JEE Main 2026 (Online) 23rd January Evening Shift

One mole of an ideal diatomic gas expands from volume V to 2V isothermally at a temperature 27 and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from 27 doing the same amount of work W, then its final temperature will be (close to) . ( e 2 = 0.693)

1. -56
2. -117
3. -30
4. -189

A block is sliding down on an inclined plane of slope and at an instant t = 0 this block is given an upward momentum so that it starts moving up on the inclined surface with velocity u. The distance (S) travelled by the block before its velocity becomes zero, is . (g = gravitational acceleration)

1. 2u2g
2. u2 2g
3. u22g
4. u22g

The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross section area of 17 cm2 and fitted with a light movable frictionless piston. The gas is heated slowly by supplying 126 J heat. If the temperature rises by 4 , then the piston will move cm. (atmospheric pressure = 105 Pa)

1. 1.55
2. 14.5
3. 15.5
4. 1.45

Two short dipoles (A, B), A having charges 2 and length 1 cm and B having charges 4 and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point P, equi-distant from the centres of both dipoles is N/C. [figure]

1. 916 2 105
2. 916 2 104
3. 9 2 104
4. 4.5 2 104

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s . The EMF induced in the loop is mV.

1. 13.2
2. 6.6
3. 1.32
4. 8.25

A bead P sliding on a frictionless semi-circular string (ACB) and it is at point S at t = 0 and at this instant the horizontal component of its velocity is v. Another bead Q of the same mass as P is ejected from point A at t = 0 along the horizontal string AB, with the speed v, friction between the beads and the respective strings may be neglected in both cases. Let tP and tQ be the respective times taken by beads P and Q to reach the point B, then the relation between tP and tQ is [figure]

1. tP < tQ
2. tP = tQ
3. tP > 1.25tQ
4. tP > tQ

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts decelerating with 3 m/s2. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 m/s. The initial height of the airplane is m. (g = 10 m/s2)

1. 92.5
2. 62.5
3. 20
4. 82.5

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k = 3 and permeability of = 2 0, is ( 0 = permeability of vacuum)

1. 6 : 1
2. 3 : 2
3. 6 : 1
4. 36 : 1

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current I = 10 ( t) A, where = 1000 rad/s. A circular conducting loop (B) of radius 1 cm coaxially slid through the solenoid at a speed v = 1 cm/s. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is 2 . The value of is . [Resistance of the loop = 10 ]

1. 80
2. 280
3. 100
4. 197

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2 : 2 : 3. The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m/s each. The velocity of the heavier fragment is m/s.

1. 24 2
2. 12
3. 12 2
4. 10 2

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25\% more charge from the battery. The dielectric constant of mica is

1. 1.0
2. 2.5
3. 1.5
4. 2.0

Which of the following pair of nuclei are isobars of the element?

1. 31H and 32He
2. 19880Hg and 19779Au
3. 21H and 31H
4. 23692U and 23892U

To compare EMF of two cells using potentiometer the balancing lengths obtained are 200 cm and 150 cm. The least count of scale is 1 cm. The percentage error in the ratio of EMFs is

1. 1.75
2. 1.55
3. 1.17
4. 1.65

Two charges 7 and -2 are placed at (-9, 0, 0) cm and (9, 0, 0) cm respectively in an external field E = Ar2 r, where A = 9 105 N m2 C-1. Considering the potential at infinity is 0, the electrostatic energy of the configuration is J.

1. 49.3
2. 1.4
3. 24.3
4. -90.7

A prism of angle 75 and refractive index 3 is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be ( 15 = 0.25 and 25 = 0.43)

1. between 15 and 20
2. 15
3. < 15
4. > 25

The current passing through a conducting loop in the form of equilateral triangle of side 4 3 cm is 2 A. The magnetic field at its centroid is 10-5 T. The value of is . (Given: 0 = 4 10-7 SI units)

1. 3 3
2. 2 3
3. 3
4. 32

For the given logic gate circuit, which of the following is the correct truth table? [figure]

1. arrayccc n & m & z \ 0 & 0 & 1 \ 0 & 1 & 1 \ 1 & 1 & 0 \ 1 & 0 & 0 array
2. arrayccc n & m & z \ 0 & 0 & 1 \ 0 & 1 & 0 \ 1 & 1 & 1 \ 1 & 0 & 0 array
3. arrayccc n & m & z \ 0 & 0 & 0 \ 0 & 1 & 1 \ 1 & 1 & 0 \ 1 & 0 & 1 array
4. arrayccc n & m & z \ 0 & 0 & 1 \ 0 & 1 & 0 \ 1 & 1 & 0 \ 1 & 0 & 0 array

A small metallic sphere of diameter 2 mm and density 10.5 g/cm3 is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm3 respectively. The terminal velocity attained by the sphere is cm/s. ( = 227 and g = 10 m/s2)

1. 1.0
2. 1.5
3. 3.0
4. 2.0

An air bubble of volume 2.9 cm3 rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17 . The volume of the bubble when it reaches the surface, where the water temperature is 27 , is cm3. (g = 10 m/s2, density of water = 103 kg/m3, and 1 atm pressure is 105 Pa)

1. 2.0
2. 4.2
3. 3.0
4. 4.5

When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is . ( -1(1.52) = 57.7 , refractive indices of air and glass are 1.00 and 1.52, respectively.)

1. 36.3
2. 39.6
3. 42.6
4. 32.3

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is cm.

The average energy released per fission for the nucleus of 23592U is 190 MeV. When all the atoms of 47 g pure 23592U undergo fission process, the energy released is 1023 MeV. The value of is . (Avogadro Number = 6 1023 per mole)

The velocity of sound in air is doubled when the temperature is raised from 0 to . The value of is .

Suppose there is a uniform circular disc of mass M kg and radius r m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by x256 M r2. The value of x is . [figure]

A ball of radius r and density dropped through a viscous liquid of density and viscosity attains its terminal velocity at time t, given by t = A a rb c d, where A is a constant and a, b, c and d are integers. The value of b + ca + d is .

Which of the following statements are TRUE about Haloform reaction? Choose the correct answer from the options given below :

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

The oxidation state of chromium in the final product formed in the reaction between KI and acidified K2Cr2O7 solution is :

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

In Carius method 0.2425 g of an organic compound gave 0.5253 g silver chloride. The percentage of chlorine in the organic compound is

1. 87.65%
2. 53.58%
3. 37.57%
4. 34.79%

[figure] Identify (P)

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

[figure] Given above is the concentration vs time plot for a dissociation reaction : A nB. Based on the data of the initial phase of the reaction (initial 10 min), the value of n is .

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

Observe the following reactions at T(K). I. A products. II. 5Br-(aq) + BrO3-(aq) + 6H+(aq) 3Br2(aq) + 3H2O(l) Both the reactions are started at 10.00 am. The rates of these reactions at 10.10 am are same. The value of - [Br-] t at 10.10 am is 2 10-4 mol L-1 min-1. The concentration of A at 10.10 am is 10-2 mol L-1. What is the first order rate constant (in min-1) of reaction I?

1. 4 10-3
2. 2 10-3
3. 10-3
4. 10-2

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. Statement I is false but Statement II is true
3. Statement I is true but Statement II is false
4. Both Statement I and Statement II are false

The work functions of two metals (MA and MB) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of MA : MB is in the ratio of 2.642 : 1. The work functions (in eV) of MA and MB are respectively.

1. 3.1, 6.2
2. 1.5, 3.0
3. 2.3, 4.6
4. 1.4, 2.8

Iodoform test can differentiate between Choose the correct answer from the options given below :

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

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 true
4. Both Statement I and Statement II are false

[figure] Consider the above electrochemical cell where a metal electrode (M) is undergoing redox reaction by forming M+ (M M+ + e-). The cation M+ is present in two different concentrations c1 and c2 as shown above. Which of the following statement is correct for generating a positive cell potential?

1. If c1 is present at anode, then c1 > c2.
2. If c1 is present at cathode, then c1 > c2.
3. If c1 is present at cathode, then c1 < c2.
4. If c1 is present at anode, then c1 = c2.

A mixed ether (P), when heated with excess of hot concentrated hydrogen iodide produces two different alkyl iodides which when treated with aq. NaOH give compounds (Q) and (R). Both (Q) and (R) give yellow precipitate with NaOI. Identify the mixed ether (P) :

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 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

Both human DNA and RNA are chiral molecules. The chirality in DNA and RNA arises due to the presence of

1. L-sugar component
2. D-sugar component
3. Chiral phosphate unit
4. Base unit

A student has been given a compound 'x' of molecular formula C6H7N. 'x' is sparingly soluble in water. However, on addition of dilute mineral acid, 'x' becomes soluble in water. 'x' when treated with CHCl3 and KOH(alc), 'y' is produced. 'y' has a specific unpleasant smell. On treatment with benzenesulphonyl chloride, 'x' gives a compound 'z' which is soluble in alkali. The number of different "H" atoms present in 'z' is :

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

Identify the INCORRECT statements from the following : Choose the correct answer from the options given below :

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

Which statements are NOT TRUE about XeO2F2? Choose the correct answer from the options given below :

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

It is noticed that Pb2+ is more stable than Pb4+ but Sn2+ is less stable than Sn4+. Observe the following reactions. PbO2 + Pb 2PbO; rG (1) SnO2 + Sn 2SnO; rG (2) Identify the correct set from the following

1. rG (1) > 0; rG (2) < 0
2. rG (1) < 0; rG (2) > 0
3. rG (1) < 0; rG (2) < 0
4. rG (1) > 0; rG (2) > 0

Identify the CORRECT set of details from the following : Choose the correct answer from the options given below :

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

Elements X and Y belong to Group 15. The difference between the electronegativity values of 'X' and phosphorus is higher than that of the difference between phosphorus and 'Y'. 'X' & 'Y' are respectively

1. As & Bi
2. Bi & N
3. N & As
4. As & Sb

Consider the following reaction of benzene. [figure] In compound (Q), the percentage of oxygen is %. (Nearest integer)

Total number of unpaired electrons present in the central metal atoms/ions of [Ni(CO)4], [NiCl4]2-, [PtCl2(NH3)2], [Ni(CN)4]2- and [Pt(CN)4]2- is .

200 cc of x 10-3 M potassium dichromate is required to oxidise 750 cc of 0.6 M Mohr's salt solution in acidic medium. Here x = .

X2(g) + Y2(g) 2Z(g) X2(g) and Y2(g) are added to a 1 L flask and it is found that the system attains the above equilibrium at T(K) with the number of moles of X2(g), Y2(g) and Z(g) being 3, 3 and 9 mol respectively (equilibrium moles). Under this condition of equilibrium, 10 mol of Z(g) is added to the flask and the temperature is maintained at T(K). Then the number of moles of Z(g) in the flask when the new equilibrium is established is . (Nearest integer)

Two liquids A and B form an ideal solution. At 320 K, the vapour pressure of the solution, containing 3 mol of A and 1 mol of B is 500 mm Hg. At the same temperature, if 1 mol of A is further added to this solution, vapour pressure of the solution increases by 20 mm Hg. Vapour pressure (in mm Hg) of B in pure state is . (Nearest integer)

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

1. 384
2. 403
3. 429
4. 455

Let k=1n ak = n2 + n. If a10 = 59 and a6 = 7a1, then + is equal to :

1. 3
2. 5
3. 7
4. 12

If z = 32 + i2, i = -1, then (z201 - i )8 is equal to

1. 1
2. 0
3. -1
4. 256

Let a, b, c be three vectors such that a b = 2( a c). If | a| = 1, | b| = 4, | c| = 2, and the angle between b and c is 60 , then | a c| is equal to

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

Consider two sets A = \x Z : |(|x - 3| - 3)| 1\ and B = \x R - \1, 2\ : (x - 2)(x - 4)x - 1 e(|x - 2|) = 0 \. Then the number of onto functions f : A B is equal to :

1. 32
2. 81
3. 79
4. 62

Let A = \0, 1, 2, , 9\. Let R be a relation on A defined by (x, y) R if and only if |x - y| is a multiple of 3. 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 correct but Statement II is incorrect
2. Both Statement I and Statement II are correct
3. Both Statement I and Statement II are incorrect
4. Statement I is incorrect but Statement II is correct

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is pq, (p, q) = 1, then p + q is equal to

1. 24
2. 22
3. 23
4. 21

Let PQ be a chord of the hyperbola x24 - y2b2 = 1, perpendicular to the x-axis such that OPQ is an equilateral triangle, O being the centre of the hyperbola. If the eccentricity of the hyperbola is 3, then the area of the triangle OPQ is

1. 2 3
2. 115
3. 8 35
4. 95

If the mean and the variance of the data array|l|c|c|c|c| Class & 4-8 & 8-12 & 12-16 & 16-20 \ Frequency & 3 & & 4 & 7 \ array are and 19 respectively, then the value of + is :

1. 21
2. 19
3. 18
4. 20

Let A(1, 2) and C(-3, -6) be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line 7x - y = 14. If B( , ) and D( , ) are the other two vertices, then | + + + | is equal to :

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

The sum of all the real solutions of the equation (x+3) (6x2 + 28x + 30 ) = 5 - 2 (6x+10) (x2 + 6x + 9 ) is equal to :

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

The least value of ( 2 - 6 + 3 2 + 2 ) is

1. 4 - 10
2. -1
3. 4 + 10
4. 1

Let 2 < < and = - 12 2. Then the value of ( 15 2 )( 8 + 8 ) + ( 15 2 )( 8 - 8 ) is equal to :

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

Let I(x) = 3 dx(4x + 6) ( 4x2 + 8x + 3 ) and I(0) = 34 + 20. If I ( 12 ) = a 2b + c, where a, b, c N, (a, b) = 1, then a + b + c is equal to :

1. 30
2. 29
3. 28
4. 31

If the points of intersection of the ellipses x2 + 2y2 - 6x - 12y + 23 = 0 and 4x2 + 2y2 - 20x - 12y + 35 = 0 lie on a circle of radius r and centre (a, b), then the value of ab + 18r2 is :

1. 53
2. 52
3. 55
4. 51

Let a = i - 2 j + 3 k, b = 2 i + j - k, c = i + j + k and v = a b. If v c = 11 and the length of the projection of b on c is p, then 9p2 is equal to

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

If f(x) = cases a|x| + x2 - 2( |x|)( |x|)x & , x 0 \ b & , x = 0 cases is continuous at x = 0, then a + b is equal to :

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

The area of the region enclosed between the circles x2 + y2 = 4 and x2 + (y - 2)2 = 4 is:

1. 23(4 - 3 3)
2. 43(2 - 3)
3. 43(2 - 3 3)
4. 23(2 - 3 3)

An equilateral triangle OAB is inscribed in the parabola y2 = 4x with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having AB as a diameter from the origin is

1. 2(8 - 3 3)
2. 4(6 + 3)
3. 4(3 - 3)
4. 2(3 + 3)

The system of linear equations x + y + z = 6 2x + 5y + az = 36 x + 2y + 3z = b has :

1. unique solution for a = 8 and b = 16
2. infinitely many solutions for a = 8 and b = 14
3. infinitely many solutions for a = 8 and b = 16
4. unique solution for a = 8 and b = 14

If the image of the point P(a, 2, a) in the line x2 = y + a1 = z1 is Q and the image of Q in the line x - 2b2 = y - a1 = z + 2b-5 is P , then a + b is equal to .

If the solution curve y = f(x) of the differential equation (x2 - 4)y' - 2xy + 2x(4 - x2)2 = 0, x > 2, passes through the point (3, 15), then the local maximum value of f is

The number of elements in the set S = \x : x [0, 100] and 0x t2 (x - t) dt = x2 \ is

Let S denote the set of 4-digit numbers abcd such that a > b > c > d and P denote the set of 5-digit numbers having product of its digits equal to 20 . Then n(S) + n(P) is equal to

Let A = bmatrix 0 & 2 & -3 \ -2 & 0 & 1 \ 3 & -1 & 0 bmatrix and B be a matrix such that B(I - A) = I + A. Then the sum of the diagonal elements of BTB is equal to