JEE Main 2025 (Online) 8th April Evening Shift

A monoatomic gas having = 53 is stored in a thermally insulated container and the gas is suddenly compressed to ( 18 )th of its initial volume. The ratio of final pressure and initial pressure is: ( is the ratio of specific heats of the gas at constant pressure and at constant volume)

1. 16
2. 32
3. 28
4. 40

A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is .

1. 607
2. 15
3. 45
4. 30

A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm, respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be

1. 70011 cm
2. 60011 cm
3. 80011 cm
4. 50011 cm

A quantity Q is formulated as X-2Y+ 32Z- 25. X, Y, and Z are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of Q is

1. 0.6
2. 0.8
3. 0.7
4. 0.1

For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as

1. A 23
2. Independent of A
3. A3
4. A 13

Figure shows a current carrying square loop ABCD of edge length 'a' lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is [figure]

1. 2 0 I3 a
2. 2 0 I3 a
3. 3 0 I 2a
4. 0 I2 a

The output voltage in the following circuit is (Consider ideal diode case) [figure]

1. 0 V
2. +5 V
3. −5 V
4. 10 V

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, y1(x, t) = 4 (kx - t) and y2(x, t) = 2 (kx - t + 2 3 ), are: (Take the angular frequency of initial waves same as )

1. [ 3, 6 ]
2. [2 3, 6 ]
3. [6, 2 3 ]
4. [6, 3 ]

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is P 1011 N m-2, where the value of P is: (Take g = 3 m/s2)

1. 2.5
2. 25
3. 10
4. 5

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take g = 10 m/s2, specific heat of water = 4200 J/(kg K))

1. 0.36 K
2. 0.23 K
3. 0.48 K
4. 0.14 K

A rod of linear mass density ' ' and length 'L' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameters is:

1. L38 2
2. L316 2
3. L34 2
4. L312

Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is v1, and that in the other string having radius of cross section R/2 is v2. Then v2v1 =

1. 8
2. 4
3. 2
4. 2

Two metal spheres of radius R and 3R have same surface charge density . If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere become 1 and 2, respectively. The ratio 1 2 is

1. 13
2. 19
3. 9
4. 3

Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. T1 and T2 are the total flying times of first and second ball, respectively, then the ratio of T1 and T2 is

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

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 correct answer from the options given below.

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

Electric charge is transferred to an irregular metallic disk as shown in the figure. If 1, 2, 3 and 4 are charge densities at given points then, choose the correct answer from the options given below: [figure]

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

An infinitely long wire has uniform linear charge density = 2 nC/m. The net flux through a Gaussian cube of side length 3 cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be x N m2 C-1, where x is: [Neglect any edge effects and use 14 0 = 9 109 SI units]

1. 6.48
2. 0.72
3. 1.44
4. 2.16

A body of mass 2 kg moving with velocity of vin = 3 i + 4 j m s-1 enters into a constant force field of 6 N directed along positive z-axis. If the body remains in the field for a period of 53 seconds, then velocity of the body when it emerges from the force field is:

1. 3 i + 4 j + 5 k
2. 4 i + 3 j + 5 k
3. 3 i + 4 j - 5 k
4. 3 i + 4 j + 5 k

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m (x < 2) from the wall, the speed of the block will be

1. 10 [1 - (2 - x)2 ] 12 m/s
2. 10 [1 - (2 - x)2 ] 32 m/s
3. 10 [1 - (2 - x)2 ] m/s
4. 10 [1 - (2 - x)2 ]2 m/s

In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green filter. In this case:

1. there shall be alternate interference fringes of red and green.
2. there shall be an interference pattern for red distinct from that for green.
3. there shall be an interference pattern, where each fringe's pattern center is green and outer edges is red.
4. there shall be no interference fringes.

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to a change of volume of 0.8 cm3. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was litre. (Take 1 atm = 105 Pa)

A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of 25 N m for 40 s, the speed increases to 2100 rpm. The diameter of the disk is m.

[figure] Space between the plates of a parallel plate capacitor of plate area 4 cm2 and separation of 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is pF. (Given 0 = 8.85 10-12 F/m)

An electron is released from rest near an infinite non-conducting sheet of uniform charge density '- '. The rate of change of de-Broglie wave length associated with the electron varies inversely as nth power of time. The numerical value of n is .

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of a uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is 1 gm/cm3.) The unknown mass is kg.

The atomic number of the element from the following with lowest 1st ionisation enthalpy is :

1. 32
2. 35
3. 19
4. 87

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

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

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

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

In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are t1 and t2 (s), respectively. The ratio t1/t2 will be:

1. 43
2. 32
3. 34
4. 23

Correct statements for an element with atomic number 9 are: Choose the correct answer from the options given below:

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

HA(aq) H+(aq) + A-(aq) The freezing point depression of a 0.1 m aqueous solution of a monobasic weak acid HA is 0.20 C. The dissociation constant for the acid is Given: Kf(H2O) = 1.8 K kg mol-1, molality ≡ molarity

1. 1.90 10-3
2. 1.38 10-3
3. 1.1 10-2
4. 1.89 10-1

What is the correct IUPAC name of the compound? [figure]

1. 1-Ethylcyclopent-2-en-3-ol
2. 4-Ethylcyclopent-2-en-1-ol
3. 1-Ethyl-3-hydroxycyclopent-2-ene
4. 4-Ethyl-1-hydroxycyclopent-2-ene

[figure] 'P' is

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

On combustion 0.210 g of an organic compound containing C, H and O gave 0.127 g H2O and 0.307 g CO2. The percentages of hydrogen and oxygen in the given organic compound respectively are:

1. 7.55, 43.85
2. 6.72, 53.41
3. 6.72, 39.87
4. 53.41, 39.6

The number of species from the following that are involved in sp3d2 hybridization is : [Co(NH3)6]3+, SF6, [CrF6]3-, [CoF6]3-, [Mn(CN)6]3-, and [MnCl6]3-

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

Which of the following binary mixtures does not show the behaviour of minimum boiling azeotropes?

1. CH3OH + CHCl3
2. C6H5OH + C6H5NH2
3. H2O + CH3COC2H5
4. CS2 + CH3COCH3

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

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

A [(ii) H3O+](i) NaOH B [(ii) H2SO4, ](i) EtOH C 'A' shows positive Lassaigne's test for N and its molar mass is 121. 'B' gives effervescence with aq NaHCO3. 'C' gives fruity smell. Identify A, B and C from the following.

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

The correct decreasing order of spin only magnetic moment values (BM) of Cu+, Cu2+, Cr2+ and Cr3+ ions is :

1. Cr3+ > Cr2+ > Cu+ > Cu2+
2. Cu+ > Cu2+ > Cr3+ > Cr2+
3. Cr2+ > Cr3+ > Cu2+ > Cu+
4. Cu2+ > Cu+ > Cr2+ > Cr3+

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

When [figure] undergoes intramolecular aldol condensation, the major product formed is :

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

Choose the correct set of reagents for the following conversion. [figure]

1. Cl2/ anhy. AlCl3; Br2/Fe; alc. KOH
2. Cl2/Fe; Br2/ anhy. AlCl3; aq. KOH
3. Br2/Fe; Cl2, ; alc. KOH
4. Br2/ anhy. AlCl3; Cl2, ; aq. KOH

Which one of the following reactions will not lead to the desired ether formation in major proportion? (iso-Bu isobutyl, sec-Bu sec-butyl, n-Pr n-propyl, tBu tert-butyl, Et ethyl)

1. [figure]
2. iso-Bu O Na + sec-BuBr sec-Bu–O–iso-Bu
3. [figure]
4. tBu O Na + EtBr tBu-O-Et

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

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

[figure] Choose the correct option for structures of A and B, respectively

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

Consider the following half cell reaction Cr2O72-(aq) + 6e- + 14H+(aq) 2Cr3+(aq) + 7H2O( ) The reaction was conducted with the ratio of [ Cr3+]2[ Cr2O72-] = 10-6. The pH value at which the EMF of the half cell will become zero is . (nearest integer value) [Given: standard half cell reduction potential E Cr2O72-,H+/Cr3+ = 1.33 V, 2.303RTF = 0.059 V.]

The energy of an electron in the first Bohr orbit of the H-atom is -13.6 eV. The magnitude of energy value of an electron in the first excited state of Be3+ is eV (nearest integer value).

The equilibrium constant for decomposition of H2O(g) H2O(g) H2(g) + 12O2(g); G = 92.34 kJ mol-1 is 8.0 10-3 at 2300 K and total pressure at equilibrium is 1 bar. Under this condition, the degree of dissociation ( ) of water is 10-2 (nearest integer value). [Assume is negligible with respect to 1]

20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The molarity of the sodium iodide solution is M. (Nearest Integer value) (Given : Na = 23, I = 127, Ag = 108, N = 14, O = 16 g mol-1)

Resonance in X2Y can be represented as [figure] The enthalpy of formation of X2Y ( X X(g) + 12Y = Y(g) X2Y(g) ) is 80 kJ mol-1. The magnitude of resonance energy of X2Y is kJ mol-1 (nearest integer value). Given: Bond energies of X X, X = X, Y = Y and X = Y are 940, 410, 500, and 602 kJ mol-1 respectively. Valence X: 3, Y: 2

Let the values of for which the shortest distance between the lines x-12 = y-23 = z-34 and x- 3 = y-44 = z-55 is 1 6 be 1 and 2. Then the radius of the circle passing through the points (0, 0), ( 1, 2) and ( 2, 1) is

1. 3
2. 5 23
3. 23
4. 4

Let f(x) = x - 1 and g(x) = ex for x R. If dydx = (e-2 x g(f(f(x))) - y x ), y(0) = 0, then y(1) is

1. 1-e3e4
2. e-1e4
3. 1-e2e4
4. 2e-1e3

If 114 + 124 + 134 + = 490, 114 + 134 + 154 + = , 124 + 144 + 164 + = , then is equal to :

1. 23
2. 14
3. 18
4. 15

Let a be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle with the positive x-axis and the equations of its diagonals are ( 3+1)x + ( 3-1)y = 0 and ( 3-1)x - ( 3+1)y + 8 3 = 0. Then a2 is equal to :

1. 48
2. 16
3. 24
4. 32

A line passing through the point P(a, 0) makes an acute angle with the positive x-axis. Let this line be rotated about the point P through an angle 2 in the clockwise direction. If in the new position, the slope of the line is 2 - 3 and its distance from the origin is 1 2, then the value of 3a2 2 - 2 3 is :

1. 8
2. 4
3. 5
4. 6

Let be a solution of x2 + x + 1 = 0, and for some a and b in R, bmatrix 4 & a & b bmatrix bmatrix 1 & 16 & 13 \ -1 & -1 & 2 \ -2 & -14 & -8 bmatrix = bmatrix 0 & 0 & 0 bmatrix. If 4 4 + m a + n b = 3, then m + n is equal to

1. 11
2. 3
3. 8
4. 7

Let the ellipse 3x2 + py2 = 4 pass through the centre C of the circle x2 + y2 - 2x - 4y - 11 = 0 of radius r. Let f1, f2 be the focal distances of the point C on the ellipse. Then 6f1f2 - r is equal to

1. 78
2. 68
3. 70
4. 74

The sum of the squares of the roots of |x-2|2 + |x-2| - 2 = 0 and the squares of the roots of x2 - 2|x-3| - 5 = 0, is

1. 24
2. 26
3. 36
4. 30

The value of -1 ( 1+ 2(2)-1 (2) ) - -1 ( 1+ 2 ( 12 )+1 ( 12 ) ) is equal to

1. - 32
2. + 52
3. - 54
4. + 32

Let A = \ [0, 2 ] : 1 + 10 Re ( 2 + i - 3i ) = 0 \. Then A 2 is equal to

1. 214 2
2. 6 2
3. 274 2
4. 8 2

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

The integral -1 32 ( | 2 x ( x) | )dx is equal to:

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

Let A = bmatrix 2 & 2+p & 2+p+q \ 4 & 6+2p & 8+3p+2q \ 6 & 12+3p & 20+6p+3q bmatrix. If (adj(adj(3A))) = 2m 3n, m, n N, then m + n is equal to

1. 22
2. 20
3. 24
4. 26

Let A = \0, 1, 2, 3, 4, 5\. Let R be a relation on A defined by (x, y) R if and only if \x, y\ \3, 4\. Then among the statements (S1): The number of elements in R is 18, and (S2): The relation R is symmetric but neither reflexive nor transitive

1. both are false
2. only (S1) is true
3. only (S2) is true
4. both are true

Let f(x) be a positive function and I1 = - 121 2x f(2x(1 - 2x)) dx and I2 = -12 f(x(1 - x)) dx. Then the value of I2I1 is equal to

1. 12
2. 9
3. 6
4. 4

There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is

1. 230
2. 210
3. 200
4. 220

If A and B are two events such that P(A) = 0.7, P(B) = 0.4 and P(A B) = 0.5, where B denotes the complement of B, then P (B (A B) ) is equal to

1. 13
2. 12
3. 14
4. 16

Let a = i + 2 j + k and b = 2 i + j - k. Let c be a unit vector in the plane of the vectors a and b and be perpendicular to a. Then such a vector c is:

1. 1 2(- i + k)
2. 1 5( j - 2 k)
3. 1 3( i - j + k)
4. 1 3(- i + j - k)

Let the function f(x) = x3 + 3x + 3, x 0 be strictly increasing in (- , 1) ( 2, ) and strictly decreasing in ( 3, 4) ( 4, 5). Then i=15 i2 is equal to

1. 48
2. 40
3. 36
4. 28

The number of integral terms in the expansion of (5 12 + 7 18 )1016 is:

1. 127
2. 128
3. 130
4. 129

The product of the last two digits of (1919)1919 is

Let the area of the bounded region \(x, y) : 0 9x y2, y 3x - 6 \ be A. Then 6A is equal to .

Let r be the radius of the circle, which touches x-axis at point (a, 0), a < 0 and the parabola y2 = 9x at the point (4, 6). Then r is equal to .

Let the area of the triangle formed by the lines x + 2 = y - 1 = z, x - 35 = y-1 = z - 11 and x-3 = y - 33 = z - 21 be A. Then A2 is equal to .

Let the domain of the function f(x) = -1 ( 4x + 53x - 7 ) be [ , ] and the domain of g(x) = 2 (2 - 6 27(2x + 5) ) be ( , ). Then |7( + ) + 4( + )| is equal to .