: 45

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth\'s surface. Kinetic energy of the satellite in this orbit is ______ $\times10^{10}$ J. (Mass of earth = $6\times10^{24}$ kg, Radius of earth = $6.4\times10^6$ m, Gravitational constant = $6.67\times10^{-11}\ Nm^2kg^{-2}$)

Correct answer: 3

Which of the following statements are true ? (A) The subsidiary quantum number $l$ describes the shape of the orbital occupied by the electron. (B) [a two-lobed dumbbell drawn along the x-axis] is the boundary surface diagram of the $2p_x$ orbital. (C) The + and − signs in the wave function of the $2p_x$ orbital refer to charge. (D) The wave function of $2p_x$ orbital is zero everywhere in the xy plane. Choose the correct answer from the options given below :

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

Correct answer: B

Match List - I with List - II. List - I (Purification technique): (A) Distillation (simple) (B) Fractional distillation (C) Distillation under reduced pressure (D) Steam distillation. List - II (Mixture of organic compounds): (I) Diesel + Petrol (II) Aniline + Water (III) Chloroform + Aniline (IV) Glycerol + Spent-lye. Choose the correct answer from the options given below :

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

Correct answer: B

Match List - I with List - II. List - I (Reaction): (A) $2C_6H_5X+2Na\xrightarrow{\text{Dry ether}}C_6H_5-C_6H_5+2NaX$ (B) $ArN_2^+X^-\xrightarrow{Cu/HCl}ArCl+N_2\uparrow+CuX$ (C) $C_2H_5Br+NaI\xrightarrow{\text{Dry acetone}}C_2H_5I+NaBr$ (D) $CH_3C(OH)(CH_3)CH_3\xrightarrow{HCl/ZnCl_2}CH_3C(Cl)(CH_3)CH_3$. List - II (Name of reaction): (I) Lucas reaction (II) Finkelstein reaction (III) Fittig reaction (IV) Gatterman reaction. Choose the correct answer from the options given below :

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

Correct answer: C

The nature of oxide ($TeO_2$) and hydride ($TeH_2$) formed by Te, respectively are :

1. A.Reducing and basic
2. B.Reducing and acidic
3. C.Oxidising and basic
4. D.Oxidising and acidic✓

Correct answer: D

Which among the following molecules is (a) involved in $sp^3d$ hybridization, (b) has different bond lengths and (c) has lone pair of electrons on the central atom ?

1. A.$SF_4$✓
2. B.$PF_5$
3. C.$XeF_2$
4. D.$XeF_4$

Correct answer: A

Formation of $Na_4[Fe(CN)_5NOS]$, a purple coloured complex formed by addition of sodium nitroprusside in sodium carbonate extract of salt indicates the presence of :

1. A.Sulphate ion
2. B.Sodium ion
3. C.Sulphite ion
4. D.Sulphide ion✓

Correct answer: D

Arrange the following in order of magnitude of work done by the system/on the system at constant temperature. (a) $|w_{reversible}|$ for expansion in infinite stages. (b) $|w_{irreversible}|$ for expansion in single stage. (c) $|w_{reversible}|$ for compression in infinite stages. (d) $|w_{irreversible}|$ for compression in single stage. Choose the correct answer from the options given below :

1. A.a > c > b > d
2. B.a > b > c > d
3. C.d > c = a > b✓
4. D.c = a > d > b

Correct answer: C

Reactant A converts to product D through the given mechanism (with the net evolution of heat) : A $\to$ B slow; $\Delta H$ = +ve. B $\to$ C fast; $\Delta H$ = −ve. C $\to$ D fast; $\Delta H$ = −ve. Which of the following represents the above reaction mechanism ?

1. A.Profile 1: the first hump (A→B) is the highest barrier, B lies above A, then two lower humps lead down through C to D, and D lies well below A✓
2. B.Profile 2: first hump high, second hump lower, third hump the tallest; D lies slightly above A
3. C.Profile 3: first hump the tallest, then two lower humps; D lies slightly above A
4. D.Profile 4: humps rise successively so the last (C→D) barrier is the highest; D lies far below A

Correct answer: A

'x' g of NaCl is added to water in a beaker with a lid. The temperature of the system is raised from 1°C to 25°C. Which out of the following plots, is best suited for the change in the molarity (M) of the solution with respect to temperature ? [Consider the solubility of NaCl remains unchanged over the temperature range]

1. A.M decreases linearly with t
2. B.M dips slightly then increases with t
3. C.M increases linearly with t
4. D.M first rises to a maximum (around 4 °C) and then decreases with t✓

Correct answer: D

When a concentrated solution of sulphanilic acid and 1-naphthylamine is treated with nitrous acid (273 K) and acidified with acetic acid, the mass (g) of 0.1 mole of product formed is : (Given molar mass in g $mol^{-1}$ H : 1, C : 12, N : 14, O : 16, S : 32)

1. A.330
2. B.343
3. C.33✓
4. D.66

Correct answer: C

The type of hybridization and the magnetic property of $[MnCl_6]^{3-}$ are,

1. A.$d^2sp^3$, paramagnetic with two unpaired electrons.
2. B.$d^2sp^3$, paramagnetic with four unpaired electrons.
3. C.$sp^3d^2$, paramagnetic with four unpaired electrons.✓
4. D.$sp^3d^2$, paramagnetic with two unpaired electrons.

Correct answer: C

Consider the following chemical equilibrium of the gas phase reaction at a constant temperature : $A(g)\rightleftharpoons B(g)+C(g)$. If p being the total pressure, $K_p$ is the pressure equilibrium constant and $\alpha$ is the degree of dissociation, then which of the following is true at equilibrium ?

1. A.If $K_p$ value is extremely high compared to p, $\alpha$ becomes much less than unity
2. B.When p increases $\alpha$ decreases✓
3. C.When p increases $\alpha$ increases
4. D.If p value is extremely high compared to $K_p$, $\alpha\approx1$

Correct answer: B

A tetrapeptide, "x" on complete hydrolysis produced glycine (Gly), alanine (Ala), valine (Val), leucine (Leu) in equimolar proportion each. The number of tetrapeptides (sequences) possible involving each of these amino acids is :

1. A.32
2. B.24✓
3. C.16
4. D.8

Correct answer: B

Given below are two statements : Statement (I) : Neopentane forms only one monosubstituted derivative. Statement (II) : Melting point of neopentane is higher than n-pentane. In the light of the above statements, choose the most appropriate answer from the options given below :

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

Correct answer: B

Which of the following graphs correctly represents the variation of thermodynamic properties of Haber's process ?

1. A.Plot 1: $-\Delta G_R^\theta/T$ highest (≈ +300 falling), $-\Delta H_R^\theta/T$ (≈ +100 falling below 0), $\Delta H_R^\theta$ flat ≈ −100, $\Delta S_R^\theta$ flat ≈ −200
2. B.Plot 2: $-\Delta H_R^\theta$ ≈ +200 falling, $-\Delta G_R^\theta/T$ ≈ +100 falling below 0, $\Delta H_R^\theta/T$ ≈ −100, $\Delta S_R^\theta/T$ ≈ −200
3. C.Plot 3: $\Delta S_R^\theta$ ≈ +200 falling to 100, $\Delta H_R^\theta$ ≈ +100, $-\Delta G_R^\theta/T$ rising from −100 to 0, $-\Delta H_R^\theta/T$ rising from −300
4. D.Plot 4: $-\Delta H_R^\theta/T$ highest (≈ +300 falling), $-\Delta G_R^\theta/T$ (≈ +100 falling below 0), $\Delta H_R^\theta$ flat ≈ −100, $\Delta S_R^\theta$ flat ≈ −200✓

Correct answer: D

Electronic configuration of four elements A, B, C and D are given below : (A) $1s^22s^22p^3$ (B) $1s^22s^22p^4$ (C) $1s^22s^22p^5$ (D) $1s^22s^22p^2$. Which of the following is the correct order of increasing electronegativity (Pauling's scale) ?

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

Correct answer: B

Consider the following reactions. From these reactions which reaction will give carboxylic acid as a major product ? (A) $R-C\equiv N\xrightarrow{\text{(i) } H^+/H_2O,\ \text{mild condition}}$ (B) $R-MgX\xrightarrow{\text{(i) } CO_2;\ \text{(ii) } H_3O^+}$ (C) $R-C\equiv N\xrightarrow{\text{(i) } SnCl_2/HCl;\ \text{(ii) } H_3O^+}$ (D) $R\cdot CH_2\cdot OH\xrightarrow{PCC}$ (E) $C_6H_5COCl\xrightarrow{\text{(i) } H_2/Pd-BaSO_4;\ \text{(ii) } Br_2\ \text{water}}$. Choose the correct answer from the options given below :

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

Correct answer: B

In 3,3-dimethylhex-1-en-4-yne, there are ______ $sp^3$, ______ $sp^2$ and ______ sp hybridised carbon atoms respectively.

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

Correct answer: B

The d-orbital electronic configuration of the complex among $[Co(en)_3]^{3+}$, $[CoF_6]^{3-}$, $[Mn(H_2O)_6]^{2+}$ and $[Zn(H_2O)_6]^{2+}$ that has the highest CFSE is :

1. A.$t_{2g}^3e_g^2$
2. B.$t_{2g}^6e_g^0$✓
3. C.$t_{2g}^6e_g^4$
4. D.$t_{2g}^4e_g^2$

Correct answer: B

In Dumas' method for estimation of nitrogen, 0.5 gram of an organic compound gave 60 mL of nitrogen collected at 300 K temperature and 715 mm Hg pressure. The percentage composition of nitrogen in the compound (Aqueous tension at 300 K = 15 mm Hg) is ______ %.

1. A.1.257
2. B.18.67
3. C.20.87
4. D.12.57✓

Correct answer: D