JEE Main 2025 (Online) 22nd January Morning Shift

A small point of mass m is placed at a distance 2R from the centre ' O ' of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is F1. A spherical part of radius R/3 is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be F2. The value of ratio F1:F2 is [figure]

1. 11 : 10
2. 12 : 11
3. 16 : 9
4. 12 : 9

If B is magnetic field and 0 is permeability of free space, then the dimensions of (B/ 0) is

1. MT-2A-1
2. L-1A
3. ML2T-2A-1
4. LT-2A-1

A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2 is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above. [figure]

1. 1732MR2
2. 1332MR2
3. 932MR2
4. 732MR2

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

1. 64 E
2. 16 E
3. E
4. 256 E

In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to |R1| and |R2|, i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is [figure]

1. - 16 ( 1|R1|- 1|R2| )
2. - 16 ( 1|R1|+ 1|R2| )
3. 16 ( 1|R1|+ 1|R2| )
4. 16 ( 1|R1|- 1|R2| )

A line charge of length a2 is kept at the center of an edge BC of a cube ABCDEFGH having edge length ' a ' as shown in the figure. If the density of line charge is C per unit length, then the total electric flux through all the faces of the cube will be . (Take, 0 as the free space permittivity) [figure]

1. a2 0
2. a8 0
3. a4 0
4. a16 0

A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity v0 at the point ' A ', the string becomes slack when the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points B and C is . [figure]

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

The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of

1. Both Cs and Li
2. Neither Cs nor Li
3. Li only
4. Cs only

An amount of ice of mass 10-3 kg and temperature -10 C is transformed to vapour of temperature 110 C by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice =2100 J kg-1 K-1, specific heat of water =4180 J kg-1 K-1, specific heat of steam =1920 J kg-1 K-1, Latent heat of ice =3.35 105 J kg-1 and Latent heat of steam =2.25 106 J kg-1 )

1. 3022 J
2. 3043 J
3. 3003 J
4. 3024 J

Which of the following circuits represents a forward biased diode? [figure] Choose the correct answer from the options given below:

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

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities 1 and 2, respectively. The frequency of 9th harmonic of closed tube is identical with 4th harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is 1: 2=1:16, then the length of the open tube is :

1. 157 cm
2. 209 cm
3. 207 cm
4. 159 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 false but Statement-II is true
2. Statement-I is true but Statement-II is false
3. Both Statement-I and Statement-II are false
4. Both Statement-I and Statement-II are true

An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 10-11 m while that for the electron in third excited state is 8.48 10-10 m. The ratio of the de Broglie wavelengths of electron in the ground state to that in the excited state is

1. 4
2. 3
3. 9
4. 16

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

An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity 106 m/s. If the magnitude of the electric field between the plates is 9.1 V/cm, then the vertical component of velocity of electron is (mass of electron =9.1 10-31 kg and charge of electron =1.6 10-19 C )

1. 1 106 m/s
2. 16 106 m/s
3. 16 104 m/s
4. 0

Which of the following resistivity ( ) v/s temperature ( T ) curves is most suitable to be used in wire bound standard resistors?

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

Given is a thin convex lens of glass (refractive index ) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself?

1. R/
2. R/(2 -1)
3. R/(2 -3)

A parallel-plate capacitor of capacitance 40 is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K=2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are

1. 8 mC and 2.0 J
2. 4 mC and 0.2 J
3. 2 mC and 0.2 J
4. 2 mC and 0.4 J

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 most appropriate answer from the options given below :

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

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance Rp=1 as shown in the figure. An external resistance of Re=2 is connected via the sliding contact. The electric current in the circuit is : [figure]

1. 1.35 A
2. 0.9 A
3. 1.0 A
4. 0.3 A

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature R=2 m. Another car approaches him from behind with a uniform speed of 90 km/hr. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of 100a is m/s2.

Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is .

Three conductors of same length having thermal conductivity k1,k2 and k3 are connected as shown in figure. [figure] Area of cross sections of 1st and 2nd conductor are same and for 3rd conductor it is double of the 1st conductor. The temperatures are given in the figure. In steady state condition, the value of is . (Given : k1=60 Js-1 m-1 K-1, k2=120 Js-1 m-1 K-1, k3=135 Js-1 m-1 K-1 )

The position vectors of two 1 kg particles, (A) and (B), are given by rA= ( 1t2 i+ 2t j+ 3t k )m and rB= ( 1t i+ 2t2 j+ 3t k )m, respectively; ( 1=1 m/s2, 2=3n m/s, 3=2 m/s, 1=2 m/s, 2=-1 m/s2, 3=4p m/s), where t is time, n and p are constants. At t=1 s, | VA |= | VB | and velocities VA and VB of the particles are orthogonal to each other. At t=1 s, the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is L kg m2 s-1. The value of L is .

A particle is projected at an angle of 30 from horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is h0 and height traversed in the last second, before it reaches the maximum height, is h1. The ratio h0:h1 is . [Take, g=10 m/s2 ]

Which of the following electrolyte can be used to obtain H2S2O8 by the process of electrolysis ?

1. Concentrated solution of sulphuric acid
2. Dilute solution of sodium sulphate.
3. Acidified dilute solution of sodium sulphate.
4. Dilute solution of sulphuric acid

Given below are two statements : In the light of the above statements, choose the most appropriate answer from the options given below :

1. Both Statement I and Statement II are incorrect
2. Both Statement I and Statement II are correct
3. Statement I is correct but Statement II is incorrect
4. Statement I is incorrect but Statement II is correct

The products formed in the following reaction sequence are : [figure]

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

From the magnetic behaviour of [NiCl4]2- (paramagnetic) and [Ni(CO)4] (diamagnetic), choose the correct geometry and oxidation state.

1. [NiCl4]2- : Ni(0), tetrahedral [Ni(CO)4] : Ni(0), square planar
2. [NiCl4]2- : NiII, tetrahedral [Ni(CO)4] : Ni(0), tetrahedral
3. [NiCl4]2- : NiII, tetrahedral [Ni(CO)4] : NiII, square planar
4. [NiCl4]2- : NiII, square planar [Ni(CO)4] : Ni(0), square planar

The compounds which give positive Fehling's test are : Choose the correct answer from the options given below :

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

Match List-I with List-II.

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

A vessel at 1000 K contains CO2 with a pressure of 0.5 atm. Some of CO2 is converted into CO on addition of graphite. If total pressure at equilibrium is 0.8 atm, then Kp is :

1. 0.18 atm
2. 0.3 atm
3. 3 atm
4. 1.8 atm

A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2 A. The amount of the aluminium deposited at the cathode is . [Given : molar mass of aluminium and chlorine are 27 g mol-1 and 35.5 g mol-1 respectively. Faraday constant = 96500 C mol-1]

1. 1.660 g
2. 1.007 g
3. 0.336 g
4. 0.441 g

How many different stereoisomers are possible for the given molecule? [figure]

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

A liquid when kept inside a thermally insulated closed vessel at 25 was mechanically stirred from outside. What will be the correct option for the following thermodynamic parameters ?

1. U = 0, q < 0, w > 0
2. U > 0, q = 0, w > 0
3. U = 0, q = 0, w = 0
4. U < 0, q = 0, w > 0

Lanthanoid ions with 4f7 configuration are : Choose the correct answer from the options given below :

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

The incorrect statements regarding geometrical isomerism are : Choose the correct answer from the options given below :

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

Given below are two statements : In the light of the above statements, choose the most appropriate answer from the options given below :

1. Both Statement I and Statement II are incorrect
2. Statement I is incorrect but Statement II is correct
3. Both Statement I and Statement II are correct
4. Statement I is correct but Statement II is incorrect

Which of the following electronegativity order is incorrect?

1. S<Cl<O<F
2. Al<Si<C<N
3. Al<Mg<B<N
4. Mg<Be<B<N

Arrange the following solutions in order of their increasing boiling points. (i) 10-4 M NaCl (ii) 10-4 M Urea (iii) 10-3 M NaCl (iv) 10-2 M NaCl

1. (i) < (ii) < (iii) < (iv)
2. (ii) < (i) < (iii) < (iv)
3. (iv) < (iii) < (i) < (ii)
4. (ii) < (i) (iii) < (iv)

In which of the following complexes the CFSE, o will be equal to zero?

1. K3[Fe(SCN)6]
2. [Fe(en)3]Cl3
3. [Fe(NH3)6]Br2
4. K4[Fe(CN)6]

Which of the following acids is a vitamin ?

1. Saccharic acid
2. Ascorbic acid
3. Aspartic acid
4. Adipic acid

Radius of the first excited state of Helium ion is given as : a0 radius of first stationary state of hydrogen atom.

1. r = a04
2. r = 2a0
3. r = 4a0
4. r = a02

The IUPAC name of the following compound is : [figure]

1. 5-Methoxycarbonyl-2-methylhexanoic acid
2. Methyl-5-carboxy-2-methylhexanoate.
3. 2-Carboxy-5-methoxycarbonylhexane.
4. Methyl-6-carboxy-2,5-dimethylhexanoate.

Consider the following sequence of reactions : [figure] Molar mass of the product formed (A) is g mol-1.

The number of molecules/ions that show linear geometry among the following is . SO2, BeCl2, CO2, N3-, NO2, F2O, XeF2, NO2+, I3-, O3

Some CO2 gas was kept in a sealed container at a pressure of 1 atm and at 273 K. This entire amount of CO2 gas was later passed through an aqueous solution of Ca(OH)2. The excess unreacted Ca(OH)2 was later neutralized with 0.1 M of 40 mL HCl. If the volume of the sealed container of CO2 was x, then x is cm3 (nearest integer). [Given : The entire amount of CO2(g) reacted with exactly half the initial amount of Ca(OH)2 present in the aqueous solution.]

In Carius method for estimation of halogens, 180 mg of an organic compound produced 143.5 mg of AgCl. The percentage composition of chlorine in the compound is %. (Given : molar mass in g mol-1 of Ag:108, Cl:35.5)

A B The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K. If the energy barrier with respect to reactant energy for such isomeric transformation is 191.48 kJ mol-1 and the frequency factor is 1020, the time required for 50\% molecules of A to become B is picoseconds (nearest integer). [R=8.314 J K-1 mol-1 ]

Which of the following statement is not true for radioactive decay?

1. Half life is 2 times of 1rate constant.
2. Decay constant increases with increase in temperature.
3. Decay constant does not depend upon temperature.
4. Amount of radioactive substance remained after three half lives is 18th of original amount.

The area of the region, inside the circle (x-2 3)2+y2=12 and outside the parabola y2=2 3 x is :

1. 3 -8
2. 6 -8
3. 3 +8
4. 6 -16

Let the foci of a hyperbola be (1,14) and (1,-12). If it passes through the point (1,6), then the length of its latus-rectum is :

1. 256
2. 1445
3. 2885
4. 245

Let z1,z2 and z3 be three complex numbers on the circle |z|=1 with (z1)= - 4, (z2)=0 and (z3)= 4. If |z1 z2+z2 z3+z3 z1 |2= + 2, , Z, then the value of 2+ 2 is :

1. 41
2. 29
3. 24
4. 31

Let L1: x-12= y-23= z-34 and L2: x-23= y-44= z-55 be two lines. Then which of the following points lies on the line of the shortest distance between L1 and L2 ?

1. ( 143,-3, 223 )
2. (2,3, 13 )
3. ( 83,-1, 13 )
4. (- 53,-7,1 )

Let A=\1,2,3, ,10\ and B= \ mn:m,n A, m<n and (m,n)=1 \. Then n(B) is equal to :

1. 29
2. 31
3. 37
4. 36

Let the triangle PQR be the image of the triangle with vertices (1,3),(3,1) and (2,4) in the line x+2y=2. If the centroid of is the point ( , ), then 15( - ) is equal to :

1. 21
2. 19
3. 22
4. 24

The product of all solutions of the equation e5( ex)2+3=x8, x>0, is :

1. e2
2. e
3. e6/5
4. e8/5

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :

1. 6084
2. 5148
3. 14950
4. 4356

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point (2,5) and intersects the circle C at exactly two points. If the set of all possible values of r is the interval ( , ), then 3 -2 is equal to :

1. 10
2. 12
3. 14
4. 15

Let x=x(y) be the solution of the differential equation y2 dx+ (x- 1y )dy=0. If x(1)=1, then x ( 12 ) is :

1. 32+e
2. 12+e
3. 3+e
4. 3-e

A coin is tossed three times. Let X denote the number of times a tail follows a head. If and 2 denote the mean and variance of X, then the value of 64 ( + 2 ) is:

1. 64
2. 32
3. 51
4. 48

Let f(x) be a real differentiable function such that f(0)=1 and f(x+y)=f(x)f'(y)+f'(x)f(y) for all x,y . Then n=1100 ef(n) is equal to :

1. 2406
2. 5220
3. 2525
4. 2384

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is mn, where (m,n)=1, then m+n is equal to :

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

Let a1,a2,a3, be a G.P. of increasing positive terms. If a1a5=28 and a2+a4=29, then a6 is equal to:

1. 812
2. 784
3. 628
4. 526

Let for f(x)=7 8x+7 6x-3 4x-3 2x, I1= 0 /4f(x) dx and I2= 0 /4x f(x) dx. Then 7I1+12I2 is equal to :

1. 2
2. 1
4. 2

The number of non-empty equivalence relations on the set \1,2,3\ is :

1. 7
2. 4
3. 5
4. 6

Let the parabola y=x2+px-3, meet the coordinate axes at the points P, Q and R. If the circle C with centre at (-1,-1) passes through the points P, Q and R, then the area of PQR is :

1. 4
2. 6
3. 5
4. 7

Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of 16 ( ( -1x )2+ ( cosec-1x )2 ) is :

1. 24 2
2. 18 2
3. 22 2
4. 31 2

Let f:R be a twice differentiable function such that f(x+y)=f(x)f(y) for all x,y . If f'(0)=4a and f satisfies f''(x)-3af'(x)-f(x)=0, a>0, then the area of the region R=\(x,y) 0 y f(ax), 0 x 2\ is :

1. e2-1
2. e4+1
3. e2+1
4. e4-1

If r=1nTr= (2n-1)(2n+1)(2n+3)(2n+5)64, then n r=1n ( 1Tr ) is equal to :

1. 23
2. 13
3. 1
4. 0

Let the function, f(x)= cases-3ax2-2, & x<1\ a2+bx, & x 1 cases be differentiable for all x , where a>1, b . If the area of the region enclosed by y=f(x) and the line y=-20 is + 3, , Z, then the value of + is .

Let c be the projection vector of b= i+4 k, >0, on the vector a= i+2 j+2 k. If | a+ c|=7, then the area of the parallelogram formed by the vectors b and c is .

If r=05 11C2r+12r+2= mn, (m,n)=1, then m-n is equal to .

Let L1: x-13= y-1-1= z+10 and L2: x-22= y0= z+4 , , be two lines, which intersect at the point B. If P is the foot of perpendicular from the point A(1,1,-1) on L2, then the value of 26 (PB)2 is .

Let A be a square matrix of order 3 such that (A)=-2 and (3 adj (-6 adj(3A) ) )=2m+n 3mn, m>n. Then 4m+2n is equal to .