JEE Main 2025 (Online) 24th January Morning Shift

An object of mass 'm' is projected from origin in a vertical xy plane at an angle 45 with the x-axis with an initial velocity v0. The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity]

1. mv032 2 g along negative z-axis
2. mv032 2 g along positive z-axis
3. mv034 2 g along positive z-axis
4. mv034 2 g along negative z-axis

The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is

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

What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5 D ? ['D' stands for dioptre]

1. 0.04
2. 0.1
3. 0.40
4. 0.01

A car of mass 'm' moves on a banked road having radius 'r' and banking angle . To avoid slipping from banked road, the maximum permissible speed of the car is v0. The coefficient of friction between the wheels of the car and the banked road is

1. = v02+rg rg+v02
2. = v02-rg rg-v02
3. = v02-rg rg+v02
4. = v02+rg rg-v02

During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is 2000 and it becomes 6000 when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is

1. 4000
2. 6000
3. 2000
4. 3000

A satellite is launched into a circular orbit of radius 'R' around the earth. A second satellite is launched into an orbit of radius 1.03 R. The time period of revolution of the second satellite is larger than the first one approximately by

1. 3%
2. 2.5%
3. 4.5%
4. 9%

A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm. If D and d are the total distance and displacement covered by the particle in 12.5 s, then Dd is

1. 10
2. 165
3. 25
4. 154

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg/m3. If the pressure inside the bubble is 2100 N/m2 greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g=10 m/s2)

1. 0.02
2. 0.05
3. 0.25
4. 0.1

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature. Choose the correct answer from the options given below:

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

Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is the electric field and 0 is the permittivity of free space between the plates, then potential energy stored in the capacitor is

1. 0E2Ad
2. 34 0E2Ad
3. 14 0E2Ad
4. 12 0E2Ad

A force F= + x2 acts on an object in the x-direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant =1 N then will be

1. 15 N/m2
2. 10 N/m2
3. 12 N/m2
4. 8 N/m2

Consider the following statements : Choose the correct answer from the options given below :

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

A parallel plate capacitor was made with two rectangular plates, each with a length of l=3 cm and breadth of b=1 cm. The distance between the plates is 3 . Out of the following, which are the ways to increase the capacitance by a factor of 10 ? Choose the correct answer from the options given below:

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

A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m. The radius of curvature of the curved surface of the lens is

1. 0.15 m
2. 0.10 m
3. 0.25 m
4. 0.20 m

A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of f1 in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of f2 when it is immersed in a liquid of refractive index 1.2. If both the lenses are made of same glass of refractive index 1.5, the ratio of f1 and f2 will be

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

An electron of mass 'm' with an initial velocity v=v0 i (v0>0) enters an electric field E=-Eo k. If the initial de Broglie wavelength is 0, the value after time t would be

1. o 1- e2Eo2t2m2vo2
2. 0
3. o 1+ e2Eo2t2m2vo2
4. o 1+ e2Eo2t2m2vo2

The amount of work done to break a big water drop of radius 'R' into 27 small drops of equal radius is 10 J. The work done required to break the same big drop into 64 small drops of equal radius will be

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

A uniform solid cylinder of mass 'm' and radius 'r' rolls along an inclined rough plane of inclination 45 . If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be

1. 2 g
2. 1 2 g
3. 13 2 g
4. 2 g3

An alternating current is given by I=IA t+IB t. The r.m.s current will be

1. IA2+IB22
2. IA2+IB22
3. |IA+IB| 2
4. IA2+IB2

For an experimental expression y= 32.3 112527.4, where all the digits are significant. Then to report the value of y we should write

1. y=1326.186
2. y=1326.2
3. y=1326.19
4. y=1330

A wire of resistance 9 is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be ohm.

A current of 5 A exists in a square loop of side 1 2 m. Then the magnitude of the magnetic field B at the centre of the square loop will be p 10-6 T. where, value of p is [Take 0=4 10-7 T m A-1].

The least count of a screw gauge is 0.01 mm. If the pitch is increased by 75% and number of divisions on the circular scale is reduced by 50%, the new least count will be 10-3 mm.

The temperature of 1 mole of an ideal monoatomic gas is increased by 50 at constant pressure. The total heat added and change in internal energy are E1 and E2, respectively. If E1E2= x9 then the value of x is .

A square loop of sides a=1 m is held normally in front of a point charge q=1 C at a distance a2. The flux of the electric field through the shaded region is 5p 1 0 N m2C, where the value of p is . [figure]

For a reaction, N2O5(g) 2NO2(g) + 12O2(g) in a constant volume container, no products were present initially. The final pressure of the system when 50\% of reaction gets completed is

1. 5/2 times of initial pressure
2. 7/2 times of initial pressure
3. 7/4 times of initial pressure
4. 5 times of initial pressure

The large difference between the melting and boiling points of oxygen and sulphur may be explained on the basis of

1. Atomicity
2. Electron gain enthalpy
3. Atomic size
4. Electronegativity

Given below are two statements I and II. 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

Consider the given plots of vapour pressure (VP) vs temperature (T/K). Which amongst the following options is correct graphical representation showing Tf, depression in the freezing point of a solvent in a solution?

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. 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

Preparation of potassium permanganate from MnO2 involves two step process in which the 1st step is a reaction with KOH and KNO3 to produce

1. K3MnO4
2. K4[Mn(OH)6]
3. K2MnO4
4. KMnO4

Which one of the carbocations from the following is most stable?

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

The product (A) formed in the following reaction sequence is [figure]

1. CH3-CH2- OH |CH-CH2-NH2
2. CH3-CH2- NH2 |CH-CH2-NH2
3. CH3- CH3 | OH |C-CH2-NH2
4. CH3- CH3 | NH2 |C-CH2-OH

Ksp for Cr(OH)3 is 1.6 10-30. What is the molar solubility of this salt in water?

1. [5]1.8 10-30
2. 1.8 10-3027
3. [4] 1.6 10-3027
4. [2]1.6 10-30

Which of the following linear combination of atomic orbitals will lead to formation of molecular orbitals in homonuclear diatomic molecules [internuclear axis in z-direction] ? Choose the correct answer from the options given below:

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

Which of the following statements are NOT true about the periodic table? Choose the correct answer from the options given below:

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

One mole of the octahedral complex compound Co(NH3)5Cl3 gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with excess of AgNO3 solution to yield two moles of AgCl(s). The structure of the complex is:

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

Which of the following statement is true with respect to H2O, NH3 and CH4 ? Choose the correct answer from the options given below:

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

Let us consider an endothermic reaction which is non-spontaneous at the freezing point of water. However, the reaction is spontaneous at boiling point of water. Choose the correct option.

1. Both and are (-ve)
2. is (+ve) but is (-ve)
3. is (-ve) but is (+ve)
4. Both and are (+ve)

Which of the following arrangements with respect to their reactivity in nucleophilic addition reaction is correct?

1. acetophenone < benzaldehyde < p-tolualdehyde < p-nitrobenzaldehyde
2. acetophenone < p-tolualdehyde < benzaldehyde < p-nitrobenzaldehyde
3. p-nitrobenzaldehyde < benzaldehyde < p-tolualdehyde < acetophenone
4. benzaldehyde < acetophenone < p-nitrobenzaldehyde < p-tolualdehyde

The carbohydrate "Ribose" present in DNA, is Choose the correct answer from the options given below:

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

Aman has been asked to synthesise the molecule [figure] He thought of preparing the molecule using an aldol condensation reaction. He found a few cyclic alkenes in his laboratory. He thought of performing ozonolysis reaction on alkene to produce a dicarbonyl compound followed by aldol reaction to prepare "x". Predict the suitable alkene that can lead to the formation of "x".

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

For the given cell Fe2+(aq) + Ag+(aq) Fe3+(aq) + Ag(s) The standard cell potential of the above reaction is Given: Ag+ + e- Ag E = xV Fe2+ + 2e- Fe E = yV Fe3+ + 3e- Fe E = zV

1. x + 2y - 3z
2. x + 2y
3. y - 2x
4. x + y - z

Following are the four molecules "P", "Q", "R" and "S". Which one among the four molecules will react with H-Br(aq) at the fastest rate? [figure]

1. Q
2. S
3. P
4. R

Which of the following ions is the strongest oxidizing agent? (Atomic Number of Ce = 58, Eu = 63, Tb = 65, Lu = 71)

1. Lu3+
2. Eu2+
3. Tb4+
4. Ce3+

37.8 g N2O5 was taken in a 1 L reaction vessel and allowed to undergo the following reaction at 500 K 2N2O5(g) 2N2O4(g) + O2(g) The total pressure at equilibrium was found to be 18.65 bar. Then, Kp = 10-2 [nearest integer] Assume N2O5 to behave ideally under these conditions. Given: R = 0.082 bar L mol-1 K-1

Among the following cations, the number of cations which will give characteristic precipitate in their identification tests with K4[Fe(CN)6] is . Cu2+, Fe3+, Ba2+, Ca2+, NH4+, Mg2+, Zn2+

Consider the following reaction occurring in the blast furnace: Fe3O4(s) + 4CO(g) 3Fe(l) + 4CO2(g) 'x' kg of iron is produced when 2.32 103 kg Fe3O4 and 2.8 102 kg CO are brought together in the furnace. The value of 'x' is . (nearest integer) Given: molar mass of Fe3O4 = 232 g mol-1 molar mass of CO = 28 g mol-1 molar mass of Fe = 56 g mol-1

Xg of benzoic acid on reaction with aq NaHCO3 released CO2 that occupied 11.2 L volume at STP. X is g.

Standard entropies of X2, Y2 and XY5 are 70, 50 and 110 J K-1 mol-1 respectively. The temperature in Kelvin at which the reaction 12X2 + 52Y2 XY5 H = -35 kJ mol-1 will be at equilibrium is (Nearest integer)

x 0 cosecx ( 2 2x+3 x- 2x+ x+4 ) is

1. 1 15
2. 12 5
3. 0
4. - 12 5

Let f:R-\0\ be a function such that f(x)-6f ( 1x )= 353x- 52. If x 0 ( 1 x+f(x) )= ; , , then +2 is equal to

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

The product of all the rational roots of the equation (x2-9x+11)2-(x-4)(x-5)=3, is equal to

1. 7
2. 21
3. 28
4. 14

For some n 10, let the coefficients of the 5 th, 6 th and 7 th terms in the binomial expansion of (1+x)n+4 be in A.P. Then the largest coefficient in the expansion of (1+x)n+4 is:

1. 10
2. 35
3. 70
4. 20

Let f(x)= 2x+2+1622x+1+2x+4+32. Then the value of 8 (f ( 115 )+f ( 215 )+ +f ( 5915 ) ) is equal to

1. 108
2. 92
3. 118
4. 102

If I(m,n)= 01xm-1(1-x)n-1dx, m,n>0, then I(9,14)+I(10,13) is

1. I(9,1)
2. I(1,13)
3. I(19,27)
4. I(9,13)

If and are the roots of the equation 2z2-3z-2i=0, where i= -1, then 16 ( 19+ 19+ 11+ 11 15+ 15 ) ( 19+ 19+ 11+ 11 15+ 15 ) is equal to

1. 441
2. 312
3. 409
4. 398

Let the product of the focal distances of the point ( 3, 12 ) on the ellipse x2a2+ y2b2=1, (a>b), be 74. Then the absolute difference of the eccentricities of two such ellipses is

1. 1-2 2 3
2. 1- 3 2
3. 3-2 22 3
4. 3-2 23 2

Let y=y(x) be the solution of the differential equation (xy-5x2 1+x2 )dx+ (1+x2 )dy=0, y(0)=0. Then y( 3) is equal to

1. 5 32
2. 152
3. 143
4. 2 2

Let in a ABC, the length of the side AC be 6, the vertex B be (1,2,3) and the vertices A, C lie on the line x-63= y-72= z-7-2. Then the area (in sq. units) of ABC is:

1. 42
2. 17
3. 56
4. 21

Let the line passing through the point (-1,2,1) and parallel to the line x-12= y+13= z4 intersect the line x+23= y-32= z-41 at the point P. Then the distance of P from the point Q(4,-5,1) is

1. 5 6
2. 5
3. 5 5
4. 10

A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8 before A throws a sum of 5. The probability, that A wins if A makes the first throw, is

1. 819
2. 919
3. 817
4. 917

Let a= i+2 j+3 k, b=3 i+ j- k and c be three vectors such that c is coplanar with a and b. If the vector c is perpendicular to b and a c=5, then | c| is equal to

1. 116
2. 13 2
3. 18
4. 16

Consider the region R= \(x,y):x y 9- 113x2, x 0 \. The area of the largest rectangle of sides parallel to the coordinate axes and inscribed in R, is:

1. 821123
2. 567121
3. 730119
4. 625111

The area of the region \(x,y):x2+4x+2 y |x+2| \ is equal to

1. 7
2. 24/5
3. 20/3
4. 5

Let Sn= 12+ 16+ 112+ 120+ upto n terms. If the sum of the first six terms of an A.P. with first term -p and common difference p is 2026 S2025, then the absolute difference between 20th and 15th terms of the A.P. is

1. 20
2. 45
3. 90
4. 25

For a statistical data x1, x2, , x10 of 10 values, a student obtained the mean as 5.5 and i=110xi2=371. He later found that he had noted two values in the data incorrectly as 4 and 5, instead of the correct values 6 and 8, respectively. The variance of the corrected data is

1. 5
2. 7
3. 9
4. 4

Let the lines 3x-4y- =0, 8x-11y-33=0, and 2x-3y+ =0 be concurrent. If the image of the point (1,2) in the line 2x-3y+ =0 is ( 5713, -4013 ), then | | is equal to

1. 91
2. 113
3. 101
4. 84

If the system of equations 2x-y+z=4 5x+ y+3z=12 100x-47y+ z=212 has infinitely many solutions, then -2 is equal to

1. 56
2. 59
3. 57
4. 55

Let circle C be the image of x2+y2-2x+4y-4=0 in the line 2x-3y+5=0 and A be the point on C such that OA is parallel to x-axis and A lies on the right hand side of the centre O of C. If B( , ), with <4, lies on C such that the length of the arc AB is (1/6)th of the perimeter of C, then - 3 is equal to

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

Let A be a 3 3 matrix such that XTAX=O for all nonzero 3 1 matrices X= bmatrixx\ \ bmatrix. If A bmatrix1\\1\\1 bmatrix= bmatrix1\\4\\-5 bmatrix, A bmatrix1\\2\\1 bmatrix= bmatrix0\\4\\-8 bmatrix, and (adj(2(A+I)))=2 3 5 , , , N, then 2+ 2+ 2 is

Let f be a differentiable function such that 2(x+2)2f(x)-3(x+2)2=10 0x(t+2)f(t) dt, x 0. Then f(2) is equal to .

Let S=\p1,p2 ,p10\ be the set of first ten prime numbers. Let A=S P, where P is the set of all possible products of distinct elements of S. Then the number of all ordered pairs (x,y), x S, y A, such that x divides y, is .

If for some , ; , + =8 and 2 ( -1 )+cosec2 ( -1 )=36, then 2+ is

The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is .