JEE Main 2025 (Online) 23rd January Morning Shift

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

A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q separated by a distance 2a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation? [figure]

1. ar 0.5
2. ar 3
3. ar 10
4. ar 20

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ' h ' in terms of the angle of incidence ' i ' and angle of refraction ' r ', if the glass slab is placed in air medium?

1. h
2. h (i-r) r
3. h (i-r) r
4. h (i-r) r

A sub-atomic particle of mass 10-30 kg is moving with a velocity 2.21 106 m/s. Under the matter wave consideration, the particle will behave closely like (h=6.63 10-34 J.s )

1. X-rays
2. Infra-red radiation
3. Gamma rays
4. Visible radiation

The position of a particle moving on x-axis is given by x(t)=A t+B 2t+Ct2+D, where t is time. The dimension of ABCD is

1. L
2. L3 T-2
3. L2 T-2
4. L2

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

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J, then the mass of the bullet is grams. (Latent heat of fusion of lead =2.5 104 J Kg-1 and specific heat capacity of lead =125 J Kg-1 K-1)

1. 20
2. 15
3. 5
4. 10

A solid sphere of mass ' m ' and radius ' r ' is allowed to roll without slipping from the highest point of an inclined plane of length ' L ' and makes an angle 30 with the horizontal. The speed of the particle at the bottom of the plane is v1. If the angle of inclination is increased to 45 while keeping L constant. Then the new speed of the sphere at the bottom of the plane is v2. The ratio v12:v22 is

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

A radioactive nucleus n2 has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n1. If initial number of both nuclei are the same, what is the ratio of number of nuclei of n2 to the number of nuclei of n1, after one half-life of n1 ?

1. 1/4
2. 1/8
3. 4
4. 8

A light hollow cube of side length 10 cm and mass 10 g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is y 10-2 s, where the value of y is (Acceleration due to gravity, g=10 m/s2, density of water =103 kg/m3 )

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

A spherical surface of radius of curvature R, separates air from glass (refractive index =1.5). The centre of curvature is in the glass medium. A point object 'O' placed in air on the optic axis of the surface, so that its real image is formed at 'I' inside glass. The line OI intersects the spherical surface at P and PO=PI. The distance PO equals to

1. 5R
2. 2R
3. 1.5R
4. 3R

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be

1. 1.5 cm
2. 2.0 cm
3. 0.5 cm
4. 1.0 cm

Refer to the circuit diagram given in the figure. which of the following observations are correct? [figure] Choose the correct answer from the options given below:

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

The electric field of an electromagnetic wave in free space is E=57 [7.5 106t-5 10-3(3x+4y) ](4 i-3 j) N/C. The associated magnetic field in Tesla is

1. B= 573 108 [7.5 106t-5 10-3(3x+4y) ]( k)
2. B= 573 108 [7.5 106t-5 10-3(3x+4y) ](5 k)
3. B=- 573 108 [7.5 106t-5 10-3(3x+4y) ]( k)
4. B=- 573 108 [7.5 106t-5 10-3(3x+4y) ](5 k)

The electric flux is = + where and are linear and surface charge density, respectively. ( ) represents

1. displacement
2. charge
3. electric field
4. area

Consider a moving coil galvanometer (MCG): Choose the correct answer from the options given below:

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

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is km . [figure]

1. 12
2. 6
3. 3
4. 9

Regarding self-inductance: Choose the correct answer from the options given below:

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

Identify the valid statements relevant to the given circuit at the instant when the key is closed. [figure] Choose the correct answer from the options given below:

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

Given a thin convex lens (refractive index 2), kept in a liquid (refractive index 1, 1< 2) having radii of curvatures |R1| and |R2|. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

1. ( 2+ 1)|R1|( 2- 1)
2. 1|R1| |R2| 2 (2|R1|+|R2| )- 1 |R1| |R2|
3. 1|R1| |R2| 2 (|R1|+|R2| )- 1|R1|
4. 1|R1| |R2| 2 (|R1|+|R2| )- 1|R2|

Two particles are located at equal distance from origin. The position vectors of those are represented by A=2 i+3n j+2 k and B=2 i-2 j+4p k, respectively. If both the vectors are at right angle to each other, the value of n-1 is .

A force f=x2y i+y2 j acts on a particle in a plane x+y=10. The work done by this force during a displacement from (0,0) to (4 m,2 m) is Joule (round off to the nearest integer)

[figure] In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of 8 A/s. At an instant when R is 12 , the value of the current in the circuit will be A.

A positive ion A and a negative ion B has charges 6.67 10-19 C and 9.6 10-10 C, and masses 19.2 10-27 kg and 9 10-27 kg respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is P 10-13, where the value of P is . (Take 14 0=9 109 Nm2C-2 and universal gravitational constant as 6.67 10-11 Nm2 kg-2 )

An ideal gas initially at 0 temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3/2, the change in temperature due to the thermodynamic process is K.

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

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

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

What amount of bromine will be required to convert 2 g of phenol into 2,4,6-tribromophenol? (Given molar mass in g mol-1 of C, H, O, Br are 12, 1, 16, 80 respectively )

1. 6.0 g
2. 10.22 g
3. 20.44 g
4. 4.0 g

The correct set of ions (aqueous solution) with same colour from the following is:

1. V2+, Cr3+, Mn3+
2. Ti4+, V4+, Mn2+
3. Sc3+, Ti3+, Cr2+
4. Zn2+, V3+, Fe3+

FeO42- +2.0 V Fe3+ 0.8 V Fe2+ -0.5 V Fe0 In the above diagram, the standard electrode potentials are given in volts (over the arrow). The value of E (FeO42-/Fe2+) is :

1. 1.2 V
2. 2.1 V
3. 1.4 V
4. 1.7 V

CrCl3 xNH3 can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of 0.558 C. Assuming 100% ionisation of this complex and coordination number of Cr is 6, the complex will be (Given Kf = 1.86 K kg mol-1)

1. [Cr(NH3)5Cl]Cl2
2. [Cr(NH3)4Cl2]Cl
3. [Cr(NH3)6]Cl3
4. [Cr(NH3)3Cl3]

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

1. [figure]
2. CH3-CH2-CH2-OH
3. [figure]
4. [figure]

Propane molecule on chlorination under photochemical condition gives two di-chloro products, “x” and “y”. Amongst “x” and “y”, “x” is an optically active molecule. How many tri-chloro products (consider only structural isomers) will be obtained from “x” when it is further treated with chlorine under the photochemical condition?

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

The incorrect statement among the following is

1. PH3 shows lower proton affinity than NH3.
2. SO2 can act as an oxidizing agent, but not as a reducing agent.
3. NO2 can dimerise easily.
4. PF3 exists but NF5 does not.

The correct stability order of the following species/molecules is : [figure]

1. q > r > p
2. q > p > r
3. p > q > r
4. r > q > p

2.8 10-3 mol of CO2 is left after removing 1021 molecules from its ' x ' mg sample. The mass of CO2 taken initially is Given: NA = 6.02 1023 mol-1

1. 98.3 mg
2. 196.2 mg
3. 150.4 mg
4. 48.2 mg

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 true
4. Both Statement I and Statement II are false

Which of the following happens when NH4OH is added gradually to the solution containing 1 M A2+ and 1M B3+ ions? Given : Ksp [A(OH)2] = 9 10-10 and Ksp [B(OH)3] = 27 10-18 at 298 K.

1. A(OH)2 will precipitate before B(OH)3
2. A(OH)2 and B(OH)3 will precipitate together
3. Both A(OH)2 and B(OH)3 do not show precipitation with NH4OH
4. B(OH)3 will precipitate before A(OH)2

Ice at -5 C is heated to become vapor with temperature of 110 C at atmospheric pressure. The entropy change associated with this process can be obtained from

1. 268 K273 K Cp,m dT + Hm, fusionTf + Hm, vaporisationTb + 273 K373 K Cp,m dT + 373 K383 K Cp,m dT
2. 268 K383 K Cp dT + Hmelting273 + Hboiling373
3. 268 K383 K Cp dT + qrevT
4. 268 K273 K Cp,mT dT + Hm, fusionTf + Hm, vaporisationTb + 273 K373 K Cp,m dTT + 373 K383 K Cp,m dTT

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

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

The element that does not belong to the same period of the remaining elements (modern periodic table) is:

1. Platinum
2. Osmium
3. Iridium
4. Palladium

The d-electronic configuration of an octahedral Co (II) complex having magnetic moment of 3.95 BM is:

1. e4t23
2. t2g6eg1
3. t2g5eg2
4. t2g3eg0

The complex that shows Facial - Meridional isomerism is :

1. [Co(en)2Cl2]+
2. [Co(NH3)3Cl3]
3. [Co(NH3)4Cl2]+
4. [Co(en)3]3+

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this? Given : Rydberg constant RH = 105 cm-1, h = 6.6 10-34 J s, c = 3 108 m/s

1. Lyman series, 1
2. Balmer series, 2
3. Paschen series, 5 3
4. Paschen series, 3

Which among the following react with Hinsberg's reagent? Choose the correct answer from the options given below :

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

For the thermal decomposition of N2O5(g) at constant volume, the following table can be formed, for the reaction mentioned below. 2N2O5(g) 2N2O4(g)+O2(g) [figure] x= 10-3 atm [nearest integer] Given : Rate constant for the reaction is 4.606 10-2 s-1.

The standard enthalpy and standard entropy of decomposition of N2O4 to NO2 are 55.0 kJ mol-1 and 175.0 J/K/mol respectively. The standard free energy change for this reaction at 25 in J mol-1 is (Nearest integer)

If 1 mM solution of ethylamine produces pH=9, then the ionization constant (Kb) of ethylamine is 10-x. The value of x is (nearest integer). [The degree of ionization of ethylamine can be neglected with respect to unity.]

Consider the following sequence of reactions to produce major product (A) [figure] Molar mass of product (A) is g mol-1. (Given molar mass in g mol-1 of C : 12, H : 1, O : 16, Br : 80, N : 14, P : 31)

During " S " estimation, 160 mg of an organic compound gives 466 mg of barium sulphate. The percentage of Sulphur in the given compound is %. (Given molar mass in g mol-1 of Ba : 137, S : 32, O : 16)

Let a curve y=f(x) pass through the points (0,5) and ( e 2,k). If the curve satisfies the differential equation 2(3+y)e2xdx-(7+e2x)dy=0, then k is equal to

1. 32
2. 8
3. 4
4. 16

Let P be the foot of the perpendicular from the point Q(10,-3,-1) on the line x-37= y-2-1= z+1-2. Then the area of the right angled triangle PQR, where R is the point (3,-2,1), is

1. 30
2. 9 15
3. 3 30
4. 8 15

The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is :

1. 34000
2. 37000
3. 35000
4. 36000

Let f(x)= e x and g(x)= x4-2x3+3x2-2x+22x2-2x+1. Then the domain of f g is

1. (0, )
2. [1, )
3. R
4. [0, )

Let the position vectors of the vertices A, B and C of a tetrahedron ABCD be i+2 j+ k, i+3 j-2 k and 2 i+ j- k respectively. The altitude from the vertex D to the opposite face ABC meets the median line segment through A of the triangle ABC at the point E. If the length of AD is 1103 and the volume of the tetrahedron is 8056 2, then the position vector of E is

1. 16 (7 i+12 j+ k )
2. 112 (7 i+4 j+3 k )
3. 16 (12 i+12 j+ k )
4. 12 ( i+4 j+7 k )

If 2 x 3 4, then -1 ( 1213 x+ 513 x ) is equal to

1. x+ -1 512
2. x- -1 43
3. x+ -1 45
4. x- -1 512

One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two faces marked 2 , two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are thrown together, is

1. 23
2. 35
3. 49
4. 12

The value of ( 70 ) ( 10 70 -1 ) is

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

If the function f(x)= cases 2x \ (k1+1)x+ (k2-1)x \, & x<0\\[2mm] 4, & x=0\\[2mm] 2x e ( 2+k1x2+k2x ), & x>0 cases is continuous at x=0, then k12+k22 is equal to :

1. 5
2. 10
3. 20
4. 8

If the system of equations ( -1)x+( -4)y+ z=5 x+( -1)y+( -4)z=7 ( +1)x+( +2)y-( +2)z=9 has infinitely many solutions, then 2+ is equal to

1. 20
2. 10
3. 6
4. 12

The value of e2e4 1x ( e (( ex)2+1 )-1e (( ex)2+1 )-1+e ((6- ex)2+1 )-1 )dx is

1. 1
2. loge 2
3. e2
4. 2

Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18 , then the total number of students is :

1. 52
2. 44
3. 40
4. 48

Let | z-i2 z+i |= 13, z C, be the equation of a circle with center at C. If the area of the triangle, whose vertices are at the points (0,0), C and ( ,0) is 11 square units, then 2 equals:

1. 12125
2. 100
3. 8125
4. 50

Let I(x)= dx(x-11) 1113(x+15) 1513. If I(37)-I(24)= 14 ( 1b 113- 1c 113 ), b,c N, then 3(b+c) is equal to

1. 39
2. 22
3. 40
4. 26

If the line 3x-2y+12=0 intersects the parabola 4y=3x2 at the points A and B, then at the vertex of the parabola, the line segment AB subtends an angle equal to

1. 2- -1 ( 32 )
2. -1 ( 97 )
3. -1 ( 119 )
4. -1 ( 45 )

If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

1. -120
2. -1200
3. -1080
4. -1020

Let the arc AC of a circle subtend a right angle at the centre O. If the point B on the arc AC, divides the arc AC such that length of arc ABlength of arc BC= 15, and OC= OA+ OB, then + 2( 3-1) is equal to

1. 2 3
2. 5 3
3. 2+ 3
4. 2- 3

Let the area of a PQR with vertices P(5,4), Q(-2,4) and R(a,b) be 35 square units. If its orthocenter and centroid are O (2, 145 ) and C(c,d) respectively, then c+2d is equal to

1. 3
2. 73
3. 2
4. 83

If A, B, and (adj (A-1 )+adj (B-1 ) ) are non-singular matrices of same order, then the inverse of A (adj (A-1 )+adj (B-1 ) )-1B, is equal to

1. AB-1|A|+ BA-1|B|
2. adj (B-1 )+adj (A-1 )
3. AB-1+A-1B
4. 1|AB| (adj(B)+adj(A) )

Let R=\(1,2),(2,3),(3,3)\ be a relation defined on the set \1,2,3,4\. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:

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

The sum of all rational terms in the expansion of (1+21/3+31/2 )6 is equal to .

If the set of all values of a, for which the equation 5x3-15x-a=0 has three distinct real roots, is the interval ( , ), then -2 is equal to .

If the equation a(b-c)x2+b(c-a)x+c(a-b)=0 has equal roots, where a+c=15 and b= 365, then a2+c2 is equal to .

Let the circle C touch the line x-y+1=0, have the centre on the positive x-axis, and cut off a chord of length 4 13 along the line -3x+2y=1. Let H be the hyperbola x2 2- y2 2=1, whose one of the foci is the centre of C and the length of the transverse axis is the diameter of C. Then 2 2+3 2 is equal to .

If the area of the larger portion bounded between the curves x2+y2=25 and y=|x-1| is 14(b +c), b,c , then b+c is equal to