JEE Main 2025 (Online) 7th April Morning Shift

If 0 denotes the permittivity of free space and E is the flux of the electric field through the area bounded by the closed surface, then dimensions of ( 0 d Edt ) are that of :

1. electric charge
2. electric field
3. electric current
4. electric potential

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility Mg = 1.2 10-5) is :

1. 53 10-5\%
2. 56 10-4\%
3. 56 10-5\%
4. 65 10-3\%

An object of mass 1000 g experiences a time dependent force F = (2t i + 3t2 j ) N. The power generated by the force at time t is:

1. (2t2 + 18t3 ) W
2. (3t3 + 5t5 ) W
3. (2t3 + 3t5 ) W
4. (2t2 + 3t3 ) W

A rod of length 5 L is bent at right angle keeping one side length as 2 L. [figure] The position of the centre of mass of the system : (Consider L = 10 cm)

1. 4 i + 9 j
2. 2 i + 3 j
3. 5 i + 8 j
4. 3 i + 7 j

An ac current is represented as i = 5 2 + 10 (650 t + 6 ) Amp The r.m.s. value of the current is

1. 10 Amp
2. 5 2 Amp
3. 100 Amp
4. 50 Amp

Two harmonic waves moving in the same direction superimpose to form a wave x = a (1.5t) (50.5t) where t is in seconds. Find the period with which they beat. (close to nearest integer)

1. 1 s
2. 4 s
3. 2 s
4. 6 s

A particle of charge q, mass m and kinetic energy E enters a magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E?

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

A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is R/n. The value of n is : [figure]

1. 16
2. 10
3. 12
4. 14

Two wires A and B are made of same material having ratio of lengths LALB = 13 and their diameters ratio dAdB = 2. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

1. 3 : 4
2. 1 : 12
3. 1 : 3
4. 1 : 6

Two plane polarized light waves combine at a certain point whose electric field components are E1 = E0 t E2 = E0 ( t + 3 ) Find the amplitude of the resultant wave.

1. 1.7 E0
2. E0
3. 0.9 E0
4. 3.4 E0

Uniform magnetic fields of different strengths (B1 and B2), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant, moves into the region 2 with velocity v and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface? [figure] (Consider the velocity of the particle to be normal to the magnetic field and B2 > B1)

1. mvqB1 (1 - B1B2 ) 2
2. mvqB1 (1 - B2B1 ) 2
3. mvqB1 (1 - B2B1 )
4. mvqB1 (1 - B1B2 )

Two projectiles are fired from ground with same initial speeds from same point at angles (45 + ) and (45 - ) with horizontal direction. The ratio of their times of flights is

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

In a hydrogen like ion, the energy difference between the 2nd excitation energy state and ground is 108.8 eV. The atomic number of the ion is:

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

Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is:

1. 5 D
2. 1 D
3. 20 D
4. 10 D

Two charges q1 and q2 are separated by a distance of 30 cm. A third charge q3 initially at 'C' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of q3 from C to D is given by q3 K4 0, the value of K is : [figure]

1. 6q2
2. 6q1
3. 8q1
4. 8q2

A lens having refractive index 1.6 has focal length of 12 cm, when it is in air. Find the focal length of the lens when it is placed in water. (Take refractive index of water as 1.28)

1. 355 mm
2. 655 mm
3. 288 mm
4. 555 mm

For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is

1. 5 : 27
2. 27 : 5
3. 3 : 4
4. 5 : 36

In the following circuit, the reading of the ammeter will be (Take Zener breakdown voltage = 4 V) [figure]

1. 60 mA
2. 80 mA
3. 10 mA
4. 24 mA

A cubic block of mass m is sliding down on an inclined plane at 60 with an acceleration of g2, the value of coefficient of kinetic friction is

1. 32
2. 23
3. 1 - 32
4. 3 - 1

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

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 1727 and power radiated by the wire is 94.2 W. Its emissivity is x8 where x = . (Given = 6.0 10-8 W m-2 K-4, = 3.14 and assume that the emissivity of wire material is same at all wavelengths.)

A, B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure. [figure] The moment of inertia of the given system about PQ axis is x15I, where I is the moment of inertia of the disc about its diameter. The value of x is .

For ac circuit shown in figure, R = 100 k and C = 100 pF and the phase difference between Vin and (VB - VA) is 90 . The input signal frequency is 10x rad/sec, where 'x' is . [figure]

A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40 cm. The value of H is cm. (Consider liquids are immiscible)

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is 10-1 J. (Take = 3.14) [figure]

An aqueous solution of HCl with pH 1.0 is diluted by adding equal volume of water (ignoring dissociation of water). The pH of HCl solution would (Given 2 = 0.30)

1. increase to 1.3
2. reduce to 0.5
3. increase to 2
4. remain same

A person's wound was exposed to some bacteria and then bacterial growth started to happen at the same place. The wound was later treated with some antibacterial medicine and the rate of bacterial decay (r) was found to be proportional with the square of the existing number of bacteria at any instance. Which of the following set of graphs correctly represents the 'before' and 'after' situation of the application of the medicine? [Given: N = No. of bacteria, t = time, bacterial growth follows 1st order kinetics.]

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

Total enthalpy change for freezing of 1 mol of water at 10 C to ice at -10 C is (Given: fusH = x kJ/mol Cp[H2O(l)] = y J mol-1 K-1 Cp[H2O(s)] = z J mol-1 K-1)

1. -x-10y-10z
2. x-10y-10z
3. -10(100x+y+z)
4. 10(100x+y+z)

Which of the following amine(s) show(s) positive carbylamine test? Choose the correct answer from the options given below:

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

Which of the following compounds is least likely to give effervescence of CO2 in presence of aq. NaHCO3?

1. Ph- NH3 Cl
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-III, C-II, D-I
2. A-III, B-IV, C-I, D-II
3. A-II, B-I, C-IV, D-III
4. A-III, B-IV, C-II, D-I

The first transition series metal 'M' has the highest enthalpy of atomisation in its series. One of its aquated ions ( Mn+) exists in green colour. The nature of the oxide formed by the above Mn+ ion is:

1. basic
2. neutral
3. amphoteric
4. acidic

The number of valence electrons present in the metal among Cr, Co, Fe and Ni which has the lowest enthalpy of atomisation is :

1. 10
2. 6
3. 9
4. 8

Which of the following is the correct IUPAC name of given organic compound (X)? [figure]

1. 4-Bromo-3-methylbut-2-ene
2. 1-Bromo-2-methylbut-2-ene
3. 3-Bromo-3-methylprop-2-ene
4. 2-Bromo-2-methylbut-2-ene

At the sea level, the dry air mass percentage composition is given as nitrogen gas: 70.0, oxygen gas: 27.0 and argon gas: 3.0. If total pressure is 1.15 atm, then calculate the ratio of following respectively: (i) partial pressure of nitrogen gas to partial pressure of oxygen gas (ii) partial pressure of oxygen gas to partial pressure of argon gas (Given: Molar mass of N, O and Ar are 14, 16 and 40 g mol-1 respectively.)

1. 5.46, 17.8
2. 2.96, 11.2
3. 4.26, 19.3
4. 2.59, 11.85

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

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

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

[figure] Which of the following statements are correct, if the threshold frequency of caesium is 5.16 1014 Hz? Choose the correct answer from the options given below:

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

The group 14 elements A and B have the first ionisation enthalpy values of 708 and 715 kJ mol-1 respectively. The above values are lowest among their group members. The nature of their ions A2+ and B4+ respectively is

1. both reducing
2. oxidising and reducing
3. both oxidising
4. reducing and oxidising

The reactions which cannot be applied to prepare an alkene by elimination, are Choose the correct answer from the options given below:

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

When a salt is treated with sodium hydroxide solution it gives gas X. On passing gas X through reagent Y a brown coloured precipitate is formed. X and Y respectively, are

1. X = NH3 and Y = HgO
2. X = NH4Cl and Y = KOH
3. X = NH3 and Y = K2HgI4 + KOH
4. X = HCl and Y = NH4Cl

Reaction A(g) 2B(g) + C(g) is a first order reaction. It was started with pure A. array|c|c| t/min & Pressure of system at time t/mm Hg \ 10 & 160 \ & 240 \ array Which of the following option is incorrect?

1. Initial pressure of A is 80 mm Hg
2. The reaction never goes to completion
3. Partial pressure of A after 10 minutes is 40 mm Hg
4. Rate constant of the reaction is 1.693 min-1

An octahedral complex having molecular composition Co 5NH3 Cl SO4 has two isomers A and B. The solution of A gives a white precipitate with AgNO3 solution and the solution of B gives white precipitate with BaCl2 solution. The type of isomerism exhibited by the complex is,

1. Co-ordinate isomerism
2. Ionisation isomerism
3. Geometrical isomerism
4. Linkage isomerism

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

An organic compound weighing 500 mg, produced 220 mg of CO2, on complete combustion. The percentage composition of carbon in the compound is %. (nearest integer) (Given molar mass in g mol-1 of C : 12, O : 16)

The number of paramagnetic complexes among [FeF6]3-, [Fe(CN)6]3-, [Mn(CN)6]3-, [Co(C2O4)3]3-, [MnCl6]3-, and [CoF6]3-, which involve d2sp3 hybridization is .

1 Faraday of electricity was passed through Cu2+(1.5 M, 1 L)/Cu and 0.1 Faraday was passed through Ag+(0.2 M, 1 L)/Ag electrolytic cells. After this the two cells were connected as shown below to make an electrochemical cell. The emf of the cell thus formed at 298 K is mV (nearest integer) [figure] Given : E Cu2+/Cu = 0.34 V E Ag+/Ag = 0.8 V 2.303RTF = 0.06 V

The percentage dissociation of a salt (MX3) solution at given temperature (van't Hoff factor i = 2) is % (Nearest integer)

Thyroxine, the hormone, has the structure given below [figure] The percentage of iodine in thyroxine is %. (nearest integer) (Given molar mass in g mol-1 C : 12, H : 1, O : 16, N : 14, I : 127)

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include at least 4 batsmen and at least 4 bowlers. One batsman and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is

1. 145
2. 165
3. 155
4. 135

Let C1 be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let C2 be the circle with centre (1, 3) that touches C1 externally at the point ( , ). If ( - )2 = mn, (m, n) = 1, then m + n is equal to

1. 22
2. 13
3. 9
4. 31

Let P be the parabola, whose focus is (-2, 1) and directrix is 2x + y + 2 = 0. Then the sum of the ordinates of the points on P, whose abscissa is -2, is

1. 52
2. 32
3. 34
4. 14

The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are and respectively, then 10( + ) is equal to

1. 447
2. 445
3. 449
4. 451

Let ABC be the triangle such that the equations of lines AB and AC be 3y - x = 2 and x + y = 2, respectively, and the points B and C lie on x-axis. If P is the orthocentre of the triangle ABC, then the area of the triangle PBC is equal to

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

x 0+ (5(x) 13 ) e (1 + 3x2 ) ( -13 x )2 (e5(x) 43 - 1 ) is equal to

1. 53
2. 1
3. 13
4. 115

Let y = y(x) be the solution curve of the differential equation x (x2 + ex )dy + (ex(x - 2)y - x3 )dx = 0, x > 0, passing through the point (1, 0). Then y(2) is equal to :

1. 22 + e2
2. 44 - e2
3. 44 + e2
4. 22 - e2

Let A be a 3 3 matrix such that |adj(adj(adj A))| = 81. If S = \n Z : (|adj(adj A)| ) (n-1)22 = |A| (3n2 - 5n - 4 ) \, then n S |A (n2 + n ) | is equal to :

1. 820
2. 866
3. 750
4. 732

The remainder when ((64)(64) )(64) is divided by 7 is equal to

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

If for [- 3, 0 ], the points (x, y) = (3 ( + 3 ), 2 ( + 6 ) ) lie on xy + x + y + = 0, then 2 + 2 + 2 is equal to :

1. 75
2. 96
3. 80
4. 72

Let the system of equations : 2x + 3y + 5z = 9 7x + 3y - 2z = 8 12x + 3y - (4 + )z = 16 - have infinitely many solutions. Then the radius of the circle centred at ( , ) and touching the line 4x = 3y is :

1. 75
2. 215
3. 7
4. 175

Let the set of all values of p R, for which both the roots of the equation x2 - (p + 2)x + (2p + 9) = 0 are negative real numbers, be the interval ( , ]. Then - 2 is equal to

1. 5
2. 0
3. 20
4. 9

Among the statements (S1) : The set \z C - \-i\ : |z| = 1 and z - iz + i is purely real \ contains exactly two elements, and (S2) : The set \z C - \-1\ : |z| = 1 and z - 1z + 1 is purely imaginary \ contains infinitely many elements.

1. both are incorrect
2. both are correct
3. only (S2) is correct
4. only (S1) is correct

The integral 0 (x+3) x1+3 2 x dx is equal to

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

Let the line L pass through (1, 1, 1) and intersect the lines x-12 = y+13 = z-14 and x-31 = y-42 = z1. Then, which of the following points lies on the line L?

1. (7, 15, 13)
2. (4, 22, 7)
3. (10, -29, -50)
4. (5, 4, 3)

If the area of the region bounded by the curves y = 4 - x24 and y = x-42 is equal to , then 6 equals

1. 210
2. 250
3. 240
4. 220

If the shortest distance between the lines x-12 = y-23 = z-34 and x1 = y = z-51 is 5 6, then the sum of all possible values of is

1. 32
2. 3
3. -3
4. - 32

Let x = -1 and x = 2 be the critical points of the function f(x) = x3 + ax2 + b e |x| + 1, x 0. Let m and M respectively be the absolute minimum and the absolute maximum values of f in the interval [-2, - 12 ]. Then |M + m| is equal to (Take e 2 = 0.7):

1. 21.1
2. 19.8
3. 22.1
4. 20.9

Let the angle , 0 < < 2 between two unit vectors a and b be -1 ( 659 ). If the vector c = 3 a + 6 b + 9( a b), then the value of 9( c a) - 3( c b) is

1. 31
2. 29
3. 24
4. 27

Let x1, x2, x3, x4 be in a geometric progression. If 2, 7, 9, 5 are subtracted respectively from x1, x2, x3, x4, then the resulting numbers are in an arithmetic progression. Then the value of 124(x1 x2 x3 x4) is:

1. 18
2. 216
3. 36
4. 72

The number of singular matrices of order 2, whose elements are from the set \2, 3, 6, 9\, is .

The number of relations on the set A = \1, 2, 3\, containing at most 6 elements including (1, 2), which are reflexive and transitive but not symmetric, is .

The number of points of discontinuity of the function f(x) = [ x22 ] - [ x], x [0, 4], where [ ] denotes the greatest integer function, is .

For n 2, let Sn denote the set of all subsets of \1, 2, , n\ with no two consecutive numbers. For example \1, 3, 5\ S6, but \1, 2, 4\ S6. Then n(S5) is equal to

Consider the hyperbola x2a2 - y2b2 = 1 having one of its foci at P(-3, 0). If the latus rectum through its other focus subtends a right angle at P and a2 b2 = 2 - , , N, then + is .