JEE Main 2025 (Online) 24th January Evening Shift

[figure] N equally spaced charges each of value q, are placed on a circle of radius R. The circle rotates about its axis with an angular velocity as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, IA-IB, for the given Amperian loops is

1. N22 q
2. N2 q
3. 2 Nq
4. N q

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of P1 and P2 are orthogonal to each other. The polarizer P3 covers both the slits with its transmission axis at 45 to those of P1 and P2. An unpolarized light of wavelength and intensity I0 is incident on P1 and P2. The intensity at a point after P3 where the path difference between the light waves from s1 and s2 is 3, is [figure]

1. I0
2. I03
3. I04
4. I02

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

The temperature of a body in air falls from 40 to 24 in 4 minutes. The temperature of the air is 16 . The temperature of the body in the next 4 minutes will be :

1. 283
2. 563
3. 423
4. 143

The output of the circuit is low (zero) for : [figure] Choose the correct answer from the options given below :

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

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) : [figure]

1. zero
2. 40
3. 5
4. 10

In photoelectric effect, the stopping potential (V0) v/s frequency ( ) curve is plotted. ( h is the Planck's constant and 0 is work function of metal ) Choose the correct answer from the options given below :

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

A small uncharged conducting sphere is placed in contact with an identical sphere but having 4 10-8 C charge and then removed to a distance such that the force of repulsion between them is 9 10-3 N. The distance between them is (Take 14 0 as 9 109 in SI units)

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

A long straight wire of a circular cross-section with radius 'a' carries a steady current I. The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance r from the centre of the wire is given by

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

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation

1. E2=pc2+m2c4
2. E2=pc2+m2c2
3. E2=p2c2+m2c4
4. E2=p2c2+m2c2

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

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be t1 and t2, respectively, then

1. t1 < t2
2. t1 = 2t2
3. t1 > t2
4. t1 = t2

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?

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

Arrange the following in the ascending order of wavelength ( ) : Choose the most appropriate answer from the options given below :

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

Young's double slit interference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm. The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm. The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m, will be:

1. 0.63 mm
2. 0.33 mm
3. 0.46 mm
4. 0.23 mm

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :

1. 34
2. 43
3. 52
4. 25

The position vector of a moving body at any instant of time is given as r= (5t2 i-5t j ) m. The magnitude and direction of velocity at t=2 s is,

1. 5 17 m/s, making an angle of -14 with -ve Y axis
2. 5 15 m/s, making an angle of -14 with +ve X axis
3. 5 17 m/s, making an angle of -14 with +ve X axis
4. 5 15 m/s, making an angle of -14 with -ve Y axis

A photograph of a landscape is captured by a drone camera at a height of 18 km. The size of the camera film is 2 cm 2 cm and the area of the landscape photographed is 400 km2. The focal length of the lens in the drone camera is :

1. 2.8 cm
2. 0.9 cm
3. 2.5 cm
4. 1.8 cm

[figure] In the first configuration (1) as shown in the figure, four identical charges (q0) are kept at the corners A, B, C and D of square of side length 'a'. In the second configuration (2), the same charges are shifted to mid points G, E, H and F, of the square. If K= 14 0, the difference between the potential energies of configuration (2) and (1) is given by :

1. Kq02a (4-2 2 )
2. Kq02a (4 2-2 )
3. Kq02a (3- 2 )
4. Kq02a (3 2-2 )

A particle oscillates along the x-axis according to the law, x(t)=x0 2 ( t2 ) where x0=1 m. The kinetic energy (K) of the particle as a function of x is correctly represented by the graph

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

The ratio of the power of a light source S1 to that of the light source S2 is 2. S1 is emitting 2 1015 photons per second at 600 nm. If the wavelength of the source S2 is 300 nm, then the number of photons per second emitted by S2 is 1014.

The increase in pressure required to decrease the volume of a water sample by 0.2\% is P 105 Nm-2. Bulk modulus of water is 2.15 109 Nm-2. The value of P is .

[figure] A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes ( 3 ) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is ML.

Acceleration due to gravity on the surface of earth is 'g'. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of earth is g.

A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per metre in the solenoid is . [Take mass of electron me=9 10-31 kg, charge of electron |qe|=1.6 10-19 C, 0=4 10-7 NA2, 1 ns=10-9 s]

The successive 5 ionisation energies of an element are 800, 2427, 3658, 25024 and 32824 kJ/mol, respectively. By using the above values predict the group in which the above element is present :

1. Group 4
2. Group 2
3. Group 13
4. Group 14

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

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

Find the compound 'A' from the following reaction sequences. A aqua-regiaB [(2) AcOH](1) KNO2, NH4OH yellow ppt

1. NiS
2. MnS
3. ZnS
4. CoS

S(g)+ 32O2(g) SO3(g)+2x kcal SO2(g)+ 12O2(g) SO3(g)+y kcal The heat of formation of SO2(g) is given by :

1. 2x+y kcal
2. 2xy kcal
3. y-2x kcal
4. x+y kcal

The structure of the major product formed in the following reaction is : [figure]

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

The elemental composition of a compound is 54.2\% C, 9.2\% H and 36.6\% O. If the molar mass of the compound is 132 g mol-1, the molecular formula of the compound is : [Given : The relative atomic mass of C:H:O=12:1:16]

1. C4H8O2
2. C6H12O6
3. C4H9O3
4. C6H12O3

Based on the data given below : E (Cr2O72-/Cr3+)=1.33 V E (Cl2/Cl-)=1.36 V E (MnO4-/Mn2+)=1.51 V E (Cr3+/Cr)=-0.74 V the strongest reducing agent is :

1. Cl-
2. MnO4-
3. Cr
4. Mn2+

For reaction [figure] The correct order of set of reagents for the above conversion is :

1. Ac2O, Br2, H2O( ), NaOH
2. H2SO4, Ac2O, Br2, H2O( ), NaOH
3. Br2 | FeBr3, H2O( ), NaOH
4. Ac2O, H2SO4, Br2, NaOH

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

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

Which of the following mixing of 1 M base and 1 M acid leads to the largest increase in temperature?

1. 50 mL HCl and 20 mL NaOH
2. 30 mL HCl and 30 mL NaOH
3. 45 mL CH3COOH and 25 mL NaOH
4. 30 mL CH3COOH and 30 mL NaOH

In the given structure, number of sp and sp2 hybridized carbon atoms present respectively are : [figure]

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

The conditions and consequence that favours the t2g3eg1 configuration in a metal complex are :

1. strong field ligand, low spin complex
2. strong field ligand, high spin complex
3. weak field ligand, high spin complex
4. weak field ligand, low spin complex

For the reaction, H2(g)+I2(g) 2HI(g) Attainment of equilibrium is predicted correctly by :

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

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

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

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

When Ethane-1,2-diamine is added progressively to an aqueous solution of Nickel (II) chloride, the sequence of colour change observed will be:

1. Pale Blue Blue Green Violet
2. Pale Blue Blue Violet Green
3. Green Pale Blue Blue Violet
4. Violet Blue Pale Blue Green

For hydrogen atom, the orbital/s with lowest energy is/are : Choose the correct answer from the options given below :

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

Identify correct statement/s : Choose the correct answer from the options given below :

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

Consider a complex reaction taking place in three steps with rate constants k1, k2 and k3 respectively. The overall rate constant k is given by the expression k= k1k3k2. If the activation energies of the three steps are 60, 30 and 10 kJ mol-1 respectively, then the overall energy of activation in kJ mol-1 is . (Nearest integer)

The hydrocarbon (X) with molar mass 80 g mol-1 and 90\% carbon has degree of unsaturation.

In Carius method of estimation of halogen, 0.25 g of an organic compound gave 0.15 g of silver bromide (AgBr). The percentage of Bromine in the organic compound is 10-1\% (Nearest integer). (Given : Molar mass of Ag is 108 and Br is 80 g mol-1)

The observed and normal molar masses of compound MX2 are 65.6 and 164 respectively. The percent degree of ionisation of MX2 is %. (Nearest integer)

The possible number of stereoisomers for 5-phenylpent-4-en-2-ol is .

In an arithmetic progression, if S40=1030 and S12=57, then S30-S10 is equal to :

1. 525
2. 505
3. 510
4. 515

Let A=[aij] be a square matrix of order 2 with entries either 0 or 1. Let E be the event that A is an invertible matrix. Then the probability P(E) is :

1. 38
2. 18
3. 316
4. 58

Let (2,3) be the largest open interval in which the function f(x)=2 e(x-2)-x2+ax+1 is strictly increasing and (b,c) be the largest open interval, in which the function g(x)=(x-1)3(x+2-a)2 is strictly decreasing. Then 100(a+b-c) is equal to :

1. 360
2. 420
3. 160
4. 280

Let A= \x (0, )- \ 2 \: (2/ )| x|+ (2/ )| x|=2 \ and B= \x 0: x( x-4)-3| x-2|+6=0 \. Then n(A ) is equal to :

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

The area of the region enclosed by the curves y=ex, y=|ex-1| and y-axis is :

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

For some a,b, let f(x)= vmatrixa+ xx&1&b\ &1+ xx&b\ &1&b+ xx vmatrix, x 0, x 0f(x)= + a+ b. Then ( + + )2 is equal to :

1. 25
2. 16
3. 9
4. 36

If > > >0, then the expression -1 \ + (1+ 2)( - ) \+ -1 \ + (1+ 2)( - ) \ + -1 \ + (1+ 2)( - ) \ is equal to :

1. 3
2. 2-( + + )
4. 0

If the system of equations x+2y-3z=2 2x+ y+5z=5 14x+3y+ z=33 has infinitely many solutions, then + is equal to :

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

Suppose A and B are the coefficients of 30th and 12th terms respectively in the binomial expansion of (1+x)2n-1. If 2A=5B, then n is equal to:

1. 20
2. 19
3. 22
4. 21

Let the position vectors of three vertices of a triangle be 4 p+ q-3 r, -5 p+ q+2 r and 2 p- q+2 r. If the position vectors of the orthocenter and the circumcenter of the triangle are p+ q+ r4 and p+ q+ r respectively, then +2 +5 is equal to :

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

If 7=5+ 17(5+ )+ 172(5+2 )+ 173(5+3 )+ , then the value of is :

1. 17
2. 1
3. 67
4. 6

If the equation of the parabola with vertex V ( 32,3 ) and the directrix x+2y=0 is x2+ y2- xy-30x-60y+225=0, then + + is equal to :

1. 6
2. 8
3. 7
4. 9

Let a=3 i- j+2 k, b= a ( i-2 k) and c= b k. Then the projection of c-2 j on a is :

1. 2 7
2. 3 7
3. 14
4. 2 14

The equation of the chord, of the ellipse x225+ y216=1, whose mid-point is (3,1) is :

1. 5x+16y=31
2. 48x+25y=169
3. 4x+122y=134
4. 25x+101y=176

Let the points ( 112, ) lie on or inside the triangle with sides x+y=11, x+2y=16 and 2x+3y=29. Then the product of the smallest and the largest values of is equal to :

1. 22
2. 33
3. 55
4. 44

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to :

1. 8925
2. 9100
3. 8575
4. 8750

Let [x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function f(x)=[x]+|x-2|, -2<x<3, is not continuous and not differentiable. Then m+n is equal to :

1. 6
2. 9
3. 8
4. 7

The number of real solution(s) of the equation x2+3x+2= \|x-3|,|x+2|\ is :

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

Let f:(0, ) be a function which is differentiable at all points of its domain and satisfies the condition x2f'(x)=2xf(x)+3, with f(1)=4. Then 2f(2) is equal to :

1. 19
2. 23
3. 29
4. 39

The function f:(- , ) (- ,1), defined by f(x)= 2x-2-x2x+2-x is :

1. One-one but not onto
2. Onto but not one-one
3. Both one-one and onto
4. Neither one-one nor onto

Let P be the image of the point Q(7,-2,5) in the line L: x-12= y+13= z4 and R(5,p,q) be a point on L. Then the square of the area of PQR is .

If 2x2+5x+9 x2+x+1 dx =x x2+x+1+ x2+x+1 + e |x+ 12+ x2+x+1 |+C, where C is the constant of integration, then +2 is equal to .

Let y=y(x) be the solution of the differential equation 2 x dydx= 2x-4y x, x (0, 2 ). If y ( 3 )=0, then y' ( 4 )+y ( 4 ) is equal to .

Number of functions f:\1,2, ,100\ \0,1\, that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to .

Let H1: x2a2- y2b2=1 and H2:- x2A2+ y2B2=1 be two hyperbolas having length of latus rectums 15 2 and 12 5 respectively. Let their eccentricities be e1= 52 and e2 respectively. If the product of the lengths of their transverse axes is 100 10, then 25e22 is equal to .