JEE Main 2025 (Online) 3rd April Evening Shift

Two cylindrical vessels of equal cross sectional area of 2 m2 contain water up to heights 10 m and 6 m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is (Density of water is 103 kg/m3 and g = 10 m/s2)

1. 1 105 J
2. 4 104 J
3. 8 104 J
4. 6 104 J

Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

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

A particle moves along the x-axis and has its displacement x varying with time t according to the equation: x = c0 (t2 - 2 ) + c(t - 2)2 where c0 and c are constants of appropriate dimensions. Then, which of the following statements is correct?

1. the acceleration of the particle is 2(c + c0)
2. the acceleration of the particle is 2c0
3. the acceleration of the particle is 2c
4. the initial velocity of the particle is 4c

[figure] Consider two blocks A and B of masses m1 = 10 kg and m2 = 5 kg that are placed on a frictionless table. The block A moves with a constant speed v = 3 m/s towards the block B kept at rest. A spring with spring constant k = 3000 N/m is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring)

1. 0.3 m
2. 0.1 m
3. 0.4 m
4. 0.2 m

A magnetic dipole experiences a torque of 80 3 N m when placed in uniform magnetic field in such a way that dipole moment makes angle of 60 with magnetic field. The potential energy of the dipole is:

1. -40 3 J
2. -80 J
3. 80 J
4. -60 J

An ideal gas exists in a state with pressure P0, volume V0. It is isothermally expanded to 4 times of its initial volume (V0), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

1. P0V0( 2 - 0.75)
2. P0V0(2 2 - 0.75)
3. P0V0(2 2 - 0.25)
4. P0V0( 2 - 0.25)

Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is:

1. 3 : 1
2. (2 2 + 1) : (2 2 - 1)
3. 9 : 1
4. (3 + 2 2) : (3 - 2 2)

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is: (in pF)

1. 600
2. 100
3. 400
4. 200

A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is 91.6\%, then the loss of power in units of cal/s is

1. 6.2
2. 2
3. 8.4
4. 4

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is:

1. 370 m/s
2. 340 m/s
3. 335 m/s
4. 360 m/s

A block of mass 1 kg, moving along x with speed vi = 10 m/s enters a rough region ranging from x = 0.1 m to x = 1.9 m. The retarding force acting on the block in this range is Fr = -kx, with k = 10 N/m. Then the final speed of the block as it crosses the rough region is:

1. 4 m/s
2. 10 m/s
3. 8 m/s
4. 6 m/s

The truth table corresponding to the circuit given below is: [figure]

1. arrayccc A & B & C \ 0 & 0 & 0 \ 0 & 1 & 0 \ 1 & 0 & 1 \ 1 & 1 & 1 array
2. arrayccc A & B & C \ 0 & 0 & 1 \ 1 & 0 & 0 \ 0 & 1 & 0 \ 1 & 1 & 0 array
3. arrayccc A & B & C \ 0 & 0 & 1 \ 0 & 1 & 0 \ 1 & 0 & 0 \ 1 & 1 & 0 array
4. arrayccc A & B & C \ 0 & 0 & 0 \ 1 & 0 & 0 \ 0 & 1 & 0 \ 1 & 1 & 1 array

A monochromatic light of frequency 5 1014 Hz travelling through air, is incident on a medium of refractive index '2'. Wavelength of the refracted light will be:

1. 400 nm
2. 300 nm
3. 600 nm
4. 500 nm

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

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

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4\% when heated by 1 . Its initial temperature must be:

1. 2500 K
2. 25
3. 250
4. 250 K

A solid steel ball of diameter 3.6 mm acquired terminal velocity 2.45 10-2 m/s while falling under gravity through an oil of density 925 kg m-3. Take density of steel as 7825 kg m-3 and g as 9.8 m/s2. The viscosity of the oil in SI unit is

1. 2.18
2. 1.68
3. 2.38
4. 1.99

A particle is projected with velocity u so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as nu225g, where value of n is: (Given, 'g' is the acceleration due to gravity.)

1. 6
2. 12
3. 18
4. 24

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

An electric bulb rated as 100 W - 220 V is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is:

1. 0.32 A
2. 0.64 A
3. 0.45 A
4. 2.2 A

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

An electron in the hydrogen atom initially in the fourth excited state makes a transition to nth energy state by emitting a photon of energy 2.86 eV. The integer value of n will be .

Light from a point source in air falls on a spherical glass surface (refractive index, = 1.5 and radius of curvature = 50 cm). The image is formed at a distance of 200 cm from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is m.

Two cells of emfs 1 V and 2 V and internal resistances 2 and 1 , respectively, are connected in series with an external resistance of 6 . The total current in the circuit is I1. Now the same two cells in parallel configuration are connected to same external resistance. In this case, the total current drawn is I2. The value of ( I1I2 ) is x3. The value of x is .

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is n times the volume of the bubble B, then, the value of n is .

A physical quantity C is related to four other quantities p, q, r and s as follows C = pq2r3 s The percentage errors in the measurement of p, q, r and s are 1\%, 2\%, 3\% and 2\%, respectively. The percentage error in the measurement of C will be %

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

Fat soluble vitamins are: Choose the correct answer from the options given below:

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

What is the correct IUPAC name of [figure] ?

1. 3-Bromo-2-hydroxy-5-nitrobenzoic acid
2. 2-Hydroxy-3-bromo-5-nitrobenzoic acid
3. 3-Bromo-4-hydroxy-1-nitrobenzoic acid
4. 5-Nitro-3-bromo-2-hydroxybenzoic acid

Mass of magnesium required to produce 220 mL of hydrogen gas at STP on reaction with excess of dil. HCl is Given: Molar mass of Mg is 24 g mol-1.

1. 0.24 mg
2. 235.7 g
3. 2.444 g
4. 236 mg

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

The correct orders among the following are Choose the correct answer from the options given below:

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

10 mL of 2 M NaOH solution is added to 20 mL of 1 M HCl solution kept in a beaker. Now, 10 mL of this mixture is poured into a volumetric flask of 100 mL containing 2 moles of HCl and made the volume up to the mark with distilled water. The solution in this flask is :

1. 0.2 M NaCl solution
2. 20 M HCl solution
3. Neutral solution
4. 10 M HCl solution

In the following series of reactions identify the major products A & B respectively : [figure]

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

Identify the diamagnetic octahedral complex ions from below ; Choose the correct answer from the options given below:

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

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

Consider the following statements related to temperature dependence of rate constants. Identify the correct statements. Choose the correct answer from the options given below:

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

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

The sequence from the following that would result in giving predominantly 3,4,5-Tribromoaniline is :

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

The major product (P) in the following reaction is : Ph- O \|C- O \|C-H [ ]KOH Major ProductP

1. Ph- O \|C-COO K
2. Ph- OH |CH-CH2OH
3. Ph- OH |CH-COO K
4. Ph- O \|C-CH2OH

The standard cell potential ( E cell ) of a fuel cell based on the oxidation of methanol in air that has been used to power television relay station is measured as 1.21 V. The standard half cell reduction potential for O2 ( E O2/H2O ) is 1.229 V. Choose the correct statement :

1. Reactants are fed at one go to each electrode.
2. Oxygen is formed at the anode.
3. The standard half cell reduction potential for the reduction of CO2 ( E CO2/CH3OH ) is 19 mV
4. Reduction of methanol takes place at the cathode.

For electrons in '2s' and '2p' orbitals, the orbital angular momentum values, respectively are:

1. 0 and 6 h2
2. 0 and 2 h2
3. 2 h2 and 0
4. h2 and 2 h2

Compounds that should not be used as primary standards in titrimetric analysis are : Choose the most appropriate answer from the options given below:

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

40 mL of a mixture of CH3COOH and HCl (aqueous solution) is titrated against 0.1 M NaOH solution conductometrically. Which of the following statement is correct? [figure]

1. The concentration of CH3COOH in the original mixture is 0.005 M
2. The concentration of HCl in the original mixture is 0.005 M
3. CH3COOH is neutralised first followed by neutralisation of HCl
4. Point 'C' indicates the complete neutralisation of HCl

In Dumas' method for estimation of nitrogen 0.4 g of an organic compound gave 60 mL of nitrogen collected at 300 K temperature and 715 mm Hg pressure. The percentage composition of nitrogen in the compound is (Given : Aqueous tension at 300 K = 15 mm Hg)

1. 15.71\%
2. 17.46\%
3. 7.85\%
4. 20.95\%

X g of nitrobenzene on nitration gave 4.2 g of m-dinitrobenzene. X = g. (nearest integer) [Given : molar mass (in g mol-1) C : 12, H : 1, O : 16, N : 14]

The total number of structural isomers possible for the substituted benzene derivatives with the molecular formula C9H12 is .

Among Sc, Mn, Co and Cu, identify the element with highest enthalpy of atomisation. The spin only magnetic moment value of that element in its +2 oxidation state is BM (in nearest integer).

A perfect gas (0.1 mol) having Cv = 1.50 R (independent of temperature) undergoes the following transformation from point 1 to point 4. If each step is reversible, the total work done (w) while going from point 1 to point 4 is (-) J (nearest integer) [Given: R = 0.082 L atm K-1 mol-1] [figure]

A sample of n-octane (1.14 g) was completely burnt in excess of oxygen in a bomb calorimeter, whose heat capacity is 5 kJ K-1. As a result of combustion reaction, the temperature of the calorimeter is increased by 5 K. The magnitude of the heat of combustion of octane at constant volume is kJ mol-1 (nearest integer).

The area of the region \(x, y) : |x - y| y 4 x\ is

1. 5123
2. 20483
3. 512
4. 10243

Line L1 of slope 2 and line L2 of slope 12 intersect at the origin O. In the first quadrant, P1, P2, , P12 are 12 points on line L1 and Q1, Q2, , Q9 are 9 points on line L2. Then the total number of triangles, that can be formed having vertices at three of the 22 points O, P1, P2, , P12, Q1, Q2, , Q9, is:

1. 1026
2. 1188
3. 1134
4. 1080

Each of the angles and that a given line makes with the positive y- and z-axes, respectively, is half of the angle that this line makes with the positive x-axis. Then the sum of all possible values of the angle is

1. 2
3. 3 4
4. 3 2

If z1, z2, z3 C are the vertices of an equilateral triangle whose centroid is z0, then k=13 (zk - z0)2 is equal to

1. 0
2. 1
3. i
4. -i

Let C be the circle of minimum area enclosing the ellipse E : x2a2 + y2b2 = 1 with eccentricity 12 and foci ( 2, 0). Let PQR be a variable triangle, whose vertex P is on the circle C and the side QR of length 2a is parallel to the major axis of E and contains the point of intersection of E with the negative y-axis. Then the maximum area of the triangle PQR is :

1. 8(3 + 2)
2. 8(2 + 3)
3. 6(3 + 2)
4. 6(2 + 3)

The shortest distance between the curves y2 = 8x and x2 + y2 + 12y + 35 = 0 is:

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

Consider the lines x(3 + 1) + y(7 + 2) = 17 + 5, being a parameter, all passing through a point P. One of these lines (say L) is farthest from the origin. If the distance of L from the point (3, 6) is d, then the value of d2 is

1. 10
2. 20
3. 15
4. 30

Let y = y(x) be the solution of the differential equation dydx + 3( 2 x)y + 3y = 2 x, y(0) = 13 + e3. Then y ( 4 ) is equal to :

1. 43
2. 23 + e3
3. 43 + e3
4. 23

Let f be a function such that f(x) + 3f ( 24x ) = 4x, x 0. Then f(3) + f(8) is equal to

1. 13
2. 11
3. 10
4. 12

Let the equation x(x + 2)(12 - k) = 2 have equal roots. Then the distance of the point (k, k2 ) from the line 3x + 4y + 5 = 0 is

1. 15
2. 12
3. 5 3
4. 15 5

Let A = \-2, -1, 0, 1, 2, 3\. Let R be a relation on A defined by xRy if and only if y = \x, 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. 11
2. 12
3. 14
4. 13

Let the Mean and Variance of five observations x1 = 1, x2 = 3, x3 = a, x4 = 7 and x5 = b, a > b, be 5 and 10 respectively. Then the Variance of the observations n + xn, n = 1, 2, , 5 is

1. 17
2. 16
3. 16.4
4. 17.4

The integral 0 8x dx4 2 x + 2 x is equal to

1. 2 2
2. 4 2
3. 2
4. 3 22

The distance of the point (7, 10, 11) from the line x-41 = y-40 = z-23 along the line x-92 = y-133 = z-176 is

1. 16
2. 12
3. 18
4. 14

If the probability that the random variable X takes the value x is given by P(X = x) = k(x + 1)3-x, x = 0, 1, 2, 3, , where k is a constant, then P(X 3) is equal to

1. 19
2. 827
3. 727
4. 49

The number of solutions of the equation (4 - 3) x - 2 3 2 x = - 41 + 3, x [-2 , 5 2 ] is

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

If the domain of the function f(x) = 7 (1 - 4 (x2 - 9x + 18 ) ) is ( , ) ( , ), then + + + is equal to

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

Let f : R R be a function defined by f(x) = ||x + 2| - 2|x| |. If m is the number of points of local minima and n is the number of points of local maxima of f, then m + n is

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

The sum 1 + 1 + 32! + 1 + 3 + 53! + 1 + 3 + 5 + 74! + up to terms, is equal to

1. 3e
2. 2e
3. 4e
4. 6e

If the four distinct points (4, 6), (-1, 5), (0, 0) and (k, 3k) lie on a circle of radius r, then 10k + r2 is equal to

1. 34
2. 32
3. 35
4. 33

If x 0 ( xx ) 1x2 = p, then 96 e p is equal to

If the equation of the hyperbola with foci (4, 2) and (8, 2) is 3x2 - y2 - x + y + = 0, then + + is equal to .

Let (1 + x + x2 )10 = a0 + a1x + a2x2 + + a20x20. If (a1 + a3 + a5 + + a19) - 11a2 = 121k, then k is equal to .

Let a = i + 2 j + k, b = 3 i - 3 j + 3 k, c = 2 i - j + 2 k and d be a vector such that b d = c d and a d = 4. Then |( a d)|2 is equal to .

Let I be the identity matrix of order 3 3 and for the matrix A = bmatrix & 2 & 3 \ 4 & 5 & 6 \ 7 & -1 & 2 bmatrix, |A| = -1. Let B be the inverse of the matrix adj (A adj (A2 ) ). Then |( B + I)| is equal to