JEE Main 2025 (Online) 22nd January Evening Shift

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

Given are statements for certain thermodynamic variables, Choose the correct answer from the options given below :

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

The torque due to the force (2 i+ j+2 k ) about the origin, acting on a particle whose position vector is ( i+ j+ k ), would be

1. j+ k
2. i- k
3. i- j+ k
4. i+ k

Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge respectively.

1. [F]= [ C M-1L-2T2 ]
2. [F]= [ C2M-2L2T2 ]
3. [F]= [ C2M-1L-2T2 ]
4. [F]= [ C M-2L-2T-2 ]

The maximum percentage error in the measurement of density of a wire is [Given, mass of wire =(0.60 0.003) g radius of wire =(0.50 0.01) cm length of wire =(10.00 0.05) cm]

1. 7
2. 8
3. 5
4. 4

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

1. h eB
2. 4h eB
3. h2 eB
4. 2h eB

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is : [figure] (Take acceleration due to gravity as 10 m/s2)

1. 3- 22
2. 2+ 33
3. 2+ 23
4. 3+ 32

A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnetic field, the plot of magnitude of induced emf ( ) with time (t) is given by

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

[figure] To obtain the given truth table, following logic gate should be placed at G :

1. NOR Gate
2. OR Gate
3. AND Gate
4. NAND Gate

A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is 4D then the power of a part of the divided lens is [figure]

1. 2D
2. 8D
3. 4D
4. D

A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be [figure]

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

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is I0. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be

1. I02
2. I0 2
3. 2I0
4. I0

For a short dipole placed at origin O , the dipole moment P is along x-axis, as shown in the figure. If the electric potential and electric field at A are V0 and E0, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y-axis is given by [figure]

1. V02 and E016
2. zero and E08
3. V0 and E04
4. zero and E016

A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.]

1. 68.7 nm
2. 137.5 nm
3. 94.8 nm
4. 275 nm

A light source of wavelength illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength 2, then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV )

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

For a diatomic gas, if 1= ( CpCv ) for rigid molecules and 2= ( CpCv ) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? (Cp and Cv are specific heats of the gas at constant pressure and volume)

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

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)

A ball of mass 100 g is projected with velocity 20 m/s at 60 with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

1. 20 J
2. 5 J
3. 15 J
4. zero

A force F=2 i+b j+ k is applied on a particle and it undergoes a displacement i-2 j- k. What will be the value of b, if work done on the particle is zero.

1. 13
2. 12
3. 0
4. 2

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

1. 2Mg
2. 32Mg
3. Mg2
4. Mg

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of 2 105 m s-1. When the electric field is switched off, the proton moves along a circular path of radius 2 cm . The magnitude of electric field is x 104 N/C. The value of x is . Take the mass of the proton =1.6 10-27 kg.

The net current flowing in the given circuit is A. [figure]

A parallel plate capacitor of area A=16 cm2 and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area A0=3.2 cm2 inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through A0 is mA .

Two long parallel wires X and Y, separated by a distance of 6 cm , carry currents of 5 A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is x 10-5 T. The value of x is . Take permeability of free space as 0=4 10-7 SI units. [figure]

A tube of length 1 m is filled completely with an ideal liquid of mass 2M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is F M in SI unit. The value of is .

When sec-butylcyclohexane reacts with bromine in the presence of sunlight, the major product is :

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

The most stable carbocation from the following is :

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

The correct order of the following complexes in terms of their crystal field stabilization energies is :

1. [Co(NH3)4]2+ < [Co(NH3)6]2+ < [Co(NH3)6]3+ < [Co(en)3]3+
2. [Co(NH3)4]2+ < [Co(NH3)6]2+ < [Co(en)3]3+ < [Co(NH3)6]3+
3. [Co(NH3)6]2+ < [Co(NH3)6]3+ < [Co(NH3)4]2+ < [Co(en)3]3+
4. [Co(en)3]3+ < [Co(NH3)6]3+ < [Co(NH3)6]2+ < [Co(NH3)4]2+

The maximum covalency of a non-metallic group 15 element ' E ' with weakest E-E bond is :

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

Identify the number of structure/s from the following which can be correlated to D-glyceraldehyde. [figure]

1. three
2. two
3. one
4. four

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

Consider the given figure and choose the correct option : [figure]

1. Activation energy of both forward and backward reaction is E1 + E2 and reactant is more stable than product.
2. Activation energy of forward reaction is E1 + E2 and product is more stable than reactant.
3. Activation energy of backward reaction is E1 and product is more stable than reactant.
4. Activation energy of forward reaction is E1 + E2 and product is less stable than reactant.

Arrange the following compounds in increasing order of their dipole moment : HBr, H2S, NF3 and CHCl3

1. HBr < H2S < NF3 < CHCl3
2. H2S < HBr < NF3 < CHCl3
3. NF3 < HBr < H2S < CHCl3
4. CHCl3 < NF3 < HBr < H2S

Density of 3 M NaCl solution is 1.25 g/mL. The molality of the solution is :

1. 2.79 m
2. 2 m
3. 1.79 m
4. 3 m

The molar solubility(s) of zirconium phosphate with molecular formula ( Zr4+ )3 ( PO43- )4 is given by relation :

1. ( Ksp5348 )1/6
2. ( Ksp8435 )1/7
3. ( Ksp6912 )1/7
4. ( Ksp9612 )1/3

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

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

Identify the homoleptic complex(es) that is/are low spin. Choose the correct answer from the options given below :

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

[figure] The maximum number of RBr producing 2-methylbutane by above sequence of reactions is . (Consider the structural isomers only)

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

The alkane from below having two secondary hydrogens is :

1. 2,2,4,5-Tetramethylheptane
2. 2,2,4,4-Tetramethylhexane
3. 4-Ethyl-3,4-dimethyloctane
4. 2,2,3,3-Tetramethylpentane

[figure] Residue (A) + HCl (dil) Compound (B) Structure of residue (A) and compound (B) formed respectively is :

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

The species which does not undergo disproportionation reaction is :

1. ClO4-
2. ClO3-
3. ClO-
4. ClO2-

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

Match the Compounds (List - I) with the appropriate Catalyst/ Reagents (List - II) for their reduction into corresponding amines. Choose the correct answer from the options given below :

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

Consider the following cases of standard enthalpy of reaction ( Hr in kJ mol-1) C2H6(g)+ 72O2(g) 2CO2(g)+3H2O(l) H1 =-1550 C(graphite)+O2(g) CO2(g) H2 =-393.5 H2(g)+ 12O2(g) H2O(l) H3 =-286 The magnitude of H f C2H6(g) is kJ mol-1 (Nearest integer).

The complex of Ni2+ ion and dimethyl glyoxime contains number of Hydrogen (H) atoms.

Niobium (Nb) and ruthenium (Ru) have “x” and “y” number of electrons in their respective 4 d orbitals. The value of x+y is .

20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is 10-2 M. (Nearest integer)

The compound with molecular formula C6H6, which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has electrons.

Let and be the distinct roots of 2x2+( )x-1=0, (0,2 ). If m and M are the minimum and the maximum values of 4+ 4, then 16(M+m) equals :

1. 27
2. 17
3. 25
4. 24

Let a line pass through two distinct points P(-2,-1,3) and Q, and be parallel to the vector 3 i+2 j+2 k. If the distance of the point Q from the point R(1,3,3) is 5, then the square of the area of PQR is equal to :

1. 148
2. 144
3. 136
4. 140

If the system of linear equations : x+y+2z=6 2x+3y+az=a+1 -x-3y+bz=2b where a,b , has infinitely many solutions, then 7a+3b is equal to :

1. 12
2. 9
3. 22
4. 16

The sum of all values of [0,2 ] satisfying 2 2 = 2 and 2 2 =3 is

2. 5 6
3. 2
4. 4

Let , , and be the coefficients of x7,x5,x3 and x respectively in the expansion of (x+ x3-1 )5+ (x- x3-1 )5, x>1. If u and v satisfy the equations u+ v=18, u+ v=20, then u+v equals :

1. 4
2. 3
3. 5
4. 8

The perpendicular distance, of the line x-12= y+2-1= z+32 from the point P(2,-10,1), is :

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

If x=f(y) is the solution of the differential equation (1+y2 )+ (x-2e -1y ) dydx=0, y (- 2, 2 ) with f(0)=1, then f ( 1 3 ) is equal to :

1. e /4
2. e /12
3. e /6
4. e /3

If A and B are two events such that P(A B)=0.1, and P(A B) and P(B A) are the roots of the equation 12x2-7x+1=0, then the value of P( A B)P( A B) is :

1. 43
2. 74
3. 94
4. 53

For a 3 3 matrix M, let trace (M) denote the sum of all the diagonal elements of M. Let A be a 3 3 matrix such that |A|= 12 and trace (A)=3. If B=adj(adj(2A)), then the value of |B|+ trace (B) equals :

1. 56
2. 132
3. 174
4. 280

If x ( x -1x 1-x2+ -1x(1-x2)3/2+ x1-x2 )dx=g(x)+C, where C is the constant of integration, then g ( 12 ) equals :

1. 6 e3
2. 6 e2
3. 4 e3
4. 4 e2

Let a and b be two unit vectors such that the angle between them is 3. If a+2 b and 3 a- b are perpendicular to each other, then the number of values of in [-1,3] is :

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

The area of the region enclosed by the curves y=x2-4x+4 and y2=16-8x is :

1. 83
2. 5
3. 8
4. 43

In a group of 3 girls and 4 boys, there are two boys B1 and B2. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but B1 and B2 are not adjacent to each other, is :

1. 120
2. 96
3. 72
4. 144

If x ( ( e1-e ) ( 1e- x1+x ) )x= , then the value of e 1+ e equals :

1. e-2
2. e2
3. e
4. e-1

Let f(x)= 0x2 t2-8t+15et dt, x . Then the numbers of local maximum and local minimum points of f, respectively, are :

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

Let A=\1,2,3,4\ and B=\1,4,9,16\. Then the number of many-one functions f:A B such that 1 f(A) is equal to :

1. 151
2. 139
3. 163
4. 127

Let the curve z(1+i)+ z(1-i)=4, z , divide the region |z-3| 1 into two parts of areas and . Then | - | equals :

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

Suppose that the number of terms in an A.P. is 2k, k . If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27, then k is equal to:

1. 8
2. 6
3. 4
4. 5

Let P(4,4 3) be a point on the parabola y2=4ax and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to :

1. 34 33
2. 343 38
3. 17 3
4. 263 38

Let E: x2a2+ y2b2=1, a>b and H: x2A2- y2B2=1. Let the distance between the foci of E and the foci of H be 2 3. If a-A=2, and the ratio of the eccentricities of E and H is 13, then the sum of the lengths of their latus rectums is equal to :

1. 10
2. 7
3. 9
4. 8

Let A(6,8), B(10 ,-10 ) and C(-10 ,10 ), be the vertices of a triangle. If L(a,9) and G(h,k) be its orthocenter and centroid respectively, then (5a-3h+6k+100 2 ) is equal to .

Let y=f(x) be the solution of the differential equation dydx+ xyx2-1= x6+4x 1-x2, -1<x<1 such that f(0)=0. If 6 -1/21/2f(x) dx=2 - then 2 is equal to .

If r=130 r2 (30Cr )230Cr-1= 229, then is equal to .

Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the parallel lines, while R lies on the other. Then (QR)2 is equal to .

Let A=\1,2,3\. The number of relations on A, containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is .