JEE Main 2025 (Online) 4th April Morning Shift

Consider the sound wave travelling in ideal gases of He, CH4, and CO2. All the gases have the same ratio P , where P is the pressure and is the density. The ratio of the speed of sound through the gases VHe : VCH4 : VCO2 is given by

1. 75 : 53 : 43
2. 53 : 43 : 43
3. 53 : 43 : 75
4. 43 : 53 : 75

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of MP LQ TR AS, where value of 'Q' and 'R' are

1. (3, -5)
2. (-2, 1)
3. (-2, 2)
4. (1, -1)

Two simple pendulums having lengths l1 and l2 with negligible string mass undergo angular displacements 1 and 2, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

1. 1 l2 = 2 l1
2. 1 l1 = 2 l2
3. 1 l22 = 2 l12
4. 1 l12 = 2 l22

In a Young's double slit experiment, the slits are separated by 0.2 mm. If the slits separation is increased to 0.4 mm, the percentage change of the fringe width is :

1. 25\%
2. 50\%
3. 0\%
4. 100\%

Current passing through a wire as function of time is given as I(t) = 0.02t + 0.01 A. The charge that will flow through the wire from t = 1 s to t = 2 s is

1. 0.02 C
2. 0.07 C
3. 0.06 C
4. 0.04 C

An alternating current is represented by the equation, i = 100 2 (100 t) ampere. The RMS value of current and the frequency of the given alternating current are

1. 100 2 A, 100 Hz
2. 50 2 A, 50 Hz
3. 100 2 A, 100 Hz
4. 100 A, 50 Hz

Two liquids A and B have A and B as contact angles in a capillary tube. If K = A / B, then identify the correct statement:

1. K is negative, then liquid A and liquid B have convex meniscus.
2. K is negative, then liquid A and liquid B have concave meniscus.
3. K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.
4. K is negative, then liquid A has concave meniscus and liquid B has convex meniscus.

Which of the following are correct expressions for torque acting on a body? ( r = position vector; p = linear momentum; L = angular momentum; = angular acceleration; I = moment of inertia; F = force; t = time) Choose the correct answer from the options given below:

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

Two infinite identical charged sheets and a charged spherical body of charge density ' ' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is: [figure]

1. | EA | = | EB |; EC > ED
2. EA = EB; EC = ED
3. EC ED; EA > EB
4. EA > EB; EC = ED

Considering the Bohr model of hydrogen-like atoms, the ratio of the radius of 5th orbit of the electron in Li2+ and He+ is

1. 32
2. 23
3. 49
4. 94

When an object is placed 40 cm away from a spherical mirror an image of magnification 12 is produced. To obtain an image with magnification of 13, the object is to be moved :

1. 20 cm away from the mirror.
2. 20 cm towards the mirror.
3. 80 cm away from the mirror.
4. 40 cm away from the mirror.

In an experiment with a closed organ pipe, it is filled with water by ( 15 )th of its volume. The frequency of the fundamental note will change by

1. 20\%
2. 25\%
3. -20\%
4. -25\%

A body of mass m is suspended by two strings making angles 1 and 2 with the horizontal ceiling with tensions T1 and T2 simultaneously. T1 and T2 are related by T1 = 3T2, the angles 1 and 2 are

1. 1 = 30 , 2 = 60 with T2 = 3mg4
2. 1 = 45 , 2 = 45 with T2 = 3mg4
3. 1 = 30 , 2 = 60 with T2 = 4mg5
4. 1 = 60 , 2 = 30 with T2 = mg2

A small mirror of mass m is suspended by a massless thread of length l. Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror (c = speed of light in vacuum and g = acceleration due to gravity)

1. = Emc gl
2. = E2mc gl
3. = 3E4mc gl
4. = 2Emc gl

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

The Boolean expression Y = A BC + A C can be realised with which of the following gate configurations. Choose the correct answer from the options given below:

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

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are 3 10-7 m and 600 m/s, respectively. Find the frequency of its collisions.

1. 5 108/s
2. 9 105/s
3. 2 1010/s
4. 2 109/s

If L and P represent the angular momentum and linear momentum respectively of a particle of mass 'm' having position vector as r = a( i t + j t). The direction of force is

1. Opposite to the direction of L
2. Opposite to the direction of L P
3. Opposite to the direction of r
4. Opposite to the direction of P

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

Two small spherical balls of mass 10 g each with charges -2 and 2 , are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charge sheet with uniform charge density of 100 /m2 such that length of rod makes an angle of 30 with electric field generated by charge sheet. Net torque acting on the rod is: (Take 0 = 8.85 10-12 C2/Nm2)

1. 1.12 Nm
2. 2.24 Nm
3. 11.2 Nm
4. 112 Nm

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is x5 where x = .

Distance between object and its image (magnified by - 13) is 30 cm. The focal length of the mirror used is ( x4 )cm, where magnitude of value of x is .

Two slabs with square cross section of different materials (1, 2) with equal sides (l) and thickness d1 and d2 such that d2 = 2d1 and l > d2. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is 2 = 2 1. If the shear modulus of material 1 is 4 109 N/m2, then shear modulus of material 2 is x 109 N/m2, where value of x is .

Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of 1 2 Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm/s, induced emf between points A and E is mV. [figure]

Four capacitors each of capacitance 16 are connected as shown in the figure. The capacitance between points A and B is : (in ). [figure]

For A2 + B2 2AB Ea for forward and backward reaction are 180 and 200 kJ mol-1 respectively. If catalyst lowers Ea for both reactions by 100 kJ mol-1. Which of the following statement is correct?

1. Catalyst does not alter the Gibbs energy change of a reaction.
2. The enthalpy change for the reaction is +20 kJ mol-1.
3. Catalyst can cause non-spontaneous reactions to occur.
4. The enthalpy change for the catalysed reaction is different from that of uncatalysed reaction.

Predict the major product of the following reaction sequence: [figure]

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

Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect? (Bohr's radius is represented by a0)

1. The probability density of finding the electron is maximum at the nucleus
2. The total energy of the electron is maximum when it is at a distance a0 from the nucleus
3. The electron can be found at a distance 2a0 from the nucleus
4. The 1s orbital is spherically symmetrical

Rate law for a reaction between A and B is given by r = k[A]n[B]m If concentration of A is doubled and concentration of B is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction ( r2r1 ) is

1. (n-m)
2. 2(n-m)
3. 12m+n
4. (m+n)

Pair of transition metal ions having the same number of unpaired electrons is

1. Ti3+, Mn2+
2. Ti2+, Co2+
3. Fe3+, Cr2+
4. V2+, Co2+

On charging the lead storage battery, the oxidation state of lead changes from x1 to y1 at the anode and from x2 to y2 at the cathode. The values of x1, y1, x2, y2 are respectively :

1. 0, +2, +4, +2
2. +2, 0, 0, +4
3. +4, +2, 0, +2
4. +2, 0, +2, +4

Aldol condensation is a popular and classical method to prepare , -unsaturated carbonyl compounds. This reaction can be both intermolecular and intramolecular. Predict which one of the following is not a product of intramolecular aldol condensation?

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

Benzene is treated with oleum to produce compound (X) which when further heated with molten sodium hydroxide followed by acidification produces compound (Y). The compound Y is treated with zinc metal to produce compound (Z). Identify the structure of compound (Z) from the following options.

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

One mole of an ideal gas expands isothermally and reversibly from 10 dm3 to 20 dm3 at 300 K. U, q and work done in the process respectively are Given: R = 8.3 J K-1 mol-1 10 = 2.3 2 = 0.30 3 = 0.48

1. 0, 21.84 kJ, -1.726 J
2. 0, 21.84 kJ, 21.84 kJ
3. 0, 1.718 kJ, -1.718 kJ
4. 0, -17.18 kJ, 1.718 J

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

Which one of the following complexes will have o = 0 and = 5.96 B.M.?

1. [FeF6]4-
2. [Mn(SCN)6]4-
3. [Co(NH3)6]3+
4. [Fe(CN)6]4-

The major product (A) formed in the following reaction sequence is [figure]

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

Given below are two statements: In the light of given 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. Statement I is false but Statement II is true
4. Both Statement I and Statement II are False

Number of stereoisomers possible for the complexes, [CrCl3(py)3] and [CrCl2(ox)2]3- are respectively (py = pyridine, ox = oxalate)

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

An organic compound (X) with molecular formula C3H6O is not readily oxidised. On reduction it gives C3H8O (Y) which reacts with HBr to give a bromide (Z) which is converted to Grignard reagent. This Grignard reagent on reaction with (X) followed by hydrolysis gives 2,3-dimethylbutan-2-ol. Compounds (X), (Y) and (Z) respectively are:

1. CH3CH2CHO, CH3CH2CH2OH, CH3CH2CH2Br
2. CH3COCH3, CH3CH(OH)CH3, CH3CH(Br)CH3
3. CH3COCH3, CH3CH2CH2OH, CH3CH(Br)CH3
4. CH3CH2CHO, CH3CH=CH2, CH3CH(Br)CH3

Let us consider a reversible reaction at temperature, T. In this reaction, both H and S were observed to have positive values. If the equilibrium temperature is Te, then the reaction becomes spontaneous at:

1. Te > T
2. T > Te
3. T = Te
4. Te = 5T

Which of the following molecule(s) show/s paramagnetic behavior? Choose the correct answer from the options given below:

1. A & C only
2. A & E Only
3. A & D Only
4. B Only

Identify the pair of reactants that upon reaction, with elimination of HCl will give rise to the dipeptide Gly-Ala.

1. NH2-CH2-COOH and NH2- CH3 |CH-COOH
2. NH2-CH2-COCl and NH3- CH3 |CH-COCl
3. NH2-CH2-COCl and NH2- CH3 |CH-COOH
4. NH2-CH2-COOH and NH2- CH3 |CH-COCl

Given below are the pairs of group 13 elements showing their relation in terms of atomic radius. (B < Al), (Al < Ga), (Ga < In) and (In < Tl). Identify the elements present in the incorrect pair and in that pair find out the element (X) that has higher ionic radius (M3+) than the other one. The atomic number of the element (X) is

1. 49
2. 81
3. 31
4. 13

XY is the membrane/partition between two chambers 1 and 2 containing sugar solutions of concentration c1 and c2 (c1 > c2) mol L-1. For the reverse osmosis to take place identify the correct condition. (Here p1 and p2 are pressures applied on chamber 1 and 2.) [figure] Choose the correct answer from the options given below:

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

The pH of a 0.01 M weak acid HX (Ka = 4 10-10) is found to be 5. Now the acid solution is diluted with excess of water so that the pH of the solution changes to 6. The new concentration of the diluted weak acid is given as x 10-4 M. The value of x is (nearest integer)

In Dumas' method for estimation of nitrogen 1 g of an organic compound gave 150 mL of nitrogen collected at 300 K temperature and 900 mm Hg pressure. The percentage composition of nitrogen in the compound is % (nearest integer) (Aqueous tension at 300 K = 15 mm Hg)

Fortification of food with iron is done using FeSO4 7H2O. The mass in grams of the FeSO4 7H2O required to achieve 12 ppm of iron in 150 kg of wheat is (Nearest integer) [Given: Molar mass of Fe, S and O respectively are 56, 32 and 16 g mol-1]

KMnO4 acts as an oxidising agent in acidic medium. 'X' is the difference between the oxidation states of Mn in reactant and product. 'Y' is the number of 'd' electrons present in the brown red precipitate formed at the end of the acetate ion test with neutral ferric chloride. The value of X + Y is .

The total number of hydrogen bonds of a DNA-double Helix strand whose one strand has the following sequence of bases is . 5'-G-G-C-A-A-A-T-C-G-G-C-T-A-3'

Let f : R R be a continuous function satisfying f(0) = 1 and f(2x) - f(x) = x for all x R. If n \f(x) - f ( x2n ) \ = G(x), then r=110 G (r2 ) is equal to

1. 215
2. 420
3. 385
4. 540

Let the shortest distance between the lines x-33 = y- -1 = z-31 and x+3-3 = y+72 = z- 4 be 3 30. Then the positive value of 5 + is

1. 42
2. 40
3. 48
4. 46

Let A = \1, 6, 11, 16, \ and B = \9, 16, 23, 30, \ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then n(A B) is

1. 3814
2. 4003
3. 4027
4. 3761

The length of the latus-rectum of the ellipse, whose foci are (2, 5) and (2, -3) and eccentricity is 45, is

1. 503
2. 185
3. 65
4. 103

Consider the equation x2 + 4x - n = 0, where n [20, 100] is a natural number. Then the number of all distinct values of n, for which the given equation has integral roots, is equal to

1. 6
2. 5
3. 8
4. 7

Consider the sets A = \(x, y) R R : x2 + y2 = 25 \, B = \(x, y) R R : x2 + 9y2 = 144 \, C = \(x, y) Z Z : x2 + y2 4 \ and D = A B. The total number of one-one functions from the set D to the set C is:

1. 15120
2. 18290
3. 17160
4. 19320

1 + 3 + 52 + 7 + 92 + up to 40 terms is equal to

1. 40870
2. 41880
3. 43890
4. 33980

If 10 4 + 15 4 = 6, then the value of 27 cosec6 + 8 6 16 8 is

1. 25
2. 35
3. 15
4. 34

The value of -11 (1 + |x| - x ) ex + ( |x| - x ) e-xex + e-x dx is equal to

1. 1 + 2 23
2. 1 - 2 23
3. 2 + 2 23
4. 3 - 2 23

Let f : [0, ) R be a differentiable function such that f(x) = 1 - 2x + 0x ex-t f(t) dt for all x [0, ). Then the area of the region bounded by y = f(x) and the coordinate axes is

1. 5
2. 2
3. 2
4. 12

The probability of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is

1. 129182
2. 1726
3. 1926
4. 103182

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is

1. 1115
2. 215
3. 35
4. 2875

Consider two vectors u = 3 i - j and v = 2 i + j - k, > 0. The angle between them is given by -1 ( 52 7 ). Let v = v1 + v2, where v1 is parallel to u and v2 is perpendicular to u. Then the value of | v1 |2 + | v2 |2 is equal to

1. 232
2. 252
3. 10
4. 14

For an integer n 2, if the arithmetic mean of all coefficients in the binomial expansion of (x + y)2n - 3 is 16, then the distance of the point P (2n - 1, n2 - 4n ) from the line x + y = 8 is

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

Let A and B be two distinct points on the line L : x - 63 = y - 72 = z - 7-2. Both A and B are at a distance 2 17 from the foot of perpendicular drawn from the point (1, 2, 3) on the line L. If O is the origin, then OA OB is equal to

1. 49
2. 21
3. 47
4. 62

Let f, g : (1, ) R be defined as f(x) = 2x + 35x + 2 and g(x) = 2 - 3x1 - x. If the range of the function f g : [2, 4] R is [ , ], then 1 - is equal to

1. 56
2. 2
3. 29
4. 68

If x 1+ (x - 1)(6 + (x - 1)) + (1 - x)(x - 1)3 = -1, where , R, then + is equal to

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

Let the three sides of a triangle lie on the lines 4x - 7y + 10 = 0, x + y = 5 and 7x + 4y = 15. Then the distance of its orthocentre from the orthocentre of the triangle formed by the lines x = 0, y = 0 and x + y = 1 is

1. 20
2. 20
3. 5
4. 5

In the expansion of ( [3]2 + 1 [3]3 )n, n N, if the ratio of 15th term from the beginning to the 15th term from the end is 16, then the value of nC3 is

1. 4960
2. 2300
3. 1040
4. 4060

Considering the principal values of the inverse trigonometric functions, -1 ( 32x + 12 1 - x2 ), - 12 < x < 1 2, is equal to

1. -5 6 - -1x
2. 5 6 - -1x
3. 6 + -1x
4. 4 + -1x

Let C be the circle x2 + (y - 1)2 = 2, E1 and E2 be two ellipses whose centres lie at the origin and major axes lie on x-axis and y-axis respectively. Let the straight line x + y = 3 touch the curves C, E1 and E2 at P(x1, y1), Q(x2, y2) and R(x3, y3) respectively. Given that P is the mid point of the line segment QR and PQ = 2 23, the value of 9(x1y1 + x2y2 + x3y3) is equal to .

Let m and n be the number of points at which the function f(x) = \x, x3, x5, , x21 \, x R, is not differentiable and not continuous, respectively. Then m + n is equal to .

Let A = bmatrix & 0 & - \ 0 & 1 & 0 \ & 0 & bmatrix. If for some (0, ), A2 = AT, then the sum of the diagonal elements of the matrix (A + I)3 + (A - I)3 - 6A is equal to .

If the area of the region \(x, y) : |x - 5| y 4 x\ is A, then 3A is equal to .

Let A = \z C : |z - 2 - i| = 3\, B = \z C : Re(z - iz) = 2\ and S = A B. Then z S |z|2 is equal to .