JEE Main 2026 (Online) 2nd April Evening Shift

Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are .

1. [ hTLM-2 ]
2. [ hT-1LM-2 ]
3. [ hTL2M-2 ]
4. [ h-1T-1LM-2 ]

A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is 5 rad/s. The coefficient of friction between the drum's inner wall surface and mass is . (Take g=10 m/s2)

1. 0.1
2. 0.5
3. 0.7
4. 0.3

Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in 2 s is m. (Take g=10 m/s2) [figure]

1. 3.33
2. 3.12
3. 2.22
4. 1.42

A particle having charge 10-9 C moving in x-y plane in fields of 0.4 j N/C and 4 10-3 k T experiences a force of (4 i+2 j ) 10-10 N. The velocity of the particle at that instant is m/s.

1. 50 i+100 j
2. 100 i+50 j
3. -50 i+100 j
4. 50 i-100 j

If X and Y are the inputs, the given circuit works as . [figure]

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

If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are . (Take radius of earth to be 6400 km and g=9.8 m/s2)

1. 11.2 km/s; 6.27 107 J
2. 11.2 km/s; 12.54 107 J
3. 8.8 km/s; 6.27 107 J
4. 8.8 km/s; 12.54 107 J

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diameter of a sphere is measured, the reading of main scale is 5 mm and 50th division of circular scale coincides with the reference line of main scale. The diameter of sphere is mm.

1. 5.045
2. 5.055
3. 5.450
4. 5.550

The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is 10-4 J. The value of is . (Take =3.14)

1. 0.86
2. 0.64
3. 1.92
4. 7.68

A mixture of carbon dioxide and oxygen has volume 8310 cm3, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are . (Assume both carbon dioxide and oxygen gases behave like ideal gases) [R = 8.31 J/mol K]

1. 0.15 and 0.18
2. 0.25 and 0.08
3. 0.21 and 0.12
4. 0.13 and 0.20

If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m3 at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is Poise. (Take g=10 m/s2)

1. 0.88
2. 8.8
3. 88.8
4. 0.088

A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is N. (Take g=10 m/s2)

1. 1980
2. 2020
3. 2000
4. 1000

An electromagnetic wave travels in free space along the x-direction. At a particular point in space and time, B=2 10-7 j T is associated with this wave. The value of corresponding electric field E at this point is V/m.

1. 60 k
2. -60 k
3. 30 k
4. -600 k

Two resistors of 200 Ω and 400 Ω are connected in series with a battery of 100 V. A bulb rated at 200 V, 100 W is connected across the 400 Ω resistance. The potential drop across the bulb is V.

1. 25
2. 50
3. 66.6
4. 100

Two metal plates (A, B) are kept horizontally with separation of ( 12 ) cm, with plate A on the top. An atomizer jet sprays oil (density 1.5 g/cm3) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials VA and VB are required on plates A and B respectively in order to ensure the droplets do not descend. The values of VA and VB are . (Neglect the air resistance to the droplets and take g=10 m/s2)

1. 100 V and 580 V
2. 580 V and 100 V
3. 60 V and 400 V
4. 0 V and -200 V

Two point charges 8 μC and -2 μC are located at x=2 cm and x=4 cm, respectively on the x-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is .

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

One side of an equilateral prism is painted by a transparent material of refractive index n2. The refractive index of prism is 1.6. The minimum value of n2 required for total internal reflection from painted face is . [figure]

1. 3 31.6
2. 3
3. 3.2 3
4. 4 35

The figure given below shows an LCR series circuit with two switches S1 and S2. When switch S1 is closed keeping S2 open, the phase difference ( ) between the current and source voltage is 30° and phase difference is 60° when S2 is closed keeping S1 open. The value of (3L1-L2) is H. [figure]

1. 92
2. 29
3. 13
4. 3

A circular current loop of radius R is placed inside square loop of side length L (L R) such that they are co-planar and their centers coincide. The permeability of free space is 0. The mutual inductance between circular loop and square loop is .

1. 2 2 0 L2R
2. 2 0 L2R
3. 2 0 R2L
4. 2 2 0 R2L

The binding energy per nucleon of 20983Bi is MeV. [Take m( 20983Bi) = 208.980388 u, mp = 1.007825 u, mn = 1.008665 u, 1 u = 931 MeV/c2]

1. 7.48
2. 7.84
3. 8.79
4. 6.94

The equation of motion of a particle is given by x=a (50t+ /3) cm. The particle will come to rest at time t1 and it will have zero acceleration at time t2. The t1 and t2 respectively are .

1. 300 s, 75 s
2. 75 s, 300 s
3. 300 s, 25 s
4. 50 s, 100 s

In a Young's double slit experiment, the intensity at some point on the screen is found to be 34 times of the maximum of the interference pattern. The path difference between the interfering waves at this point is x where is wavelength of the incident light. The value of x is .

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of hydrogen atom .

5 moles of unknown gas is heated at constant volume from 10 °C to 20 °C. The molar specific heat of this gas at constant pressure cp = 8 cal/mol.°C and R = 8.36 J/mol.°C. The change in the internal energy of the gas is calorie.

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at 30 cm above the paper. If the radius of curvature of the lens is 60 cm then the refractive index of the lens material is 10. The value of is .

Moment of inertia about an axis AB for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass of 10 kg and radius R about an axis parallel to AB axis with separation of 3 m as shown in figure below. The value of R is given as 2. The value of is . [figure]

The ratio of mass percentage (w/w) of C : H in a hydrocarbon is 12 : 1. It has two carbon atoms. The weight (in g) of CO2(g) formed when 3.38 g of this hydrocarbon is completely burnt in oxygen is : (Given : Molar mass in g mol-1 C : 12, H : 1, O : 16)

1. 5.68
2. 11.44
3. 22.74
4. 17.05

The first and second ionization constants of a weak dibasic acid H2A are 8.1 10-8 and 1.0 10-13 respectively. 0.1 mol of H2A was dissolved in 1 L of 0.1 M HCl solution. The concentration of HA- in the resultant solution is:

1. 0.1 M
2. 9.53 10-6 M
3. 8.1 10-8 M
4. 1.0 10-13 M

SF4 is isostructural with : Choose the correct answer from the options given below :

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

Gas 'A' undergoes change from state 'X' to state 'Y'. In this process, the heat absorbed and work done by the gas is 10 J and 18 J respectively. Now gas is brought back to state 'X' by another process during which 6 J of heat is evolved. In the reverse process of 'Y' to 'X',

1. 18 J of the work is done by the gas 'A'.
2. 2 J of the work is done by the gas 'A'.
3. 12 J of the work is done on the gas 'A' by the surrounding.
4. 14 J of the work is done on the gas 'A' by the surrounding.

Solution A is prepared by dissolving 1 g of a protein (molar mass = 50,000 g mol-1) in 0.5 L of water at 300 K. Its osmotic pressure is x bar. Solution B is made by dissolving 2 g of the same protein in 1 L of water at 300 K. Osmotic pressure of solution B is y bar. Entire solution of A is mixed with entire solution of B at the same temperature. The osmotic pressure of resultant solution is z bar. x, y and z respectively are: (R = 0.083 L bar mol-1 K-1)

1. 9.96 10-4; 9.96 10-4; 9.96 10-4
2. 9.96 10-4; 9.96 10-4; 19.92 10-4
3. 4.98 10-4; 4.98 10-4; 9.96 10-4
4. 4.98 10-4; 4.98 10-4; 4.98 10-4

At 25°C, 20.0 mL of 0.2 M weak monoprotic acid HX is titrated against 0.2 M NaOH. The pH of the solution (a) at the start of the titration (when NaOH has not been added) and (b) when 10 mL of NaOH is added respectively, are : Given : Ka = 5 10-4 pKa = 3.3 1

1. array|c|c| (a) & (b) \ 0.7 & 2.0 \ array
2. array|c|c| (a) & (b) \ 2.0 & 3.3 \ array
3. array|c|c| (a) & (b) \ 1.1 & 2.2 \ array
4. array|c|c| (a) & (b) \ 3.0 & 2.2 \ array

Consider the reaction aX bY, for which the rate constant at 30°C is 1 10-3 mol-1 L s-1. Which of the following statements are true? Choose the correct answer from the options given below:

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

The correct set that contains all kinds (basic, acidic, amphoteric and neutral) of oxides is :

1. Na2O, K2O, Al2O3 and As2O3
2. Al2O3, As2O3, CO and NO
3. K2O, Cl2O7, As2O3 and NO
4. Na2O, N2O, Al2O3 and CO

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

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

Which of the following complexes will show coordination isomerism? Choose the correct answer from the options given below:

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

Complete combustion of X g of an organic compound gave 0.25 g of CO2 and 0.12 g of H2O. If the % of carbon is 25% and of hydrogen is 4.89%, then X = 10-3 g. (Nearest integer) (Molar mass of C, H and O are 12, 1 and 16 g mol-1 respectively.)

1. 273
2. 27
3. 2730
4. 227

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 compound (X) on (i) on heating in the presence of anhydrous AlCl3 and HCl gas gives 2,4-dimethyl pentane (ii) aromatization gives toluene and (iii) cyclisation gives methyl cyclohexane The correct name of compound (X) is:

1. Hept-2-ene
2. Hept-1,3,5-triene
3. Heptane
4. Hept-2,4,6-triene

Correct statements regarding alkyl halides (R–X) among the following are : Choose the correct answer from the options given below :

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

An organic compound “x” where molar ratio of C, O and H are equal, on treatment with 50% KOH under reflux followed by acidification produced “y”. The most likely structure of “y” is: [Molar mass of ‘x’ is 58 g mol-1]

1. [figure]
2. CH3-CH=CH-CH=O
3. [figure]
4. [figure]

A molecule (X) with following structure under mild acidic condition is hydrolysed to produce (Y) and (Z). Identify the correct statements about (Y) and (Z). [figure] Choose the correct answer from the options given below :

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

Identify compounds A and E in the following reaction sequence. [figure]

1. A = [figure] E = [figure]
2. A = [figure] E = [figure]
3. A = [figure] E = [figure]
4. A = [figure] E = [figure]

Identify the correct pair having amino acid (A) and the hormone (B) that is iodinated derivative of the amino acid (A). (T and Y represent one letter code for amino acids)

1. Amino acid (A) - T Hormone (B) - Insulin
2. Amino acid (A) - T Hormone (B) - Thyroxine
3. Amino acid (A) - Y Hormone (B) - Thyroxine
4. Amino acid (A) - Y Hormone (B) - Insulin

Among Fe2+, Fe3+, Cr2+ and Zn2+, the ion that shows positive borax bead test and with highest ionisation enthalpy is :

1. Fe2+
2. Zn2+
3. Cr2+
4. Fe3+

The surface of sodium metal is irradiated with radiation of wavelength x nm. The kinetic energy of ejected electrons is 2.8 10-20 J. The work function of sodium is 2.3 eV. The value of x is 102 nm. (Nearest integer) (Given : h = 6.6 10-34 J s; 1 eV = 1.6 10-19 J; c = 3.0 108 m s-1)

Consider the following gas phase reaction being carried out in a closed vessel at 25°C. 2A(g) 4B(g) + C(g) array|c|c| time (min) & total pressure of the system (mm Hg) \ 30 & 300 \ & 600 \ array The pressure of C(g) at 30 minutes time interval would be mm Hg. (nearest integer)

Consider the following two half-cell reactions along with the standard reduction potential given : CO2 + 6H+ + 6e- CH3OH + H2O E red = 0.02 V 12O2 + 2H+ + 2e- H2O E red = 1.23 V A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of 1 bar pressure and 298 K temperature. The fuel cell works with 80% efficiency. If the work derived from the cell using 1 mol of CH3OH is used to compress an ideal gas isothermally against a constant pressure of 1 kPa, then the change in the volume of the gas, V = m3. (nearest integer) Given : F = 96500 C mol-1

Number of paramagnetic ions among the following d- and f-block metal ions is . Mn2+, Cu2+, Zn2+, Yb2+, Sc3+, La3+, Gd3+, Lu3+, Ti4+, Ce4+ (Atomic number of Mn = 25, Cu = 29, Zn = 30, Yb = 70, Sc = 21, La = 57, Gd = 64, Lu = 71, Ti = 22, Ce = 58)

Consider the following reactions sequence [figure] When the product (P) is subjected to Carius analysis using AgNO3, 1.0 g of the product (P) will produce g of the precipitate of AgBr. (Nearest Integer) (Given : molar mass in g mol-1 C : 12, H : 1, O : 16, N : 14, Br : 80, Ag : 108)

Let , be the roots of the equation x2-3x+r=0, and 2, 2 be the roots of the equation x2+3x+r=0. If the roots of the equation x2+6x=m are 2 + +2r and -2 - r2, then m is equal to :

1. -135
2. -567
3. 135
4. 567

Let the circles C1 : |z|=r and C2 : |z-3-4i|=5, z C, be such that C2 lies within C1. If z1 moves on C1, z2 moves on C2 and |z1-z2|=2, then |z1-z2| is equal to :

1. 12
2. 17
3. 22
4. 24

If the system of equations x+5y+6z=4, 2x+3y+4z=7, x+6y+az=b has infinitely many solutions, then the point (a, b) lies on the line

1. y-x=3
2. x-y=3
3. x+y=11
4. x+y=12

Let a1, a2, a3, be an A.P. and g1=a1, g2, g3, be an increasing G.P. If a1=a2+g2=1 and a3+g3=4, then a10+g5 is equal to:

1. 81
2. 76
3. 62
4. 55

The sum 131+ 13+231+3+ 13+23+331+3+5+ up to 8 terms, is :

1. 70
2. 71
3. 72
4. 73

If for 3 r 30, (30C30-r )+3 (30C31-r )+3 (30C32-r )+ (30C33-r )=mCr, then m equals :

1. 31
2. 32
3. 33
4. 34

Let pn denote the total number of triangles formed by joining the vertices of an n-side regular polygon. If pn+1-pn=66, then the sum of all distinct prime divisors of n is :

1. 7
2. 8
3. 5
4. 6

A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is mn, (m, n)=1, then m+n is equal to :

1. 53
2. 55
3. 107
4. 105

The mean and variance of n observations are 8 and 16, respectively. If the sum of the first (n-1) observations is 48 and the sum of squares of the first (n-1) observations is 496, then the value of n is :

1. 21
2. 16
3. 13
4. 7

Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x+(k-1)y+3=0 and 2x+k2y-4=0. If the line x-y+2=0 intersects the circle at the points A and B, then (AB)2 is equal to :

1. 10
2. 27
3. 18
4. 34

Let O be the origin, and P and Q be two points on the rectangular hyperbola xy=12 such that the midpoint of the line segment PQ is ( 12, - 12 ). Then the area of the triangle OPQ equals :

1. 32
2. 52
3. 72
4. 92

Let the parabola y=x2+px+q passing through the point (1, -1) be such that the distance between its vertex and the x-axis is minimum. Then the value of p2+q2 is :

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

Let P=\ [0, 4 ] : 2 1\ and S=\a Z : 2( 8 - 8 ) 2 =a2, P\. Then n(S) is:

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

Let the vectors a=- i+ j+3 k and b= i+3 j+ k. For some , R, let c= a+ b. If c (3 i-6 j+2 k )=10 and c ( i+ j+ k )=-2, then | c|2 is equal to :

1. 8
2. 12
3. 14
4. 15

Let the point A be the foot of perpendicular drawn from the point P(a, b, 0) on the line x-12= y-21= z- 3. If the midpoint of the line segment PA is (0, 34, - 14 ), then the value of a2+b2+ 2 is equal to :

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

Two adjacent sides of a parallelogram PQRS are given by PQ= j+ k and PS= i- j. If the side PS is rotated about the point P by an acute angle in the plane of the parallelogram so that it becomes perpendicular to the side PQ, then 2 ( 5 2 )- 2 ( 2 ) is equal to:

1. 12
2. 32
3. 34
4. 2 35

The value of 020 ( 4 x+ 4 x )dx is equal to:

1. 15 2
2. 25
3. 15
4. 25 2

Let f(x) be a polynomial of degree 5, and have extrema at x=1 and x=-1. If x 0 ( f(x)x3 )=-5, then f(2)-f(-2) is equal to:

1. 0
2. 50
3. 92
4. 112

Let f(x)= ( 16x+24x2+2x-15 )dx. If f(4)=14 e(3) and f(7)= e (2 3 ), , N, then + is equal to :

1. 31
2. 37
3. 39
4. 41

Let x=x(y) be the solution of the differential equation 2y2 dxdy-2xy+x2=0, y>1, x(e)=e. Then x (e2 ) is equal to:

1. 32e2
2. 23e2
3. e2
4. 2e2

Let A=\2, 3, 4, 5, 6\. Let R be a relation on the set A A given by (x, y)R(z, w) if and only if x divides z and y w. Then the number of elements in R is .

Consider the matrices A= bmatrix2 & -2\ 4 & -2 bmatrix and B= bmatrix3 & 9\ 1 & 3 bmatrix. If matrices P and Q are such that PA=B and AQ=B, then the absolute value of the sum of the diagonal elements of 2(P+Q) is .

Let A be the point (3, 0) and circles with variable diameter AB touch the circle x2+y2=36 internally. Let the curve C be the locus of the point B. If the eccentricity of C is e, then 72e2 is equal to .

If the area of the region bounded by 16x2-9y2=144 and 8x-3y=24 is A, then 3 (A+6 e(3) ) is equal to .

The number of points in the interval [2, 4], at which the function f(x)= [x2-x- 12 ], where [ ] denotes the greatest integer function, is discontinuous, is .