JEE Main 2025 (Online) 2nd April Evening Shift

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. 38Mr2
2. 2Mr2
3. 12Mr2
4. 32Mr2

In a moving coil galvanometer, two moving coils M1 and M2 have the following particulars : R1 = 5 , N1 = 15, A1 = 3.6 10-3 m2, B1 = 0.25 T R2 = 7 , N2 = 21, A2 = 1.8 10-3 m2, B2 = 0.50 T Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of M1 and M2 ?

1. 1 : 1
2. 1 : 3
3. 1 : 2
4. 1 : 4

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the most appropriate answer from the options given below :

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

If 0 and 0 are the permeability and permittivity of free space, respectively, then the dimension of ( 1 0 0 ) is :

1. T2/L
2. L2/T2
3. T2/L2
4. L/T2

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. y = 2 (0.83x - 3.35t) cm
2. y = 2 (0.83x - 3.5t) cm
3. y = 2 (0.13x - 0.5t) cm
4. y = 2 (3.35x - 0.83t) cm

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. B2Al4 0
2. B2Al2 0
3. B2Al 0
4. B2Al

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. 2
2. 1/2
3. 1/3
4. 3

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

1. r, 3r
2. 2r, 3 r
3. 3 r, 2r
4. 3 r, r

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

1. P = 0, Q = 1
2. P = 1, Q = 0
3. P = 0, Q = 0
4. P = 1, Q = 1

An electron with mass 'm' with an initial velocity (t = 0) v = v0 i (v0 > 0) enters a magnetic field B = B0 j. If the initial de Broglie wavelength at t = 0 is 0 then its value after time 't' would be :

1. 0 1 - e2 B02 t2m2
2. 0
3. 0 1 + e2 B02 t2m2
4. 0 1 + e2 B02 t2m2

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 curvature on both sides (R1 R2), without any change in lens power then possible combination of R1 and R2 is :

1. 13 cm and 17 cm
2. 15 cm and 17 cm
3. 13 cm and 13 cm
4. 16 cm and 19 cm

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 : [figure]

1. 1 V
2. 14 V
3. 34 V
4. 25 V

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. 4 r2 T [2 - 21/3 ]
2. 4 r2 T[1 + 2]
3. 4 r2 T [2 - 22/3 ]
4. 4 r2 T[ 2 - 1]

Energy released when two deuterons (1H2 ) fuse to form a helium nucleus (2He4 ) is : (Given : Binding energy per nucleon of 1H2 = 1.1 MeV and binding energy per nucleon of 2He4 = 7.0 MeV)

1. 26.8 MeV
2. 8.1 MeV
3. 23.6 MeV
4. 5.9 MeV

Match List - I with List - II. Choose the correct answer from the options given below :

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

Consider a circular loop that is uniformly charged and has a radius a 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
2. a/2
3. 0
4. a/ 2

[figure] A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions T1 and T2, respectively, are (in N) : (Take acceleration due to gravity 10 m/s2)

1. 5 3, 5
2. 5 3, 5 3
3. 5, 5
4. 5, 5 3

Identify the characteristics of an adiabatic process in a monoatomic gas. Choose the correct answer from the options given below :

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

Given a charge q, current I and permeability of vacuum 0. Which of the following quantity has the dimension of momentum ?

1. qI/ 0
2. q2 0 I
3. q 0/I
4. q 0 I

Assuming the validity of Bohr's atomic model for hydrogen-like ions the radius of Li++ ion in its ground state is given by 1Xa0, where X = (Where a0 is the first Bohr's radius.)

1. 2
2. 9
3. 1
4. 3

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 2. The angle of incidence (in degrees) is

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.

[figure] A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by a force of 10 N as shown in figure. The established torque produces an angular acceleration of 2 rad/s2. Moment of inertia of the wheel is kg m2. (Acceleration due to gravity = 10 m/s2)

The internal energy of air in 4 m 4 m 3 m sized room at 1 atmospheric pressure will be 106 J (Consider air as diatomic molecule)

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 1010 J. (Mass of earth = 6 1024 kg, Radius of earth = 6.4 106 m, Gravitational constant = 6.67 10-11 N m2 kg-2)

Given below are two statements: In the light of the above statements, choose the most appropriate answer from the options given below:

1. Statement I is incorrect but Statement II is correct
2. Both Statement I and Statement II are correct
3. Statement I is correct but Statement II is incorrect
4. Both Statement I and Statement II are incorrect

Match List-I with List-II. Choose the correct answer from the options given below:

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

Electronic configuration of four elements A, B, C and D are given below: (A) 1s2 2s2 2p3 (B) 1s2 2s2 2p4 (C) 1s2 2s2 2p5 (D) 1s2 2s2 2p2 Which of the following is the correct order of increasing electronegativity (Pauling's scale)?

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

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. 32
2. 24
3. 8
4. 16

Which among the following molecules is (a) involved in sp3d hybridization, (b) has different bond lengths and (c) has lone pair of electrons on the central atom?

1. XeF4
2. XeF2
3. PF5
4. SF4

In 3,3-dimethylhex-1-en-4-yne, there are sp3, sp2 and sp hybridised carbon atoms respectively.

1. 4, 2, 2
2. 2, 4, 2
3. 3, 3, 2
4. 2, 2, 4

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. 20.87
2. 12.57
3. 1.257
4. 18.67

Which of the following statements are true? Choose the correct answer from the options given below:

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

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

1. d > c = a > b
2. c = a > d > b
3. a > c > b > d
4. a > b > c > 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. 330
2. 33
3. 343
4. 66

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

1. [figure]
2. [figure]
3. [figure]
4. [figure]

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

1. [figure]
2. [figure]
3. [figure]
4. [figure]

Formation of Na4[Fe(CN)5NOS], a purple coloured complex formed by addition of sodium nitroprusside in sodium carbonate extract of salt indicates the presence of:

1. Sulphide ion
2. Sulphite ion
3. Sulphate ion
4. Sodium ion

Consider the following reactions. From these reactions which reaction will give carboxylic acid as a major product? Choose the correct answer from the options given below:

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

The nature of oxide (TeO2) and hydride (TeH2) formed by Te, respectively are:

1. Reducing and basic
2. Reducing and acidic
3. Oxidising and acidic
4. Oxidising and basic

'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. [figure]
2. [figure]
3. [figure]
4. [figure]

The type of hybridization and the magnetic property of [MnCl6]3- are,

1. sp3d2, paramagnetic with four unpaired electrons.
2. d2sp3, paramagnetic with four unpaired electrons.
3. sp3d2, paramagnetic with two unpaired electrons.
4. d2sp3, paramagnetic with two unpaired electrons.

Match List-I with List-II. Choose the correct answer from the options given below:

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

The d-orbital electronic configuration of the complex among [Co(en)3]3+, [CoF6]3-, [Mn(H2O)6]2+ and [Zn(H2O)6]2+ that has the highest CFSE is:

1. t2g6eg0
2. t2g3eg2
3. t2g4eg2
4. t2g6eg4

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

1. If Kp value is extremely high compared to p, becomes much less than unity
2. When p increases, increases
3. If p value is extremely high compared to Kp, 1
4. When p increases, decreases

For the reaction A B the following graph was obtained. The time required (in seconds) for the concentration of A to reduce to 2.5 g L-1 (if the initial concentration of A was 50 g L-1) is . (Nearest integer) Given : 2 = 0.3010 [figure]

When 1 g each of compounds AB and AB2 are dissolved in 15 g of water separately, they increased the boiling point of water by 2.7 K and 1.5 K respectively. The atomic mass of A (in amu) is 10-1 (Nearest integer) (Given : Molal boiling point elevation constant is 0.5 K kg mol-1)

The spin-only magnetic moment value of Mn+ ion formed among Ni, Zn, Mn and Cu that has the least enthalpy of atomisation is . (in nearest integer) Here n is equal to the number of diamagnetic complexes among K2[NiCl4], [Zn(H2O)6]Cl2, K3[Mn(CN)6] and [Cu(PPh3)3I]

0.2\% (w/v) solution of NaOH is measured to have resistivity 870.0 m m. The molar conductivity of the solution will be 102 mS dm2 mol-1. (Nearest integer)

[figure] Consider the above sequence of reactions. 151 g of 2-bromopentane is made to react. Yield of major product P is 80\% whereas Q is 100\%. Mass of product Q obtained is g. (Given molar mass in g mol-1 H : 1, C : 12, O : 16, Br : 80)

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. 103
2. 106
3. 100
4. 105

Let f : [1, ) [2, ) be a differentiable function. If 10 1x f(t) dt = 5xf(x) - x5 - 9 for all x 1, then the value of f(3) is :

1. 22
2. 26
3. 32
4. 18

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 : [figure]

1. 5880
2. 840
3. 960
4. 5760

Let the point P of the focal chord PQ of the parabola y2 = 16x be (1, -4). If the focus of the parabola divides the chord PQ in the ratio m : n, (m, n) = 1, then m2 + n2 is equal to :

1. 17
2. 37
3. 10
4. 26

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

1. 30
2. 26
3. 22
4. 18

Let A be a 3 3 real matrix such that A2(A - 2I) - 4(A - I) = O, where I and O are the identity and null matrices, respectively. If A5 = A2 + A + I, where , , and are real constants, then + + is equal to :

1. 76
2. 12
3. 4
4. 20

If x 0 (2x) + a (4x) - bx4 is finite, then (a + b) is equal to:

1. 0
2. 34
3. -1
4. 12

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( , , ), then + + is equal to :

1. 463
2. 18
3. 13
4. 473

If [- 7 6, 4 3 ], then the number of solutions of 3 cosec2 - 2( 3 - 1) cosec - 4 = 0, is equal to :

1. 7
2. 10
3. 6
4. 8

Let A = \1, 2, 3, , 100\ and R be a relation on A such that R = \(a, b) : a = 2b + 1\. Let (a1, a2), (a2, a3), (a3, a4), , (ak, ak+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. 6
2. 8
3. 7
4. 5

If the domain of the function f(x) = 1 10 + 3x - x2 + 1 x + |x| is (a, b), then (1 + a)2 + b2 is equal to :

1. 29
2. 30
3. 25
4. 26

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 b2 + c2 is :

1. 90
2. 83
3. 93
4. 97

The line L1 is parallel to the vector a = -3 i + 2 j + 4 k and passes through the point (7, 6, 2) and the line L2 is parallel to the vector b = 2 i + j + 3 k and passes through the point (5, 3, 4). The shortest distance between the lines L1 and L2 is :

1. 23 38
2. 21 38
3. 23 57
4. 21 57

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 212. Then the number of terms which are integers in the A.P. is :

1. 6
2. 4
3. 8
4. 10

Let (a, b) be the point of intersection of the curve x2 = 2y and the straight line y - 2x - 6 = 0 in the second quadrant. Then the integral I = ab 9x21 + 5x dx is equal to :

1. 27
2. 18
3. 24
4. 21

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. 3 19
2. 316
3. 4 17
4. 57

If r=010 ( 10r+1 - 110r ) 11Cr+1 = 11 - 11111010, then is equal to :

1. 11
2. 20
3. 24
4. 15

4 01 ( 1 3 + x2 + 1 + x2 )dx - 3 e( 3) is equal to :

1. 2 - 2 - e(1 + 2)
2. 2 + 2 + e(1 + 2)
3. 2 + 2 - e(1 + 2)
4. 2 - 2 + e(1 + 2)

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

1. 15
2. 18
3. 12
4. 9

Given three identical bags each containing 10 balls, whose colours are as follows : arraylccc & Red & Blue & Green \ Bag I & 3 & 2 & 5 \ Bag II & 4 & 3 & 3 \ Bag III & 5 & 1 & 4 array 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 ( 1p + 1q ) is:

1. 6
2. 9
3. 7
4. 8

If y = ( 3 + -1 x2 ), then (x - y)2 + 3y2 is equal to .

If the set of all a R - \1\, for which the roots of the equation (1 - a)x2 + 2(a - 3)x + 9 = 0 are positive is (- , - ] [ , ), then 2 + + is equal to .

If the sum of the first 10 terms of the series 4 11 + 4 14 + 4 21 + 4 24 + 4 31 + 4 34 + is mn, where (m, n) = 1, then m + n is equal to .

Let y = y(x) be the solution of the differential equation dydx + 2y 2 x = 2 2 x + 3 x 2 x such that y(0) = 54. Then 12 (y ( 4 ) - e-2 ) is equal to .

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 .