JEE Main 2025 (Online) 29th January Evening Shift

[figure] Three equal masses m are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At t=0, they are given an initial velocity VA=V0 AC, VB=V0 BA and VC=V0 CB. Here, AC, CB and BA are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

1. 12 a mV0
2. 3 a mV0
3. 32 a mV0
4. 32 a mV0

In an experiment with photoelectric effect, the stopping potential,

1. is ( 1e ) times the maximum kinetic energy of the emitted photoelectrons
2. increases with increase in the intensity of the incident light
3. decreases with increase in the intensity of the incident light
4. increases with increase in the wavelength of the incident light

The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level, is

1. 3
2. 6
3. 1
4. 0

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have

1. low thermal conductivity and high electrical conductivity
2. low thermal conductivity and low electrical conductivity
3. high thermal conductivity and high electrical conductivity
4. high thermal conductivity and low electrical conductivity

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

A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e., dmdt v. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

1. P v
2. P v
3. P2 v3
4. P2 v5

A plane electromagnetic wave propagates along the + x direction in free space. The components of the electric field, E and magnetic field, B vectors associated with the wave in Cartesian frame are

1. Ex, By
2. Ey, Bx
3. Ey, Bz
4. Ez, By

A cup of coffee cools from 90 to 80 in t minutes when the room temperature is 20 . The time taken by the similar cup of coffee to cool from 80 to 60 at the same room temperature is:

1. 135t
2. 1013t
3. 513t
4. 1310t

A convex lens made of glass (refractive index = 1.5) has focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to

1. 96 cm
2. 72 cm
3. 24 cm
4. 48 cm

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

1. k2k1
2. k1k2
3. k2k1
4. k1k2

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

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

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

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

Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B. The separation between the images of O, formed by each refracting surface is : [figure]

1. 0.124R
2. 0.114R
3. 0.411R
4. 0.214R

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

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

A poly-atomic molecule (CV=3R, CP=4R, where R is gas constant) goes from phase space point A ( PA=105 Pa, VA=4 10-6 m3 ) to point B ( PB=5 104 Pa, VB=6 10-6 m3 ) to point C ( PC=104 Pa, VC=8 10-6 m3 ). A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is : [figure]

1. 500R( 3+ 4)
2. 450R( 4- 3)
3. 500R 2
4. 400R 4

Two identical symmetric double convex lenses of focal length f are cut into two equal parts L1, L2 by AB plane and L3, L4 by XY plane as shown in figure respectively. The ratio of focal lengths of lenses L1 and L3 is [figure]

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

A point charge causes an electric flux of -2 104 N m2 C-1 to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given 0=8.85 10-12 C2 N-1 m-2)

1. 17.7 10-8 C
2. -17.7 10-8 C
3. 15.7 10-8 C
4. -15.7 10-8 C

A capacitor, C1=6 is charged to a potential difference of V0=5 V using a 5V battery. The battery is removed and another capacitor, C2=12 is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges (q1 and q2) on the capacitors C1 and C2 when equilibrium condition is reached. [figure]

1. q1=10 , q2=20
2. q1=15 , q2=30
3. q1=20 , q2=10
4. q1=30 , q2=15

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density 0. Choose the correct option from the following. [figure]

1. Torque on dipole is zero and net force is directed away from the sheet.
2. Potential energy of dipole is minimum and torque is zero.
3. Potential energy and torque both are maximum.
4. Torque on dipole is zero and net force acts towards the sheet.

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. Both (A) and (R) are true and (R) is the correct explanation of (A)
3. (A) is false but (R) is true
4. (A) is true but (R) is false

A physical quantity Q is related to four observables a, b, c, d as follows : Q= ab4cd where, a=(60 3) Pa; b=(20 0.1) m; c=(40 0.2) N s m-2 and d=(50 0.1) m, then the percentage error in Q is x1000, where x= .

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is .

Two planets, A and B are orbiting a common star in circular orbits of radii RA and RB, respectively, with RB=2RA. The planet B is 4 2 times more massive than planet A. The ratio ( LBLA ) of angular momentum (LB) of planet B to that of planet A (LA) is closest to integer .

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A. If the rate of change of potential difference between the plates is 7 108 V/s then the integer value of the distance between the parallel plates is (Take, 0=9 10-12 Fm, = 227) .

The magnetic field inside a 200 turns solenoid of radius 10 cm is 2.9 10-4 Tesla. If the solenoid carries a current of 0.29 A, then the length of the solenoid is cm.

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

Identify the essential amino acids from below: Choose the correct answer from the options given below:

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

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

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

0.1 M solution of KI reacts with excess of H2SO4 and KIO3 solutions. According to equation 5I- + IO3- + 6H+ 3I2 + 3H2O Identify the correct statements : Choose the correct answer from the options given below :

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

The type of oxide formed by the element among Li, Na, Be, Mg, B and Al that has the least atomic radius is :

1. AO
2. AO2
3. A2O
4. A2O3

Which one of the following reaction sequences will give an azo dye?

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

Identify the homoleptic complexes with odd number of d electrons in the central metal : Choose the correct answer from the options given below :

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

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

Which one of the following, with HBr will give a phenol?

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

The calculated spin-only magnetic moments K3[Fe(OH)6] and K4[Fe(OH)6] respectively are :

1. 4.90 and 4.90 B.M.
2. 4.90 and 5.92 B.M.
3. 5.92 and 4.90 B.M.
4. 3.87 and 4.90 B.M.

Consider the equilibrium CO(g) + 3H2(g) CH4(g) + H2O(g) If the pressure applied over the system increases by two fold at constant temperature then

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

First ionisation enthalpy values of first four group 15 elements are given below. Choose the correct value for the element that is a main component of apatite family :

1. 834 kJ mol-1
2. 947 kJ mol-1
3. 1402 kJ mol-1
4. 1012 kJ mol-1

For hydrogen like species, which of the following graphs provides the most appropriate representation of E vs Z plot for a constant n? [E : Energy of the stationary state, Z : atomic number, n = principal quantum number]

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

If C (diamond) C (graphite) + X kJ mol-1 C (diamond) + O2(g) CO2(g) + Y kJ mol-1 C (graphite) + O2(g) CO2(g) + Z kJ mol-1 at constant temperature. Then

1. -X = Y + Z
2. X = Y - Z
3. X = -Y + Z
4. X = Y + Z

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

Total number of sigma ( ) and pi( ) bonds respectively present in hex-1-en-4-yne are:

1. 14 and 3
2. 11 and 3
3. 13 and 3
4. 3 and 13

Which among the following halides will generate the most stable carbocation in the nucleophilic substitution reaction?

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

Drug X becomes ineffective after 50\% decomposition. The original concentration of drug in a bottle was 16 mg/mL which becomes 4 mg/mL in 12 months. The expiry time of the drug in months is . Assume that the decomposition of the drug follows first order kinetics.

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

O2 gas will be evolved as a product of electrolysis of : Choose the correct answer from the options given below :

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

Total number of non-bonded electrons present in NO2- ion based on Lewis theory is .

Consider the following low-spin complexes K3[Co(NO2)6], K4[Fe(CN)6], K3[Fe(CN)6], Cu2[Fe(CN)6] and Zn2[Fe(CN)6] The sum of the spin-only magnetic moment values of complexes having yellow colour is B.M. (answer in nearest integer)

In the sulphur estimation, 0.20 g of a pure organic compound gave 0.40 g of barium sulphate. The percentage of sulphur in the compound is 10-1\%. (Molar mass : O = 16, S = 32, Ba = 137 in g mol-1)

In the Claisen-Schmidt reaction to prepare dibenzalacetone from 5.3 g of benzaldehyde, a total of 3.51 g of product was obtained. The percentage yield in this reaction was %.

Isomeric hydrocarbons negative Baeyer's test (Molecular formula C9H12) The total number of isomers from above with four different non-aliphatic substitution sites is -

Let S = N \0\. Define a relation R from S to R by : R = \(x, y) : e y = x e ( 25 ), x S, y R \. Then, the sum of all the elements in the range of R is equal to :

1. 32
2. 109
3. 52
4. 53

Let A = [aij] be a 2 2 matrix such that aij \0, 1\ for all i and j. Let the random variable X denote the possible values of the determinant of the matrix A. Then, the variance of X is:

1. 58
2. 14
3. 34
4. 38

Let a straight line L pass through the point P(2, -1, 3) and be perpendicular to the lines x-12 = y+11 = z-3-2 and x-31 = y-23 = z+24. If the line L intersects the yz-plane at the point Q, then the distance between the points P and Q is:

1. 10
2. 2
3. 2 3
4. 3

If the domain of the function 5(18x - x2 - 77) is ( , ) and the domain of the function (x-1) ( 2x2 + 3x - 2x2 - 3x - 4 ) is ( , ), then 2 + 2 + 2 is equal to:

1. 186
2. 179
3. 195
4. 174

Let a be a unit vector perpendicular to the vectors b = i - 2 j + 3 k and c = 2 i + 3 j - k, and a makes an angle of -1 (- 13 ) with the vector i + j + k. If a makes an angle of 3 with the vector i + j + k, then the value of is:

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

Let , ( ) be the values of m, for which the equations x + y + z = 1, x + 2y + 4z = m and x + 4y + 10z = m2 have infinitely many solutions. Then the value of n=110(n + n ) is equal to :

1. 3410
2. 560
3. 3080
4. 440

If the set of all a R, for which the equation 2x2 + (a - 5)x + 15 = 3a has no real root, is the interval ( , ), and X = \x Z; < x < \, then x X x2 is equal to:

1. 2139
2. 2119
3. 2109
4. 2129

Let the line x + y = 1 meet the axes of x and y at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB, where O is the origin and the points M and N lie on the lines OB and AB, respectively. If the area of the triangle AMN is 49 of the area of the triangle OAB and AN : NB = : 1, then the sum of all possible value(s) of is:

1. 12
2. 52
3. 2
4. 136

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is 2945, then n is equal to:

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

The remainder, when 7103 is divided by 23, is equal to:

1. 9
2. 6
3. 14
4. 17

If x + y = 109 is the equation of the chord of the ellipse x29 + y24 = 1, whose mid point is ( 52, 12 ). then + is equal to :

1. 37
2. 46
3. 72
4. 58

Let a circle C pass through the points (4, 2) and (0, 2), and its centre lie on 3x + 2y + 2 = 0. Then the length of the chord, of the circle C, whose mid-point is (1, 2), is:

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

If for the solution curve y = f(x) of the differential equation dydx + ( x)y = 2 + x(1 + 2 x)2, x ( - 2, 2 ), f ( 3 ) = 310, then f ( 4 ) is equal to:

1. 5 - 32 2
2. 4 - 214
3. 9 3 + 310(4 + 3)
4. 3 + 110(4 + 3)

Let A = [aij] be a matrix of order 3 3, with aij = ( 2)i+j. If the sum of all the elements in the third row of A2 is + 2, , Z, then + is equal to :

1. 210
2. 280
3. 224
4. 168

If x + 2 x = 1, x (0, 2 ), then ( 12x + 12x) + 3( 10x + 10x + 8 x + 8 x) + ( 6 x + 6 x) is equal to:

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

Let f(x)= 0x t (t2-9t+20 )dt, 1 x 5. If the range of f is [ , ], then 4( + ) equals :

1. 253
2. 157
3. 154
4. 125

Let the area enclosed between the curves |y|=1-x2 and x2+y2=1 be . If 9 = + ; , are integers, then the value of | - | equals:

1. 15
2. 18
3. 33
4. 27

Let P be the foot of the perpendicular from the point (1,2,2) on the line L: x-11= y+1-1= z-22. Let the line r= (- i+ j-2 k )+ ( i- j+ k ), , intersect the line L at Q. Then 2(PQ)2 is equal to :

1. 25
2. 27
3. 19
4. 29

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440th position in this arrangement is :

1. PRNAKU
2. PRKAUN
3. PRKANU
4. PRNAUK

Let the function f(x)= (x2-1 ) |x2-ax+2 |+ |x| be not differentiable at the two points x= =2 and x= . Then the distance of the point ( , ) from the line 12x+5y+10=0 is equal to :

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

If 24 0 4 ( |4x- 12 |+[2 x] )dx=2 + , where [ ] denotes the greatest integer function, then is equal to .

Let y2=12x be the parabola and S be its focus. Let PQ be a focal chord of the parabola such that (SP)(SQ)= 1474. Let C be the circle described taking PQ as a diameter. If the equation of a circle C is 64x2+64y2- x-64 3 y= , then - is equal to .

Let integers a, b [-3,3] be such that a+b 0. Then the number of all possible ordered pairs (a, b), for which | z-az+b |=1 and vmatrixz+1& & 2\ &z+ 2&1\ 2&1&z+ vmatrix=1, z C, where and 2 are the roots of x2+x+1=0, is equal to .

If t 0 ( 01(3x+5)t dx ) 1t= 5e ( 85 ) 23, then is equal to .

Let a1,a2, ,a2024 be an Arithmetic Progression such that a1+(a5+a10+a15+ +a2020)+a2024=2233. Then a1+a2+a3+ +a2024 is equal to .