JEE Main 2026 (Online) 28th January Morning Shift

Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure. If the mass of each disc is 600 gm and applied torque between two discs is 43 105 dyne.cm, the angular acceleration of the discs about the given axis AB is rad/s2. [figure]

1. 100
2. 22
3. 27
4. 11

Which of the following best represents the temperature versus heat supplied graph for water, in the range of -20 C to 120 C?

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

Assuming in forward bias condition there is a voltage drop of 0.7 V across a silicon diode, the current through diode D1 in the circuit is mA. (Assume all diodes in the given circuit are identical) [figure]

1. 17.6
2. 18.8
3. 20.15
4. 11.7

The electric current in the circuit is given as i = io(t/T). The r.m.s current for the period t = 0 to t = T is .

1. io 2
2. io 3
3. io
4. io 6

A block of mass 5 kg is moving on an inclined plane which makes an angle of 30 with the horizontal. Friction coefficient between the block and inclined plane surface is 32. The force to be applied on the block so that the block will move down without acceleration is N. (g = 10 m/s2).

1. 25
2. 12.5
3. 15
4. 7.5

A particle of mass m falls from rest through a resistive medium having resistive force, F = -kv, where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time (t) ?

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

An atom 83X is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleus is recorded by :

1. 150\%
2. 900\%
3. 125\%
4. 225\%

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, 4th mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and 5th division of vernier scale coincides with a main scale division. Measured length of cylinder is mm. (Least count of Vernier calliper = 0.1 mm)

1. 15.5
2. 15.4
3. 15.9
4. 15.1

The magnetic field at the centre of a current carrying circular loop of radius R is 16 . The magnetic field at a distance x = 3R on its axis from the centre is .

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

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire Q is . ( 0 = 4 10-7 T m/A) [figure]

1. 6 10-6 N towards P
2. 6 10-6 N towards R
3. 6 10-7 N towards P
4. 6 10-7 N towards R

The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index = 1.7) are same. If the curvature of plano-concave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is

1. 2 : 5
2. 5 : 2
3. 12 : 5
4. 5 : 12

The electric field of an electromagnetic wave travelling through a medium is given by E(x, t) = 25 (2.0 1015 t - 107 x ) n then the refractive index of the medium is . (All given measurements are in SI units)

1. 2
2. 1.2
3. 1.5
4. 1.7

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is m. (g = 10 m/s2)

1. 3.8
2. 4.0
3. 4.2
4. 2.5

For the two cells having same EMF E and internal resistance r, the current passing through the external resistor 6 is same when both the cells are connected either in parallel or in series. The value of internal resistance r is .

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

10 kg of ice at -10 C is added to 100 kg of water to lower its temperature from 25 C. Consider no heat exchange to surroundings. The decrement to the temperature of water is C. (specific heat of ice = 2100 J/kg C, specific heat of water = 4200 J/kg C, latent heat of fusion of ice = 3.36 105 J/kg)

1. 15
2. 10
3. 6.67
4. 11.6

Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is . 14 0 = 9 109 N m2/C2

1. 3.3
2. 27
3. 2.7
4. 5.4

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

In the potentiometer, when the cell in the secondary circuit is shunted with 4 resistance, the balance is obtained at the length 120 cm of wire. Now when the same cell is shunted with 12 resistance, the balance is shifted to a length of 180 cm. The internal resistance of cell is

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

Two wires A and B made of different materials of lengths 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0 10-5 m2 and 4.5 10-5 m2, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of A to that of B is x : 3. The value of x is

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

In the following p - V diagram the equation of state along the curved path is given by (V - 2)2 = 4ap where a is a constant. The total work done in the closed path is [figure]

1. + 13a
2. - 1a
3. 12a
4. - 13a

A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is n cm. The value of n is

The displacement of a particle, executing simple harmonic motion with time period T, is expressed as x(t) = A t, where A is the amplitude. The maximum value of potential energy of this oscillator is found at t = T/2 . The value of is .

The equivalent resistance between the points A and B in the following circuit is x5 . The value of x is . [figure]

A convex lens of refractive index 1.5 and focal length f = 18 cm is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is f. The value of is . (refractive index of water = 4/3)

The ratio of de Broglie wavelength of a deuteron with kinetic energy E to that of an alpha particle with kinetic energy 2E, is n : 1. The value of n is . (Assume mass of proton = mass of neutron)

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

20.0 dm3 of an ideal gas 'X' at 600 K and 0.5 MPa undergoes isothermal reversible expansion until pressure of the gas is 0.2 MPa. Which of the following option is correct? (Given: 2 = 0.3010 and 5 = 0.6989)

1. w = -9.1 kJ, U = 0, H = 0, q = 9.1 kJ
2. w = 9.1 J, U = 9.1 J, H = 0; q = 0
3. w = -3.9 kJ, U = 0, H = 0; q = 3.9 kJ
4. w = +4.1 kJ, U = 0, H = 0; q = -4.1 kJ

In period 4 of the periodic table, the elements with highest and lowest atomic radii are respectively.

1. Rb & Br
2. Na & Cl
3. K & Br
4. K & Se

Method used for separation of mixture of products (B and C) obtained in the following reaction is [figure]

1. simple distillation
2. sublimation
3. fractional distillation
4. steam distillation

Regarding the hydrides of group 15 elements EH3 (E = N, P, As, Sb), select the correct statement from the following : Choose the correct answer from the options given below :

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

Given below are two statements for the following reaction sequence. [figure] 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. Both Statement I and Statement II are true
3. Statement I is false but Statement II is true
4. Both Statement I and Statement II are false

Ph-CH=CH2 [HBr](PhCOO)2 Product Consider the above reaction Identify the correct statements. Choose the correct answer from the options given below :

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

An organic compound undergoes first order decomposition. The time taken for decomposition to ( 18 )th and ( 110 )th of its initial concentration are t1/8 and t1/10 respectively. What is the value of t1/8 t1/10 10? ( 2 = 0.3)

1. 30
2. 9
3. 3
4. 0.9

In the given pentapeptide, find out an essential amino acid (Y) and the sequence present in the pentapeptide : [figure] Choose the correct answer from the options given below :

1. arrayll(Y) & (Sequence) \ Serine & Thr-Ser-Asp-Ala-Gly array
2. arrayll(Y) & (Sequence) \ Serine & Ser-Asp-Thr-Ala-Gly array
3. arrayll(Y) & (Sequence) \ Threonine & Ser-Thr-Asp-Gly-Ala array
4. arrayll(Y) & (Sequence) \ Threonine & Thr-Ser-Asp-Gly-Ala array

At T(K), 2 moles of liquid A and 3 moles of liquid B are mixed. The vapour pressure of ideal solution formed is 320 mm Hg. At this stage, one mole of A and one mole of B are added to the solution. The vapour pressure is now measured as 328.6 mm Hg. The vapour pressure (in mm Hg) of A and B are respectively:

1. 400, 300
2. 600, 400
3. 500, 200
4. 300, 200

The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series. (R = Rydberg constant)

1. 5R36, 3R16, 21R100
2. 7R144, 3R16, 16R255
3. 3R4, 3R16, 7R144
4. 5R36, 8R9, 15R16

Consider the following reaction sequence : [figure] Compound (y) develops characteristic colour with neutral FeCl3 solution. Identify the INCORRECT statement from the following for the above sequence.

1. Compound y will dissolve in NaHCO3 and evolve a gas.
2. Compound x is more acidic than compound y.
3. Both compounds x and y will dissolve in NaOH.
4. Both compounds x and y will burn with sooty flame.

CORRECT order of stability for the following is CH2=CH-, CH3-CH2-, CH C-

1. CH C- > CH3-CH2- > CH2=CH-
2. CH2=CH- > CH C- > CH3-CH2-
3. CH C- > CH2=CH- > CH3-CH2-
4. CH3-CH2- > CH2=CH- > CH C-

[figure] Figure 1. electron probability density for 2s orbital [figure] Figure 2. wave function for 2s orbital Which of the following point in Figure 2 most accurately represents the nodal surface as shown in Figure 1?

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

Given below are the four isomeric compounds (P, Q, R, S) [figure] Identify correct statements from below. Choose the correct option.

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

Consider a weak base 'B' of pKb = 5.699. 'x' mL of 0.02 M HCl and 'y' mL of 0.02 M weak base 'B' are mixed to make 100 mL of a buffer of pH 9 at 25 . The values of 'x' and 'y' respectively are : [Given : 2 = 0.3010, 3 = 0.4771, 5 = 0.699]

1. arraycc x & y \ 42.7 & 57.3 array
2. arraycc x & y \ 14.3 & 85.7 array
3. arraycc x & y \ 85.7 & 14.3 array
4. arraycc x & y \ 11.1 & 88.9 array

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

Consider the following reactions giving major product. Identify the correct reaction.

1. [figure]
2. [figure]
3. [figure]
4. H3CCH2- O \|C-NH2 + Br2 + 4 KOH (alc) H3CCH2NH2 + 2KBr + K2CO3 + 2H2O

The correct statement among the following is:

1. [Ni(CN)4]2- and [NiCl4]2- are diamagnetic and Ni(CO)4 is paramagnetic.
2. Ni(CO)4 is diamagnetic and [NiCl4]2- and [Ni(CN)4]2- are paramagnetic.
3. Ni(CO)4 and [NiCl4]2- are diamagnetic and [Ni(CN)4]2- is paramagnetic.
4. Ni(CO)4 and [Ni(CN)4]2- are diamagnetic and [NiCl4]2- is paramagnetic.

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

Consider the following redox reaction taking place in acidic medium BH4-(aq) + ClO3-(aq) H2BO3-(aq) + Cl-(aq) If the Nernst equation for the above balanced reaction is Ecell = E cell - RTnF Q, then the value of n is . (Nearest integer)

X is the number of geometrical isomers exhibited by [Pt(NH3)(H2O)BrCl]. Y is the number of optically inactive isomer(s) exhibited by [CrCl2(ox)2]3-. Z is the number of geometrical isomers exhibited by [Co(NH3)3(NO2)3]. The value of X + Y + Z is .

Consider the dissociation equilibrium of the following weak acid HA H+(aq) + A-(aq) If the pKa of the acid is 4, then the pH of 10 mM HA solution is . (Nearest integer) [Given: The degree of dissociation can be neglected with respect to unity]

0.53 g of an organic compound (x) when heated with excess of nitric acid (concentrated) and then with silver nitrate gave 0.75 g of silver bromide precipitate. 1.0 g of (x) gave 1.32 g of CO2 gas on combustion. The percentage of hydrogen in the compound (x) is %. [Nearest Integer] [Given: Molar mass in g mol-1 H : 1, C : 12, Br : 80, Ag : 108, O : 16; Compound (x) : CxHyBrz]

500 mL of 1.2 M KI solution is mixed with 500 mL of 0.2 M KMnO4 solution in basic medium. The liberated iodine was titrated with standard 0.1 M Na2S2O3 solution in the presence of starch indicator till the blue color disappeared. The volume (in L) of Na2S2O3 consumed is . (Nearest integer)

The area of the region R = \(x, y) : xy 8, 1 y x2, x 0\ is

1. 23(20 e(2) + 9)
2. 13(40 e(2) + 27)
3. 13(49 e(2) - 15)
4. 23(24 e(2) - 7)

If g(x) = 3x2 + 2x - 3, f(0) = -3 and 4g(f(x)) = 3x2 - 32x + 72, then f(g(2)) is equal to:

1. 72
2. - 256
3. 256
4. - 72

A bag contains 10 balls out of which k are red and (10 − k) are black, where 0 k 10. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:

1. 7110
2. 711
3. 755
4. 1455

The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2, 3, 5, 10, 11, 13, 15, 21, then the mean deviation about the median of all the 10 observations is

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

If α, β, where α < β, are the roots of the equation x2 - ( + 3)x + 3 = 0 such that 1 - 1 = 13, then the sum of all possible values of λ is

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

Let y = x be the equation of a chord of the circle C1 (in the closed half-plane x 0) of diameter 10 passing through the origin. Let C2 be another circle described on the given chord as its diameter. If the equation of the chord of the circle C2, which passes through the point (2, 3) and is farthest from the center of C2, is x + ay + b = 0, then a − b is equal to

1. −6
2. 10
3. 6
4. −2

Let S = \x3 + ax2 + bx + c : a, b, c N and a, b, c 20\ be a set of polynomials. Then the number of polynomials in S, which are divisible by x2 + 2, is

1. 6
2. 120
3. 20
4. 10

Let A, B and C be three 2 × 2 matrices with real entries such that B = (I + A)-1 and A + C = I. If BC = bmatrix 1 & -5 \ -1 & 2 bmatrix and CB bmatrix x1 \ x2 bmatrix = bmatrix 12 \ -6 bmatrix, then x1 + x2 is

1. 4
2. 2
3. 0
4. −2

Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line x + 2 2y = 4. If the co-ordinates of the vertex A are (α, β), then the greatest integer less than or equal to | + 2 | is

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

Let f be a polynomial function such that f(x2 + 1) = x4 + 5x2 + 2, for all x R. Then 03 f(x) dx is equal to

1. 332
2. 53
3. 272
4. 413

If ( 1 - 5 2 x 5 x 2 x )dx = f(x) + C, where C is the constant of integration, then f ( 6 ) - f ( 4 ) is equal to

1. 1 3(26 - 3)
2. 4 3(8 - 6)
3. 1 3(26 + 3)
4. 2 3(4 + 6)

Let z be a complex number such that |z − 6| = 5 and |z + 2 − 6i| = 5. Then the value of z3 + 3z2 - 15z + 141 is equal to :

1. 61
2. 37
3. 42
4. 50

The value of k=1 (-1)k+1 ( k(k+1)k! ) is

1. e/2
2. e
3. 2/e
4. 1/e

The common difference of the A.P.: a1, a2, , am is 13 more than the common difference of the A.P.: b1, b2, , bn. If b31 = -277, b43 = -385 and a78 = 327, then a1 is equal to

1. 21
2. 19
3. 24
4. 16

The value of x 0 e ( (ex) (e2x) (e10x) )e2 - e2 x is equal to

1. (e10 - 1)2e2(e2 - 1)
2. (e20 - 1)2e2(e2 - 1)
3. (e10 - 1)2(e2 - 1)
4. (e20 - 1)2(e2 - 1)

Let S = \1, 2, 3, 4, 5, 6, 7, 8, 9\. Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let y be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,

1. 56x = 9y
2. 21x = 4y
3. 45x = 7y
4. 29x = 5y

Let y = y(x) be the solution of the differential equation x dydx - 2y = x3 (2 - x3 ) 2 y, x 0. If y(2) = 0, then (y(1)) is equal to

1. - 74
2. - 34
3. 34
4. 74

If (A - B) A + 2 C 2 A = 1, A, B, C (0, 2 ), then

1. A, C, B are in A.P.
2. A, C, B are in G.P.
3. A, B, C are in G.P.
4. A, B, C are in A.P.

If the distances of the point (1, 2, a) from the line x - 11 = y2 = z - 11 along the lines L1 : x - 13 = y - 24 = z - ab and L2 : x - 11 = y - 24 = z - ac are equal, then a + b + c is equal to

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

For three unit vectors a, b, c satisfying | a - b|2 + | b - c|2 + | c - a|2 = 9 and |2 a + k b + k c| = 3, the positive value of k is :

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

For some (0, 2 ), let the eccentricity and the length of the latus rectum of the hyperbola x2 - y2 2 = 8 be e1 and l1, respectively, and let the eccentricity and the length of the latus rectum of the ellipse x2 2 + y2 = 6 be e2 and l2, respectively. If e12 = e22 ( 2 + 1 ), then ( l1 l2e1 e2 ) 2 is equal to .

In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is R - (a, b), then a2 + b2 is equal to .

If k = ( 4 + 12 -1 ( 23 ) ) + ( 12 -1 ( 23 ) ), then the number of solutions of the equation -1(kx - 1) = -1x - -1x is .

The value of r=120 ( | ( 0r x| x|dx ) | ) is .

Let PQR be a triangle such that PQ = -2 i - j + 2 k and PR = a i + b j - 4 k, a, b Z. Let S be the point on QR, which is equidistant from the lines PQ and PR. If | PR| = 9 and PS is parallel to i - 7 j + 2 k, then the value of 3a - 4b is .