JEE Main 2025 (Online) 3rd April Morning Shift

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 cm3 and temperature 27 . The change in temperature when the gas is adiabatically compressed to 200 cm3 is: (Take = 1.5; is the ratio of specific heats at constant pressure and at constant volume)

1. 300 K
2. 600 K
3. 327 K
4. 522 K

A person measures mass of 3 different particles as 435.42 g, 226.3 g and 0.125 g. According to the rules for arithmetic operations with significant figures, the addition of the masses of 3 particles will be.

1. 661.845 g
2. 661.84 g
3. 662 g
4. 661.8 g

A wire of length 25 m and cross-sectional area 5 mm2 having resistivity of 2 10-6 m is bent into a complete circle. The resistance between diametrically opposite points will be

1. 100
2. 2.5
3. 12.5
4. 50

The angle of projection of a particle is measured from the vertical axis as and the maximum height reached by the particle is hm. Here hm as function of can be presented as

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

The work function of a metal is 3 eV. The color of the visible light that is required to cause emission of photoelectrons is

1. Red
2. Green
3. Blue
4. Yellow

Match the 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-II, B-IV, C-III, D-I
3. A-I, B-III, C-IV, D-II
4. A-III, B-II, C-I, D-IV

Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area 0.5 m2. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is: (g = 10 m/s2)

1. 2 m/s
2. 5 m/s
3. 3 m/s
4. 4 m/s

Consider following statements for refraction of light through prism, when angle of deviation is minimum. Choose the correct answer from the options given below :

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

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constants 1 and 2, as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are C1 and C2 respectively, then C1C2 is: First Configuration [figure] Second Configuration [figure]

1. 0( 1 + 2)2
2. 1 22( 1 + 2)2
3. 4 1 2( 1 + 2)2
4. 1 2 1 + 2

During the melting of a slab of ice at 273 K at atmospheric pressure :

1. Internal energy of ice-water system remains unchanged.
2. Positive work is done by the ice-water system on the atmosphere.
3. Positive work is done on the ice-water system by the atmosphere.
4. Internal energy of the ice-water system decreases.

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is [figure]

1. 2.5 m/s2
2. 3.5 m/s2
3. 0.25 m/s2
4. 0.35 m/s2

[figure] A piston of mass M is hung from a massless spring whose restoring force law goes as F = -kx3, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with 'n' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height L0 to L1, the total energy delivered by the filament is: (Assume spring to be in its natural length before heating)

1. nRT ( L1L0 ) + Mg(L1 - L0) + 3k4 (L14 - L04 )
2. nRT ( L1L0 ) + Mg(L1 - L0) + k4 (L14 - L04 )
3. nRT ( L12L02 ) + Mg2(L1 - L0) + k4 (L14 - L04 )
4. 3nRT ( L1L0 ) + 2Mg(L1 - L0) + k3 (L13 - L03 )

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

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

A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

1. S4, 3gS2
2. S2, 3gS2
3. S4, 3gS2
4. S2, 3gS2

[figure] Two blocks of masses m and M, (M > m), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then ( = coefficient of friction between the two blocks) Choose the correct answer from the options given below :

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

Which of the following curves possibly represent one-dimensional motion of a particle? Choose the correct answer from the options given below :

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

The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm. The refractive index of the lens material is

1. 1.4
2. 1.8
3. 1.5
4. 1.2

The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell respectively, are:

1. 0 V, 120 V, 40 V
2. 120 V, 120 V, 80 V
3. 40 V, 40 V, 80 V
4. 0 V, 0 V, 80 V

The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed 2 m away from it, is

1. 3 10-8 Pascals
2. 0
3. 1.5 10-8 Pascals
4. 6 10-8 Pascals

Choose the correct logic circuit for the given truth table having inputs A and B. [figure]

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

In the figure shown below, a resistance of 150.4 is connected in series to an ammeter A of resistance 240 . A shunt resistance of 10 is connected in parallel with the ammeter. The reading of the ammeter is mA. [figure]

A loop ABCDA, carrying current I = 12 A, is placed in a plane, consists of two semi-circular segments of radius R1 = 6 m and R2 = 4 m. The magnitude of the resultant magnetic field at center O is k 10-7 T. The value of k is . (Given 0 = 4 10-7 T m A-1) [figure]

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of x is .

Three identical spheres of mass m are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time T = 4 seconds. If the sides of the triangle are increased to length 2a and also the masses of the spheres are made 2 m, then they will collide after seconds.

A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to a uniform magnetic field of strength 0.15 T. The magnetic force on the wire is mN.

The correct order of the complexes [Co(NH3)5(H2O)]3+ (A), [Co(NH3)6]3+ (B), [Co(CN)6]3- (C) and [CoCl(NH3)5]2+ (D) in terms of wavelength of light absorbed is

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

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

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

Identify [A], [B] and [C], respectively in the following reaction sequence : [figure]

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

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

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

Which of the following postulate of Bohr's model of hydrogen atom is not in agreement with quantum mechanical model of an atom?

1. The electron in a H atom's stationary state moves in a circle around the nucleus.
2. An atom can take only certain distinct energies E1, E2, E3, etc. These allowed states of constant energy are called the stationary states of atom.
3. An atom in a stationary state does not emit electromagnetic radiation as long as it stays in the same state.
4. When an electron makes a transition from a higher energy stationary state to a lower energy stationary state, then it emits a photon of light.

In the following system, PCl5(g) PCl3(g) + Cl2(g) at equilibrium, upon addition of xenon gas at constant T & p, the concentration of

1. PCl5, PCl3 & Cl2 remain constant
2. PCl3 will increase
3. Cl2 will decrease
4. PCl5 will increase

In the following reactions, which one is NOT correct?

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

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

1. Statement I is false but Statement II is true
2. Both Statement I and Statement II are true
3. Both Statement I and Statement II are false
4. Statement I is true but Statement II is false

Which compound would give 3-methyl-6-oxoheptanal upon ozonolysis?

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

2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is: (Given : Ebullioscopic constant of water = 0.52 K kg mol-1)

1. 377.3 K
2. 379.2 K
3. 375.3 K
4. 277.3 K

Which of the following properties will change when system containing solution 1 will become solution 2 ? [figure]

1. Molar heat capacity
2. Concentration
3. Gibbs free energy
4. Density

Identify the correct statements from the following. Choose the correct answer from the options given below:

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

The least acidic compound, among the following is: [figure]

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

Among 10-9 g (each) of the following elements, which one will have the highest number of atoms? Element: Pb, Po, Pr and Pt

1. Pr
2. Pt
3. Po
4. Pb

The metal ions that have the calculated spin-only magnetic moment value of 4.9 B.M. are : Choose the correct answer from the options given below:

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

Which of the following is the correct structure of L-Fructose?

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

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

1. Statement I is true but Statement II is false
2. Statement I is false but Statement II is true
3. Both Statement I and Statement II are true
4. Both Statement I and Statement II are false

Correct order of limiting molar conductivity for cations in water at 298 K is :

1. H+ > Na+ > K+ > Ca2+ > Mg2+
2. H+ > Ca2+ > Mg2+ > K+ > Na+
3. Mg2+ > H+ > Ca2+ > K+ > Na+
4. H+ > Na+ > Ca2+ > Mg2+ > K+

In a reaction A + B C, initial concentrations of A and B are related as [A]0 = 8[B]0. The half-lives of A and B are 10 min and 40 min, respectively. If they start to disappear at the same time, both following first order kinetics, after how much time will the concentration of both the reactants be same?

1. 20 min
2. 40 min
3. 80 min
4. 60 min

Number of molecules from below which cannot give iodoform reaction is : Ethanol, Isopropyl alcohol, Bromoacetone, 2-Butanol, 2-Butanone, Butanal, 2-Pentanone, 3-Pentanone, Pentanal and 3-Pentanol.

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

During estimation of nitrogen by Dumas' method of compound X (0.42 g) [figure] mL of N2 gas will be liberated at STP. (nearest integer) (Given molar mass in g mol-1 : C : 12, H : 1, N : 14)

Consider the following reactions A + Little amountNaCl + H2SO4 CrO2Cl2 + Side Products CrO2Cl2(Vapour) + NaOH B + NaCl + H2O B + H+ C + H2O The number of terminal 'O' present in the compound 'C' is

0.5 g of an organic compound on combustion gave 1.46 g of CO2 and 0.9 g of H2O. The percentage of carbon in the compound is . (Nearest integer) [Given : Molar mass (in g mol-1) C : 12, H : 1, O : 16]

The number of optical isomers exhibited by the iron complex (A) obtained from the following reaction is . FeCl3 + KOH + H2C2O4 A

Given : sub H [C (graphite)] = 710 kJ mol-1 C-H H = 414 kJ mol-1 H-H H = 436 kJ mol-1 C=C H = 611 kJ mol-1 The f H for CH2=CH2 is kJ mol-1 (nearest integer value)

If the domain of the function f(x) = e ( 2x-35+4x ) + -1 ( 4+3x2-x ) is [ , ), then 2 + 4 is equal to

1. 4
2. 3
3. 7
4. 5

Let a1, a2, a3, be a G.P. of increasing positive numbers. If a3 a5 = 729 and a2 + a4 = 1114, then 24(a1 + a2 + a3) is equal to

1. 128
2. 129
3. 131
4. 130

The sum 1 + 3 + 11 + 25 + 45 + 71 + upto 20 terms, is equal to

1. 7240
2. 8124
3. 7130
4. 6982

The number of solutions of the equation 2x + 3 x = , x [-2 , 2 ] - \ 2, 3 2 \ is:

1. 4
2. 5
3. 3
4. 6

Let A = \-3, -2, -1, 0, 1, 2, 3\. Let R be a relation on A defined by x R y if and only if 0 x2 + 2y 4. Let l be the number of elements in R and m be the minimum number of elements required to be added in R to make it a reflexive relation. Then l + m is equal to

1. 18
2. 20
3. 17
4. 19

The radius of the smallest circle which touches the parabolas y = x2 + 2 and x = y2 + 2 is

1. 7 216
2. 7 28
3. 7 22
4. 7 24

Let f(x) = x3 3 - x2 dx. If 5f( 2) = -4, then f(1) is equal to

1. - 6 25
2. - 8 25
3. - 2 25
4. - 4 25

Let the domain of the function f(x) = 2 4 6 (3 + 4x - x2) be (a, b). If 0b-a [x2] dx = p - q - r, p, q, r N, (p, q, r) = 1, where [ ] is the greatest integer function, then p + q + r is equal to

1. 10
2. 11
3. 9
4. 8

Let and be the roots of x2 + 3x - 16 = 0, and and be the roots of x2 + 3x - 1 = 0. If Pn = n + n and Qn = n + n, then P25 + 3P242P23 + Q25 - Q23Q24 is equal to

1. 4
2. 3
3. 5
4. 7

Let a line passing through the point (4, 1, 0) intersect the line L1 : x-12 = y-23 = z-34 at the point A( , , ) and the line L2 : x - 6 = y = -z + 4 at the point B(a, b, c). Then vmatrix 1 & 0 & 1 \ & & \ a & b & c vmatrix is equal to

1. 16
2. 6
3. 8
4. 12

Let f(x) = cases (1 + ax)1/x, & x < 0 \ 1 + b, & x = 0 \ (x+4)1/2 - 2(x+c)1/3 - 2, & x > 0 cases be continuous at x = 0. Then ea bc is equal to:

1. 64
2. 48
3. 36
4. 72

A line passing through the point P( 5, 5) intersects the ellipse x236 + y225 = 1 at A and B such that (PA) (PB) is maximum. Then 5 (PA2 + PB2 ) is equal to :

1. 290
2. 377
3. 338
4. 218

Line L1 passes through the point (1, 2, 3) and is parallel to z-axis. Line L2 passes through the point ( , 5, 6) and is parallel to y-axis. Let for = 1, 2, 2 < 1, the shortest distance between the two lines be 3. Then the square of the distance of the point ( 1, 2, 7) from the line L1 is

1. 25
2. 32
3. 40
4. 37

Let g be a differentiable function such that 0x g(t) dt = x - 0x t g(t) dt, x 0 and let y = y(x) satisfy the differential equation dydx - y x = 2(x+1) x g(x), x [0, 2 ). If y(0) = 0, then y ( 3 ) is equal to

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

The sum of all rational terms in the expansion of (2+ 3)8 is :

1. 16923
2. 18817
3. 3763
4. 33845

If r=19 ( r+32r ) 9Cr = ( 32 )9 - , , N, then ( + )2 is equal to

1. 27
2. 81
3. 18
4. 9

Let z C be such that z2+3iz-2+i = 2+3i. Then the sum of all possible values of z2 is :

1. -19+2i
2. -19-2i
3. 19-2i
4. 19+2i

If y(x) = vmatrix x & x & x+ x+1 \ 27 & 28 & 27 \ 1 & 1 & 1 vmatrix, x R, then d2ydx2 + y is equal to

1. 28
2. 27
3. -1
4. 1

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines L1: 2x+y+6=0 and L2: 4x+2y-p=0, p>0, at the points A and B, respectively. If AB = 9 2 and the foot of the perpendicular from the point A on the line L2 is M, then AMBM is equal to

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

Let A be a matrix of order 3 3 and |A| = 5. If |2 adj(3A adj(2A))| = 2 3 5 , , , N, then + + is equal to

1. 26
2. 27
3. 25
4. 28

All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number n be denoted by Wn. Let the probability P(Wn) of choosing the word Wn satisfy P(Wn) = 2 P(Wn-1), n > 1. If P(CDBEA) = 2 2 -1, , N, then + is equal to

Let a = i + j + k, b = 3 i + 2 j - k, c = j + k and d be a unit vector such that a d = b d and c d = 1. If c is perpendicular to a, then |3 d + c|2 is equal to

Let the product of the focal distances of the point P(4, 2 3) on the hyperbola H: x2a2 - y2b2 = 1 be 32. Let the length of the conjugate axis of H be p and the length of its latus rectum be q. Then p2 + q2 is equal to

The area of the region bounded by the curve y = \|x|, x|x-2|\, the x-axis and the lines x = -2 and x = 4 is equal to

If the number of seven-digit numbers, such that the sum of their digits is even, is m n 10n; m, n \1, 2, 3, , 9\, then m + n is equal to