JEE Main 2025 (Online) 4th April Evening Shift

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :

1. 45 cm
2. 15 cm
3. 22.5 cm
4. 7.5 cm

A radioactive material P first decays into Q and then Q decays to non-radioactive material R. Which of the following figure represents time dependent mass of P, Q and R ?

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

Displacement of a wave is expressed as x(t)=5 (628t+ 2 )m. The wavelength of the wave when its velocity is 300 m/s is : ( =3.14)

1. 0.33 m
2. 0.5 m
3. 3 m
4. 5 m

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB at 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC ? [figure]

1. 2E
2. Zero
3. E/2
4. 2E

A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is 8 m/s. The speed of the particle on the rim of the wheel at the same level as the centre of the wheel, will be :

1. 4 2 m/s
2. 8 m/s
3. 4 m/s
4. 8 2 m/s

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of [MP LQ TR AS ]. The values of P and Q are :

1. -1, 0
2. 0, -1
3. -1, 1
4. 1, -1

The displacement x versus time graph is shown below. [figure] Choose the correct answer from the options given below :

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

Consider a rectangular sheet of solid material of length l = 9 cm and width d = 4 cm. The coefficient of linear expansion is = 3.1 10-5 K-1 at room temperature and one atmospheric pressure. The mass of sheet m = 0.1 kg and the specific heat capacity Cv = 900 J kg-1 K-1. If the amount of heat supplied to the material is 8.1 102 J then change in area of the rectangular sheet is :

1. 2.0 10-6 m2
2. 6.0 10-7 m2
3. 3.0 10-7 m2
4. 4.0 10-7 m2

An object is kept at rest at a distance of 3R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is : (Assume M = mass of earth, G = Universal gravitational constant)

1. 3GMR
2. 2GMR
3. GM2R
4. GMR

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 105 N at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement of the rod axis from its original position would be : (shear modulus, G = 1010 N/m2)

1. 1/160
2. 1/2
3. 1/4
4. 1/40

For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equal to 15 cm. The vernier scale attached to the microscope has 25 divisions equal to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm) :

1. 0.002
2. 0.0025
3. 0.0005
4. 0.001

Three parallel plate capacitors C1, C2 and C3 each of capacitance 5 are connected as shown in figure. The effective capacitance between points A and B, when the space between the parallel plates of C1 capacitor is filled with a dielectric medium having dielectric constant of 4, is : [figure]

1. 9
2. 30
3. 7.5
4. 22.5

A block of mass 25 kg is pulled along a horizontal surface by a force at an angle 45 with the horizontal. The friction coefficient between the block and the surface is 0.25. The block travels at a uniform velocity. The work done by the applied force during a displacement of 5 m of the block is :

1. 490 J
2. 970 J
3. 735 J
4. 245 J

There are two vessels filled with an ideal gas where volume of one is double the volume of the other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa).

1. 24
2. 4.4
3. 18
4. 6

Two polarisers P1 and P2 are placed in such a way that the intensity of the transmitted light will be zero. A third polariser P3 is inserted in between P1 and P2, at particular angle between P2 and P3. The transmitted intensity of the light passing through all three polarisers is maximum. The angle between the polarisers P2 and P3 is :

1. /6
2. 3
3. 4
4. /8

Match List - I with List - II. Q = Heat supplied W = Work done by the system U = Change in internal energy P = Pressure of the system V = Change in volume of the system Choose the correct answer from the options given below :

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

There are 'n' number of identical electric bulbs, each is designed to draw a power p independently from the mains supply. They are now joined in series across the mains supply. The total power drawn by the combination is :

1. np
2. p
3. pn2
4. pn

From the combination of resistors with resistance values R1 = R2 = R3 = 5 and R4 = 10 , which of the following combination is the best circuit to get an equivalent resistance of 6 ?

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

Consider an n-type semiconductor in which ne and nh are number of electrons and holes, respectively. Choose the correct answer from the options given below :

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

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

A solid sphere with uniform density and radius R is rotating initially with constant angular velocity ( 1) about its diameter. After some time during the rotation it starts losing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius becomes R/2 is x 1. The value of x is .

An inductor of self inductance 1 H is connected in series with a resistor of 100 ohm and an ac supply of 100 volt, 50 Hz. Maximum current flowing in the circuit is A.

If an optical medium possesses a relative permeability of 10 and relative permittivity of 10.0885, then the velocity of light is greater in vacuum than that in this medium by times. ( 0 = 4 10-7 H/m, 0 = 8.85 10-12 F/m, c = 3 108 m/s)

A particle of charge 1.6 and mass 16 is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is s (rounded off to the nearest integer). ( = 3.14)

In a Young's double slit experiment, two slits are located 1.5 mm apart. The distance of screen from slits is 2 m and the wavelength of the source is 400 nm. If the 20 maxima of the double slit pattern are contained within the central maximum of the single slit diffraction pattern, then the width of each slit is x 10-3 cm, where x-value is .

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

Consider the following plots of log of rate constant k (log k) vs 1T for three different reactions. The correct order of activation energies of these reactions is : [figure]

1. Ea2 > Ea1 > Ea3
2. Ea1 > Ea3 > Ea2
3. Ea3 > Ea2 > Ea1
4. Ea1 > Ea2 > Ea3

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

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

Which among the following compounds give yellow solid when reacted with NaOI/NaOH? Choose the correct answer from the options given below :

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

Consider the ground state of chromium atom (Z = 24). How many electrons are with Azimuthal quantum number l = 1 and l = 2 respectively ?

1. 16 and 5
2. 12 and 5
3. 12 and 4
4. 16 and 4

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

The IUPAC name of the following compound is: HC C-CH2- OH |CH-CH2-CH=CH2

1. 4-Hydroxyhept-6-en-1-yne
2. Hept-1-en-6-yn-4-ol
3. Hept-6-en-1-yn-4-ol
4. 4-Hydroxyhept-1-en-6-yne

Half life of zero order reaction A product is 1 hour, when initial concentration of reactant is 2.0 mol L-1. The time required to decrease concentration of A from 0.50 to 0.25 mol L-1 is :

1. 0.5 hour
2. 15 min
3. 60 min
4. 4 hour

The incorrect relationship in the following pairs in relation to ionisation enthalpies is :

1. Mn2+ < Fe2+
2. Mn+ < Mn2+
3. Mn+ < Cr+
4. Fe2+ < Fe3+

A toxic compound "A" when reacted with NaCN in aqueous acidic medium yields an edible cooking component and food preservative "B". "B" is converted to "C" by diborane and can be used as an additive to petrol to reduce emission. "C" upon reaction with oleum at 140 C yields an inhalable anesthetic "D". Identify "A", "B", "C" & "D", respectively :

1. Methanol; acetic acid; ethanol; diethyl ether
2. Ethanol; acetonitrile; ethylamine; ethylene
3. Methanol; formaldehyde; methyl chloride; chloroform
4. Acetaldehyde; 2-hydroxypropanoic acid; propanoic acid; dipropyl ether

In which pairs, the first ion is more stable than the second?

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

'X' is the number of electrons in t2g orbitals of the most stable complex ion among [Fe(NH3)6]3+, [FeCl6]3-, [Fe(C2O4)3]3- and [Fe(H2O)6]3+. The nature of oxide of vanadium of the type V2OX is :

1. Amphoteric
2. Acidic
3. Basic
4. Neutral

The correct order of basicity for the following molecules is : [figure]

1. R > P > Q
2. P > Q > R
3. R > Q > P
4. Q > P > R

Consider the given data : (a) HCl(g) + 10H2O(l) HCl 10H2O; H = -69.01 kJ mol-1 (b) HCl(g) + 40H2O(l) HCl 40H2O; H = -72.79 kJ mol-1 Choose the correct statement :

1. The heat of dilution for the HCl (HCl 10H2O to HCl 40H2O) is 3.78 kJ mol-1.
2. Dissolution of gas in water is an endothermic process.
3. The heat of solution depends on the amount of solvent.
4. The heat of formation of HCl solution is represented by both (a) and (b).

Consider the following molecule(X). [figure] The major product formed when the given molecule (X) is treated with HBr (1 eq) is :

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

The correct order of [FeF6]3-, [CoF6]3-, [Ni(CO)4] and [Ni(CN)4]2- complex species based on the number of unpaired electrons present is:

1. [CoF6]3- > [FeF6]3- > [Ni(CO)4] > [Ni(CN)4]2-
2. [FeF6]3- > [CoF6]3- > [Ni(CN)4]2- > [Ni(CO)4]
3. [FeF6]3- > [CoF6]3- > [Ni(CN)4]2- = [Ni(CO)4]
4. [Ni(CN)4]2- > [FeF6]3- > [CoF6]3- > [Ni(CO)4]

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

A dipeptide, "x" on complete hydrolysis gives "y" and "z". "y" on treatment with aq. HNO2 produces lactic acid. On the other hand "z" on heating gives the following cyclic molecule. [figure] Based on the information given, the dipeptide "x" is :

1. alanine-alanine
2. valine-glycine
3. valine-leucine
4. alanine-glycine

The elements of Group 13 with highest and lowest first ionisation enthalpies are respectively :

1. B & Tl
2. Tl & B
3. B & In
4. B & Ga

Sea water, which can be considered as a 6 molar (6 M) solution of NaCl, has a density of 2 g mL-1. The concentration of dissolved oxygen (O2) in sea water is 5.8 ppm. Then the concentration of dissolved oxygen (O2) in sea water, in terms of molality, is x 10-4 m. x = . (Nearest integer) Given: Molar mass of NaCl is 58.5 g mol-1 Molar mass of O2 is 32 g mol-1

The amount of calcium oxide produced on heating 150 kg limestone (75% pure) is kg. (Nearest integer) Given: Molar mass (in g mol-1) of Ca-40, O-16, C-12

A metal complex with a formula MCl4 3NH3 is involved in sp3d2 hybridisation. It upon reaction with excess of AgNO3 solution gives 'x' moles of AgCl. Consider 'x' is equal to the number of lone pairs of electrons present in the central atom of BrF5. Then the number of geometrical isomers exhibited by the complex is .

The molar conductance of an infinitely dilute solution of ammonium chloride was found to be 185 S cm2 mol-1 and the ionic conductances of hydroxide and chloride ions are 170 and 70 S cm2 mol-1, respectively. If molar conductance of 0.02 M solution of ammonium hydroxide is 85.5 S cm2 mol-1, its degree of dissociation is given by x 10-1. The value of x is . (Nearest integer)

x mg of Mg(OH)2 (molar mass = 58 g mol-1) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is mg. (Nearest integer) (Given : Mg(OH)2 is assumed to dissociate completely in H2O)

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

1. 17
2. 18
3. 15
4. 16

Let the domains of the functions f(x) = 4 3 7 (8 - 2 (x2 + 4x + 5 ) ) and g(x) = -1 ( 7x + 10x - 2 ) be ( , ) and [ , ], respectively. Then 2 + 2 + 2 + 2 is equal to :

1. 15
2. 13
3. 16
4. 14

Let the mean and the standard deviation of the observations 2, 3, 3, 4, 5, 7, a, b be 4 and 2 respectively. Then the mean deviation about the mode of these observations is :

1. 12
2. 34
3. 1
4. 2

Let the sum of the focal distances of the point P(4, 3) on the hyperbola H: x2a2 - y2b2 = 1 be 8 53. If for H, the length of the latus rectum is l and the product of the focal distances of the point P is m, then 9l2 + 6m is equal to :

1. 187
2. 184
3. 186
4. 185

Let a > 0. If the function f(x) = 6x3 - 45ax2 + 108a2x + 1 attains its local maximum and minimum values at the points x1 and x2 respectively such that x1 x2 = 54, then a + x1 + x2 is equal to :

1. 15
2. 13
3. 24
4. 18

Let the matrix A = bmatrix 1 & 0 & 0 \ 1 & 0 & 1 \ 0 & 1 & 0 bmatrix satisfy An = An-2 + A2 - I for n 3. Then the sum of all the elements of A50 is :

1. 44
2. 39
3. 52
4. 53

If a curve y = y(x) passes through the point (1, 2 ) and satisfies the differential equation (7x4 y - ex cosec y ) dxdy = x5, x 1, then at x = 2, the value of y is :

1. 2e2 + e64
2. 2e2 - e64
3. 2e2 - e128
4. 2e2 + e128

If the sum of the first 20 terms of the series 4 14 + 3 12 + 14 + 4 24 + 3 22 + 24 + 4 34 + 3 32 + 34 + 4 44 + 3 42 + 44 + is mn, where m and n are coprime, then m + n is equal to :

1. 423
2. 421
3. 422
4. 420

Let for two distinct values of p the lines y = x + p touch the ellipse E: x242 + y232 = 1 at the points A and B. Let the line y = x intersect E at the points C and D. Then the area of the quadrilateral ABCD is equal to :

1. 48
2. 20
3. 24
4. 36

The centre of a circle C is at the centre of the ellipse E: x2a2 + y2b2 = 1, a > b. Let C pass through the foci F1 and F2 of E such that the circle C and the ellipse E intersect at four points. Let P be one of these four points. If the area of the triangle PF1F2 is 30 and the length of the major axis of E is 17, then the distance between the foci of E is :

1. 12
2. 26
3. 13
4. 132

A line passing through the point A(-2, 0) touches the parabola P: y2 = x - 2 at the point B in the first quadrant. The area of the region bounded by the line AB, parabola P and the x-axis, is :

1. 3
2. 73
3. 83
4. 2

Let the product of 1 = (8 + i) + (7 + 4i) and 2 = (1 + 8i) + (4 + 7i) be + i , i = -1. Let p and q be the maximum and the minimum values of + respectively. Then p + q is equal to :

1. 130
2. 150
3. 160
4. 140

If 12 (15C1 ) + 22 (15C2 ) + 32 (15C3 ) + + 152 (15C15 ) = 2m 3n 5k, where m, n, k N, then m + n + k is equal to :

1. 20
2. 19
3. 18
4. 21

Let A be the point of intersection of the lines L1: x-71= y-50= z-3-1 and L2: x-13= y+34= z+75. Let B and C be the points on the lines L1 and L2 respectively such that AB=AC= 15. Then the square of the area of the triangle ABC is :

1. 63
2. 57
3. 60
4. 54

The sum of the infinite series -1 ( 74 )+ -1 ( 194 )+ -1 ( 394 )+ -1 ( 674 )+ is :

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

The axis of a parabola is the line y=x and its vertex and focus are in the first quadrant at distances 2 and 2 2 units from the origin, respectively. If the point (1, k) lies on the parabola, then a possible value of k is :

1. 8
2. 3
3. 9
4. 4

Let f(x)+2f ( 1x )=x2+5 and 2g(x)-3g ( 12 )=x, x>0. If = 12 f(x) dx, and = 12 g(x) dx, then the value of 9 + is :

1. 0
2. 10
3. 1
4. 11

Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of B be 36 and q respectively. Let d and D be the common differences of A.P.'s in A and B respectively such that D=d+3, d>0. If p+qp-q= 195, then p-q is equal to

1. 540
2. 450
3. 600
4. 630

Let the values of p, for which the shortest distance between the lines x+13= y4= z5 and r=(p i+2 j+ k)+ (2 i+3 j+4 k) is 1 6, be a, b, (a<b). Then the length of the latus rectum of the ellipse x2a2+ y2b2=1 is :

1. 32
2. 9
3. 18
4. 23

Let f be a differentiable function on R such that f(2)=1, f'(2)=4. Let x 0(f(2+x))3/x=e . Then the number of times the curve y=4x3-4x2-4( -7)x- meets x-axis is :

1. 3
2. 1
3. 2
4. 0

If ( 1+x2+x )10 ( 1+x2-x )9 dx= 1m ( ( 1+x2+x )n (n 1+x2-x ) )+C where C is the constant of integration and m, n N, then m+n is equal to .

A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is 1150, then n is equal to .

Let the three sides of a triangle ABC be given by the vectors 2 i- j+ k, i-3 j-5 k and 3 i-4 j-4 k. Let G be the centroid of the triangle ABC. Then 6 (| AG|2+| BG|2+| CG|2 ) is equal to .

If is a root of the equation x2+x+1=0 and k=1n ( k+ 1 k )2=20, then n is equal to .

Let m and n, (m<n), be two 2-digit numbers. Then the total number of pairs (m, n), such that (m, n)=6, is .