JEE Main 2025 (Online) 2nd April Morning Shift

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density + and -2 . The force experienced by a point charge +q placed at the mid point between two plates will be: [figure]

1. 3 q4 0
2. 3 q2 0
3. q4 0
4. q2 0

A monochromatic light of wavelength is incident on a metallic plate having work function . An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point B. The distance between A and B is : (Given : The magnitude of charge of an electron is e and mass is m, h is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

1. 2m ( hc - )/eB
2. 8 m ( hc - )/eB
3. m(hc/ - )/eB
4. 2 m(hc/ - )/eB

[figure] A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image of an object 'O', is : (C is the center of curvature of the spherical surface and R is the radius of curvature)

1. 0.24 m left to the spherical surface
2. 0.24 m right to the spherical surface
3. 0.4 m left to the spherical surface
4. 0.4 m right to the spherical surface

A river is flowing from west to east direction with speed of 9 km h-1. If a boat capable of moving at a maximum speed of 27 km h-1 in still water, crosses the river in half a minute, while moving with maximum speed at an angle of 150 to direction of river flow, then the width of the river is :

1. 112.5 m
2. 75 m
3. 300 m
4. 112.5 3 m

Moment of inertia of a rod of mass 'M' and length 'L' about an axis passing through its center and normal to its length is ' '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :

1. /4
2. /8
4. /2

Let B1 be the magnitude of magnetic field at center of a circular coil of radius R carrying current I. Let B2 be the magnitude of magnetic field at an axial distance 'x' from the center. For x : R = 3 : 4, B2B1 is :

1. 64 : 125
2. 25 : 16
3. 4 : 5
4. 16 : 25

A light wave is propagating with plane wave fronts of the type x + y + z = constant. The angle made by the direction of wave propagation with the x-axis is :

1. -1(2/3)
2. -1 ( 1 3 )
3. -1 ( 13 )
4. -1 ( 23 )

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

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

A particle is subjected to two simple harmonic motions as : x1 = 7 5t cm and x2 = 2 7 (5t + 3 )cm where x is displacement and t is time in seconds. The maximum acceleration of the particle is x 10-2 m s-2. The value of x is :

1. 5 7
2. 125
3. 25 7
4. 175

A square lamina OABC of length 10 cm is pivoted at 'O'. Forces act at lamina as shown in figure. If lamina remains stationary, then the magnitude of F is : [figure]

1. 10 N
2. 0 (zero)
3. 10 2 N
4. 20 N

A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is:

1. (3d/4, 0, 0)
2. (d/4, 0, 0)
3. (4d/3, 0, 0)
4. (d/3, 0, 0)

A slanted object AB is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is : [figure]

1. -
2. - 2
3. -45
4. +45

Considering Bohr's atomic model for hydrogen atom : Choose the correct answer from the options given below :

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

In an adiabatic process, which of the following statements is true?

1. The internal energy of the gas decreases as the temperature increases
2. The molar heat capacity is zero
3. Work done by the gas equals the increase in internal energy
4. The molar heat capacity is infinite

The equation for real gas is given by (P + aV2 )(V - b) = RT, where P, V, T and R are the pressure, volume, temperature and gas constant, respectively. The dimension of ab-2 is equivalent to that of :

1. Compressibility
2. Planck's constant
3. Energy density
4. Strain

The relationship between the magnetic susceptibility ( ) and the magnetic permeability ( ) is given by : ( 0 is the permeability of free space and r is relative permeability)

1. = 0 - 1
2. = r 0 + 1
3. = r + 1
4. = 1 - 0

The battery of a mobile phone is rated as 4.2 V, 5800 mAh. How much energy is stored in it when fully charged?

1. 87.7 kJ
2. 43.8 kJ
3. 48.7 kJ
4. 24.4 kJ

A zener diode with 5 V zener voltage is used to regulate an unregulated dc voltage input of 25 V. For a 400 resistor connected in series, the zener current is found to be 4 times load current. The load current (IL) and load resistance (RL) are :

1. IL = 0.02 mA; RL = 250
2. IL = 10 A; RL = 0.5
3. IL = 10 mA; RL = 500
4. IL = 20 mA; RL = 250

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m, would be: [figure]

1. 20 rad/s
2. 30 rad/s
3. 10 rad/s
4. 0 rad/s

A small bob of mass 100 mg and charge +10 is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density ' ' as shown in figure. If string subtends an angle of 45 with the sheet at equilibrium the charge density of sheet will be: (Given, 0 = 8.85 10-12 Fm and acceleration due to gravity, g = 10 ms2) [figure]

1. 1.77 nC/m2
2. 0.885 nC/m2
3. 885 nC/m2
4. 17.7 nC/m2

A steel wire of length 2 m and Young's modulus 2.0 1011 N m-2 is stretched by a force. If Poisson's ratio and transverse strain for the wire are 0.2 and 10-3 respectively, then the elastic potential energy density of the wire is 105 (in SI units).

A is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. B is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If A B = (1 + 1n ), then the value of n is .

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 cm2 with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density 1.5 103 kg/m3. What force one needs to apply on the hinged door so that it does not get opened? (Acceleration due to gravity = 10 m/s2)

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is 30 in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is .

A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next 32x distance. The average velocity in this motion is 507 m/s. If v1 is 5 m/s then v2 = m/s.

Consider the following compound (X) [figure] The most stable and least stable carbon radicals, respectively, produced by homolytic cleavage of corresponding C-H bond are :

1. III, II
2. II, IV
3. I, IV
4. II, I

CaCO3(s)+2HCl(aq) CaCl2(aq)+CO2(g)+H2O(l) Consider the above reaction, what mass of CaCl2 will be formed if 250 mL of 0.76 M HCl reacts with 1000 g of CaCO3 ? (Given : Molar mass of Ca, C, O, H and Cl are 40, 12, 16, 1 and 35.5 g mol-1, respectively)

1. 3.908 g
2. 2.636 g
3. 10.545 g
4. 5.272 g

If equal volumes of AB2 and XY (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of AY2 at 300 K ? (Given Ksp (at 300 K) for AY2 = 5.2 10-7)

1. 2.0 10-4 M AB2, 0.8 10-3 M XY
2. 2.0 10-2 M AB2, 2.0 10-2 M XY
3. 1.5 10-4 M AB2, 1.5 10-3 M XY
4. 3.6 10-3 M AB2, 5.0 10-4 M XY

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

Designate whether each of the following compounds is aromatic or not aromatic. [figure]

1. a, c, d, e, h aromatic and b, f, g not aromatic
2. b, e, f, g aromatic and a, c, d, h not aromatic
3. a, b, c, d aromatic and e, f, g, h not aromatic
4. e, g aromatic and a, b, c, d, f, h not aromatic

Choose the correct tests with respective observations. Choose the correct answer from the options given below :

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

A solution is made by mixing one mole of volatile liquid A with 3 moles of volatile liquid B. The vapour pressure of pure A is 200 mm Hg and that of the solution is 500 mm Hg. The vapour pressure of pure B and the least volatile component of the solution, respectively, are:

1. 1400 mm Hg, A
2. 1400 mm Hg, B
3. 600 mm Hg, A
4. 600 mm Hg, B

A molecule with the formula AX4Y has all its elements from p-block. Element A is rarest, monoatomic, non-radioactive from its group and has the lowest ionization enthalpy value among A, X and Y. Elements X and Y have first and second highest electronegativity values respectively among all the known elements. The shape of the molecule is:

1. Pentagonal planar
2. Square pyramidal
3. Trigonal bipyramidal
4. Octahedral

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

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

On complete combustion 1.0 g of an organic compound (X) gave 1.46 g of CO2 and 0.567 g of H2O. The empirical formula mass of compound (X) is g. (Given molar mass in g mol-1 C : 12, H : 1, O : 16)

1. 60
2. 45
3. 30
4. 15

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

An optically active alkyl halide C4H9Br [A] reacts with hot KOH dissolved in ethanol and forms alkene [B] as major product which reacts with bromine to give dibromide [C]. The compound [C] is converted into a gas [D] upon reacting with alcoholic NaNH2. During hydration 18 gram of water is added to 1 mole of gas [D] on warming with mercuric sulphate and dilute acid at 333 K to form compound [E]. The IUPAC name of compound [E] is :

1. Butan-2-ol
2. But-2-yne
3. Butan-2-one
4. Butan-1-al

[figure] Two vessels A and B are connected via stopcock. The vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true ?

1. dq 0
2. The pressure in the vessel B before opening the stopcock is zero
3. dw 0
4. dU 0

Among SO2, NF3, NH3, XeF2, ClF3 and SF4, the hybridization of the molecule with nonzero dipole moment and highest number of lone-pairs of electrons on the central atom is

1. sp3
2. dsp2
3. sp3d2
4. sp3d

Which of the following graph correctly represents the plots of KH at 1 bar for gases in water versus temperature?

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

According to Bohr's model of hydrogen atom, which of the following statement is incorrect?

1. Radius of 4th orbit is four times larger than that of 2nd orbit
2. Radius of 8th orbit is four times larger than that of 4th orbit
3. Radius of 6th orbit is three times larger than that of 4th orbit
4. Radius of 3rd orbit is nine times larger than that of 1st orbit

Identify the correct statement among the following :

1. All naturally occurring amino acids except glycine contain one chiral centre.
2. Amino acid, cysteine can easily undergo dimerisation due to the presence of free SH group.
3. Glutamic acid is the only amino acid that contains a –COOH group at the side chain.
4. All naturally occurring amino acids are optically active.

The correct order of basic nature in aqueous solution for the bases NH3, H2N-NH2, CH3CH2NH2, (CH3CH2)2NH and (CH3CH2)3N is :

1. NH3 < H2N-NH2 < (CH3CH2)3N < CH3CH2NH2 < (CH3CH2)2NH
2. H2N-NH2 < NH3 < (CH3CH2)3N < CH3CH2NH2 < (CH3CH2)2NH
3. H2N-NH2 < NH3 < CH3CH2NH2 < (CH3CH2)3N < (CH3CH2)2NH
4. NH3 < H2N-NH2 < CH3CH2NH2 < (CH3CH2)2NH < (CH3CH2)3N

The property/properties that show irregularity in first four elements of group-17 is/are Choose the correct answer from the options given below :

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

Consider the following molecules: [figure] The correct order of rate of hydrolysis is :

1. p > q > r > s
2. r > q > p > s
3. p > r > q > s
4. q > p > r > s

For the reaction A products. [figure] The concentration of A at 10 minutes is 10-3 mol L-1 (nearest integer). The reaction was started with 2.5 mol L-1 of A.

0.1 mol of the following given antiviral compound (P) will weigh 10-1 g (nearest integer). [figure] (Given : molar mass in g mol-1 H : 1, C : 12, N : 14, O : 16, F : 19, I : 127)

Consider the following electrochemical cell at standard condition. Au(s) | QH2, Q | NH4X(0.01 M) || Ag+(1 M) | Ag(s) Ecell = +0.4 V The couple QH2/Q represents quinhydrone electrode, the half cell reaction is given below: [figure] [Given : E0 Ag+/Ag = +0.8 V and 2.303RTF = 0.06 V] The pKb value of the ammonium halide salt (NH4X) used here is . (nearest integer)

Consider the following equilibrium, CO(g) + 2H2(g) CH3OH(g) 0.1 mol of CO along with a catalyst is present in a 2 dm3 flask maintained at 500 K. Hydrogen is introduced into the flask until the pressure is 5 bar and 0.04 mol of CH3OH is formed. The Kp is 10-3 (nearest integer). Given : R = 0.08 dm3 bar K-1 mol-1 Assume only methanol is formed as the product and the system follows ideal gas behaviour.

A transition metal (M) among Mn, Cr, Co and Fe has the highest standard electrode potential (M3+/M2+). It forms a metal complex of the type [M(CN)6]4-. The number of electrons present in the eg orbital of the complex is .

Let A = bmatrix & -1 \ 6 & bmatrix, > 0, such that (A) = 0 and + = 1. If I denotes 2 2 identity matrix, then the matrix (I + A)8 is :

1. bmatrix 257 & -64 \ 514 & -127 bmatrix
2. bmatrix 766 & -255 \ 1530 & -509 bmatrix
3. bmatrix 1025 & -511 \ 2024 & -1024 bmatrix
4. bmatrix 4 & -1 \ 6 & -1 bmatrix

Let the vertices Q and R of the triangle PQR lie on the line x+35 = y-12 = z+43, QR = 5 and the coordinates of the point P be (0, 2, 3). If the area of the triangle PQR is mn then :

1. 2m - 5 21 n = 0
2. m - 5 21 n = 0
3. 5m - 21 2 n = 0
4. 5m - 2 21 n = 0

Let a R and A be a matrix of order 3 3 such that (A) = -4 and A + I = bmatrix 1 & a & 1 \ 2 & 1 & 0 \ a & 1 & 2 bmatrix, where I is the identity matrix of order 3 3. If ((a + 1) adj((a - 1)A)) is 2m 3n, m, n \0, 1, 2, , 20\, then m + n is equal to :

1. 14
2. 17
3. 15
4. 16

If [-2 , 2 ], then the number of solutions of 2 2 2 + (2 - 6) - 3 = 0, is equal to:

1. 8
2. 6
3. 10
4. 12

If S and S′ are the foci of the ellipse x218 + y29 = 1 and P be a point on the ellipse, then (SP S'P) + (SP S'P) is equal to :

1. 3(6 + 2)
2. 3(1 + 2)
3. 27
4. 9

Let the focal chord PQ of the parabola y2 = 4x make an angle of 60 with the positive x axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the y-axis at the point (0, ), then 5 2 is equal to:

1. 15
2. 25
3. 20
4. 30

If the function f(x) = 2x3 - 9ax2 + 12a2x + 1, where a > 0, attains its local maximum and local minimum values at p and q, respectively, such that p2 = q, then f(3) is equal to :

1. 55
2. 37
3. 10
4. 23

Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be 5, 6 and 7 square units respectively. Then the area (in square units) of the BCD is equal to :

1. 110
2. 12
3. 340
4. 7 3

Let z be a complex number such that |z| = 1. If 2 + k2 zk + z = kz, k R, then the maximum distance of k + ik2 from the circle |z - (1 + 2i)| = 1 is :

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

Let one focus of the hyperbola H : x2a2 - y2b2 = 1 be at ( 10, 0) and the corresponding directrix be x = 9 10. If e and l respectively are the eccentricity and the length of the latus rectum of H, then 9(e2 + l) is equal to :

1. 12
2. 14
3. 15
4. 16

The largest n N such that 3n divides 50 ! is :

1. 22
2. 20
3. 21
4. 23

Let Pn = n + n, n N. If P10 = 123, P9 = 76, P8 = 47 and P1 = 1, then the quadratic equation having roots 1 and 1 is :

1. x2 + x - 1 = 0
2. x2 - x + 1 = 0
3. x2 + x + 1 = 0
4. x2 - x - 1 = 0

If a is a nonzero vector such that its projections on the vectors 2 i - j + 2 k, i + 2 j - 2 k and k are equal, then a unit vector along a is :

1. 1 155(-7 i + 9 j + 5 k)
2. 1 155(-7 i + 9 j - 5 k)
3. 1 155(7 i + 9 j - 5 k)
4. 1 155(7 i + 9 j + 5 k)

If the system of linear equations 3x + y + z = 3 2x + y - z = -3 x + 2y + z = 4 has infinitely many solutions, then the value of 22 - 9 is :

1. 31
2. 37
3. 43
4. 49

Let f : R R be a twice differentiable function such that ( x y)(f(2x + 2y) - f(2x - 2y)) = ( x y)(f(2x + 2y) + f(2x - 2y)), for all x, y R. If f'(0) = 12, then the value of 24f'' ( 5 3 ) is :

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

Let A be the set of all functions f : Z Z and R be a relation on A such that R = \(f, g) : f(0) = g(1) and f(1) = g(0)\. Then R is :

1. Symmetric and transitive but not reflexive
2. Symmetric but neither reflexive nor transitive
3. Transitive but neither reflexive nor symmetric
4. Reflexive but neither symmetric nor transitive

The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is equal to :

1. 360
2. 2520
3. 1820
4. 45

For , , R, if x 0 x2 x + ( - 1)ex2 2x - x = 3, then + - is equal to :

1. -1
2. 4
3. 6
4. 7

The term independent of x in the expansion of ( (x + 1)(x2/3 + 1 - x1/3) - (x - 1)(x - x1/2) )10, x > 1, is :

1. 240
2. 120
3. 150
4. 210

Let a1, a2, a3, be in an A.P. such that k=112 a2k-1 = - 725a1, a1 0. If k=1n ak = 0, then n is :

1. 18
2. 17
3. 11
4. 10

Three distinct numbers are selected randomly from the set \1, 2, 3, , 40\. If the probability, that the selected numbers are in an increasing G.P., is mn, (m, n) = 1, then m + n is equal to .

Let f : R R be a thrice differentiable odd function satisfying f'(x) 0, f''(x) = f(x), f(0) = 0, f'(0) = 3. Then 9f( e 3) is equal to .

If the area of the region \(x, y) : |4 - x2 | y x2, y 4, x 0 \ is ( 80 2 - ), , N, then + is equal to .

The absolute difference between the squares of the radii of the two circles passing through the point (-9, 4) and touching the lines x + y = 3 and x - y = 3, is equal to .

Let [.] denote the greatest integer function. If 0e3 [ 1ex-1 ] dx = - e 2, then 3 is equal to .