JEE Main 2026 (Online) 8th April Evening Shift

A new unit ( ) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of units if light takes 6 min. 40 s to cover this distance?

1. 200
2. 400
3. 300
4. 500

Consider the equation H= xp qErts Where H = magnetic field intensity; E = electric field, = permittivity, x = distance, t = time The values of p, q, r and s respectively are :

1. 1, 1, 1, 1
2. -1, 1, 2, 1
3. 1, -1, -2, 1
4. -1, -2, -2, 1

A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take g=10 m/s2)

1. -1(0.5)
2. -1(0.75)
3. -1(1.125)
4. -1(0.25)

A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is m. (Take g=10 m/s2)

1. 85
2. 150
3. 129
4. 125

A thin biconvex lens is prepared from the glass ( =1.5) both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of cm.

1. 10
2. 12.5
3. 13
4. 13.5

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of R is m. (Take g=10 m/s2)

1. 250
2. 25
3. 500
4. 125

A solid cylinder having radius R and length L is slipping on a rough horizontal plane. At time t=0 the cylinder has a translational velocity v0=49 m/s, perpendicular to its axis and a rotational velocity v0/4R about the centre. The time taken by the cylinder to start rolling is seconds. (coefficient of kinetic friction K=0.25 and g=9.8 m/s2)

1. 15
2. 5
3. 10
4. 7.5

A liquid of density 600 kg/m3 flowing steadily in a tube of varying cross-section. The cross-section at a point A is 1.0 cm2 and that at B is 20 mm2. Both the points A and B are in same horizontal plane, the speed of the liquid at A is 10 cm/s. The difference in pressures at A and B points is Pa.

1. 18
2. 144
3. 36
4. 72

A spherical liquid drop of radius R acquires the terminal velocity v1 when falls through a gas of viscosity . Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity v2 falling through the same gas. The ratio of terminal velocities v1/v2 is .

1. 4
2. 0.25
3. 32
4. 16

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is 4 cm2. The gas is heated slowly to raise the temperature by 1.2 °C during which the piston moves by 25 mm. The amount of heat supplied to the gas is J. (Atmospheric pressure = 100 kPa, R=8.3 J/mol. K) (Neglect mass of the piston)

1. 24.8
2. 10.96
3. 15.04
4. 29.98

Initial pressure and volume of a monoatomic ideal gas are P and V. The change in internal energy of this gas in adiabatic expansion to volume Vfinal=27V is J.

1. -2PV (3 3-1 )
2. 43PV
3. - 43PV
4. 34PV

The frequency of oscillation of a mass m suspended by a spring is 1. If the length of the spring is cut to half, the same mass oscillates with frequency 2. The value of 2 1 is .

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

A monochromatic source of light operating at 15 kW emits 2.5 1022 photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to . (Take h=6.6 10-34 J.s and c=3 108 m/s).

1. Microwave
2. Infrared
3. Visible
4. Ultraviolet

A current carrying circular loop of radius 2 cm with unit normal n= k+ i 2 is placed in a magnetic field, B=B0 (3 i+2 k ). If B0=4 10-3 T and current I=100 2 A, the torque experienced by the loop is Wb.A. ( =3.14)

1. 16 10-5 k
2. 5024 10-7 k
3. 5024 10-7 i
4. 5024 10-7 j

A 30 cm long solenoid has 10 turns per cm and area of 5 cm2. The current through the solenoid coil varies from 2 A to 4 A in 3.14 s. The e.m.f. induced in the coil is 10-5 V. The value is .

1. 60
2. 12
3. 120
4. 34

Two point charges q1=3 μC and q2=-4 μC are placed at points (2 i+3 j+3 k ) and ( i+ j+ k ) respectively. Force on charge q2 is N. (Take 14 0=9 109 SI Units)

1. (12 i+24 j+24 k ) 10-3
2. (4 i+8 j+8 k ) 10-3
3. (3 i+6 j+6 k ) 10-3
4. (-4 i-8 j-8 k ) 10-3

Light ray incident along a vector AO ( AO=2 i-3 j ) emerges out along vector OB ( OB=C i-4 j ) as shown in the figure below. The value of C is . [figure]

1. 1.6
2. 0.16
3. 11.6
4. 16

K1 and K2 be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength 1 and 2, respectively. If 1=2 2 then the work function of material is given by :

1. K2+2K1
2. 2K2-K1
3. K1-2K2
4. K2-2K1

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous -decay with same Q value of 1 MeV. The ratio of energies of -rays produced by A and B is .

1. 25482650
2. 27062646
3. 25972600
4. 28622499

The output Y for the given inputs A and B to the circuit is : [figure]

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

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1 μF when the space between the plates is filled with an insulating material of resistivity 1 1013 Ωm and resistance 17.7 1014 Ω. Relative permittivity of the insulating material is 107. The value of is . (Take permittivity of free space =8.85 10-12 F/m)

Some distant star is to be observed by some telescope of diameter of objective lens a, at an angular resolution of 3.0 10-7 radian. If the wavelength of light from the star reaching the telescope is 500 nm, the minimum diameter of the objective lens of the telescope is cm. (nearest integer)

A 5 mg particle carrying a charge of 5 10-6 C is moving with velocity of (3 i+2 k ) 10-2 m/s in a region having magnetic field B=0.1 k Wb/m2. It moves a distance of meter along k when it completes 5 revolutions. The value of is .

The stored charge in the capacitor in steady state of the following circuit is μC. [figure]

Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of 5 m/s and 12 m/s, respectively. The distances traversed by the masses in the 5th second are 104 m and 129 m, respectively. The ratio of their momenta after 10 s is x8. The value of x is .

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

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

Given below are two statements : Given : Molar mass of C, H, O, Cl are 12, 1, 16 and 35.5 g mol-1, respectively 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

Bromine trifluoride autoionizes to form BrF2 and BrF4 . The shapes of the cation and anion are respectively and .

1. bent, square planar
2. linear, square planar
3. bent, see-saw
4. linear, tetrahedral

Which of the following statements are not correct? Choose the correct answer from the options given below :

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

Consider the following reactions in which all the reactants and products are present in gaseous state 2xy x2 + y2 K1 = 2.5 105 xy + 12z2 xyz K2 = 5 10-3 The value of K3 for the equilibrium 12x2 + 12y2 + 12z2 xyz is :

1. 2.5 10-3
2. 2.5 103
3. 1.0 10-5
4. 5 10-3

Given at 298 K : E Fe2+/Fe = X Volt E Fe3+/Fe = Y Volt The E Fe3+/Fe2+ in Volt at 298 K is given by :

1. 2X − 3Y
2. 3Y − 2X
3. 3Y + 2X
4. Y + X

Given below are two statements : R = 8.314 J K-1 mol-1 and 1 cal = 4.2 J 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

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

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

Find the correct statements related to group 15 hydrides. Choose the correct answer from the options given below :

1. A and B only
2. B and C only
3. A, B, C and D
4. A, C and D 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 correct
2. Both Statement I and Statement II are incorrect
3. Statement I is correct but Statement II is incorrect
4. Statement I is incorrect but Statement II is correct

Given below are two statements for catalytic properties of transition metals. In the light of the above statements, choose the correct answer from the options given below :

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

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 major product of which of the following reaction is not obtained by rearrangement reaction ?

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

The total number of aromatic compounds/species from the following is [figure]

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

n-Butane on monochlorination under photochemical condition gives an optically active compound "P". "P" on further chlorination gives dichloro compounds. The number of dichloro compounds obtained (ignore stereoisomers) is :

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

Consider the following reaction. [figure] The major product (P) formed is :

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

Which statements are True? Choose the correct answer from the options given below :

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

The incorrect statement from the following with respect to carbohydrates is :

1. All monosaccharides are reducing sugars.
2. The monosaccharide units obtained from hydrolysis of oligosaccharides are always the same.
3. Starch and cellulose are typical examples of polysaccharides, which are very high molecular weight compounds of more than ten monosaccharide units.
4. Open chain and cyclic structures co-exist at equilibrium that are responsible for certain properties as in the case of D-(+)-glucose.

Which of the following amino acid will give violet coloured complex with neutral ferric chloride solution?

1. Threonine
2. Serine
3. Tyrosine
4. Cysteine

Number of paramagnetic complexes among the following is . [MnBr4]2-, [NiCl4]2-, [Ni(CN)4]2-, [Ni(CO)4], [CoF6]3-, [Fe(CN)6]4-, [Mn(CN)6]3-, [Ti(CN)6]3-, [Cu(H2O)6]2+, [Co(C2O4)3]3-

'x' is the product which is obtained from benzene by reacting it with carbon monoxide and hydrogen chloride in the presence of cuprous chloride. 'y' is the major product obtained from the benzene by reacting it with ethanoyl chloride in the presence of anhydrous AlCl3. Product (major) obtained by heating x and y in the presence of alkali is z. Total number of π (pi) electrons in z is .

Consider two radiations of wavelengths 1. 1 = 2000 Å 2. 2 = 6000 Å The ratio of the energies of these two radiations ( E1E2 ) is (Nearest integer).

Consider the reaction 2H2S(g) + 3O2(g) 2H2O(l) + 2SO2(g) The magnitude of enthalpy change for the reaction in kJ mol-1 is . (Nearest integer) Given : f H (H2S) = -20.1 kJ mol-1 f H (H2O) = -286.0 kJ mol-1 f H (SO2) = -297.0 kJ mol-1

Solid carbon, CaO and CaCO3 are mixed and allowed to attain equilibrium at T K. CaCO3(s) CaO(s) + CO2(g) Kp1 = 0.08 atm C(s) + CO2(g) 2CO(g) Kp2 = 2 atm The partial pressure of CO is 10-1 atm

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

Consider the relation R on the set \-2, -1, 0, 1, 2\ defined by (a, b) R if and only if 1+ab>0. Then, among the statements :

1. Only I is true
2. Only II is true
3. Both I and II are true
4. Neither I nor II is true

The number of values of z C, satisfying the equations |z-(4+8i)|= 10 and |z-(3+5i)|+|z-(5+11i)|=4 5, is :

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

If the system of linear equations : x+y+z=6, x+2y+5z=10, 2x+3y+ z= has infinitely many solutions, then the value of + equals :

1. 12
2. 16
3. 22
4. 28

Let A= bmatrix & 1 & 2\ 2 & 3 & 0\ 0 & 4 & 5 bmatrix and B= bmatrix1 & 0 & 0\ 0 & -5 & 0\ 0 & 4 & -2 bmatrix+adj(A). If (B)=66, then (adj(A)) equals :

1. 289
2. 361
3. 441
4. 529

Let =3+4+8+9+13+14+ upto 40 terms. If ( ) 1020 is a root of the equation x2+x-2=0, (0, 2 ), then 2 +3 2 is equal to :

1. 2
2. 74
3. 52
4. 32

A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are 25, 15 and 25. The probabilities that the candidate reaches late at the examination centre are 15, 13 and 14 if the candidate uses bus, scooter and car, respectively. Given that the candidate reached late at the examination centre, the probability that the candidate travelled by bus is :

1. 1137
2. 1237
3. 1337
4. 1437

A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to :

1. 5.96
2. 6.14
3. 6.04
4. 6.24

If 26 ( 233 (12C2 )+ 255 (12C4 )+ 277 (12C6 ) . .+ + 21313 (12C12 ) )=313- , then is equal to :

1. 45
2. 48
3. 51
4. 54

A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is :

1. 18
2. 36
3. 39
4. 72

If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0, meets the co-ordinate axes at the points P and Q, then the locus of the mid point of PQ is :

1. x+y-7=0
2. x+y-14xy=0
3. 2x+y+14xy=0
4. x+2y-14xy=0

Let O be the vertex of the parabola y2=4x and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the length of its latus rectum is :

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

Let =3 -1 ( 611 ) and =3 -1 ( 49 ), where inverse trigonometric functions take only the principal values. 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

For the function f(x)=e |x|-|x|, x R, consider the following 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

Let a=4 i- j+3 k, b=10 i+2 j- k and a vector c be such that 2 ( a b )+3 ( b c )= 0. If a c=15, then c ( i+ j-3 k ) is equal to :

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

Let the foot of perpendicular from the point ( , 2, 3) on the line x-41= y-92= z-51 be the point (1, , 2). Then the distance between the lines x-12= y-23= z+46 and x- 2= y- 3= z+56 is equal to :

1. 127
2. 1457
3. 1467
4. 1437

The value of the integral 02 x (x2+x+1 ) ( x+1 ) ( x4+x2+1 ) dx is equal to :

1. 13 e (3-2 2 )
2. 23 e (4+ 2 )
3. 23 e (3+2 2 )
4. 13 e (1+6 2 )

Let y=y(x) be the solution of the differential equation x 1-x2 dy+ (y 1-x2-x -1x )dx=0, x (0, 1), x 1-y(x)=1. Then y ( 12 ) equals :

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

Let f : (1, ) R be a function defined as f(x)= x-1x+1. Let fi+1(x)=f (fi(x) ), i=1, 2, , 25, where f1(x)=f(x). If g(x)+f26(x)=0, x (1, ), then the area of the region bounded by the curves y=g(x), 2y=2x-3, y=0 and x=4 is :

1. 18+ e 2
2. 14+ e 2
3. 56+3 e 2
4. 56+ e 2

Let f(x)= cases 13, & x 2\ b(1- x)( -2x)2, & x> 2 cases. If f is continuous at x= 2, then the value of 03b-6 |x2+2x-3 |dx is :

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

Let x2f (a2+7a+3 )+ y2f(3a+15)=1 represent an ellipse with major axis along y-axis, where f is a strictly decreasing positive function on R. If the set of all possible values of a is R-[ , ], then 2+ 2 is equal to :

1. 28
2. 40
3. 61
4. 24

The sum of squares of all the real solutions of the equation (x+1) (2x2+5x+3 )=4- (2x+3) (x2+2x+1 ) is equal to .

If /6 /4 ( (x- 3 ) (x+ 3 )+1 )dx = e ( 3-1 ), then 9 2 is equal to .

Let a line L1 pass through the origin and be perpendicular to the lines L2 : r=(3+t) i+(2t-1) j+(2t+4) k and L3 : r=(3+2s) i+(3+2s) j+(2+s) k, t, s R. If (a, b, c), a Z, is the point on L3 at a distance of 17 from the point of intersection of L1 and L2, then (a+b+c)2 is equal to .

Consider the circle C : x2+y2-6x-8y-11=0. Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle x2+y2- x- y- =0, then + +2 is equal to .

Let f be a polynomial function such that 2(f(x))= ( 2 (2+ 23+ 29+ ) ) 3 (1+ f(x)f ( 1x ) ), x>0 and f(6)=37. Then n=110f(n) is equal to .