JEE Main 2026 (Online) 21st January Morning Shift

A conducting circular loop of area 1.0 m2 is placed perpendicular to a magnetic field which varies as B = (100t) Tesla. If the resistance of the loop is 100 , then the average thermal energy dissipated in the loop in one period is J.

1. 2
2. 2
4. 2

A 4 kg mass moves under the influence of a force F = (4t3 i - 3t j) N where t is the time in second. If mass starts from origin at t = 0, the velocity and position after t = 2 s will be:

1. v = 3 i + 32 j r = 65 i + j
2. v = 4 i - 32 j r = 65 i - j
3. v = 4 i - 32 j r = 85 i - j
4. v = 4 i + 52 j r = 85 i + 2 j

In an experiment the values of two spring constants were measured as k1 = (10 0.2) N/m and k2 = (20 0.3) N/m. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

1. 1.33%
2. 2.67%
3. 1.67%
4. 2.33%

Consider a modified Bernoulli equation. (P + ABt2 ) + g(h + Bt) + 12 V2 = constant If t has the dimension of time then the dimensions of A and B are , respectively.

1. [ ML0T-1] and [M0LT]
2. [ ML0T-2] and [ M0LT-1]
3. [ ML0T-2] and [ M0LT-2]
4. [ ML0T-1] and [ M0LT-1]

An aluminium and a steel rod having same lengths and cross-sections are joined to make total length of 120 cm at 30 . The coefficients of linear expansion of aluminium and steel are 24 10-6/ and 1.2 10-5/ , respectively. The length of this composite rod when its temperature is raised to 100 , is cm.

1. 120.20
2. 120.06
3. 120.15
4. 120.03

Two strings (A, B) having linear densities A = 2 10-4 kg/m and B = 4 10-4 kg/m and lengths LA = 2.5 m and LB = 1.5 m respectively are joined. Free ends of A and B are tied to two rigid supports C and D, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from C and D ends, take time t1 and t2, respectively, to reach the joint. The ratio t1/t2 is:

1. 1.90
2. 1.18
3. 1.08
4. 1.67

The electric field in a plane electromagnetic wave is given by : Ey = 69 [0.6 103x - 1.8 1011t ] V/m. The expression for magnetic field associated with this electromagnetic wave is T.

1. Bz = 2.3 10-7 [0.6 103x - 1.8 1011t ]
2. Bz = 2.3 10-7 [0.6 103x + 1.8 1011t ]
3. By = 2.3 10-7 [0.6 103x - 1.8 1011t ]
4. By = 69 [0.6 103x + 1.8 1011t ]

A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness ( 13 )rd of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

1. 3CK2(2K+1)2
2. 4KC3K-1
3. CK2+K
4. 3KC2K+1

The given circuit works as : [figure]

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

A point charge of 10-8 C is placed at origin. The work done in moving a point charge 2 from point A(4, 4, 2) m to B(2, 2, 1) m is J. ( 14 0 = 9 109 in SI units)

1. 30 10-6
2. 0
3. 15 10-6
4. 45 10-6

A light wave described by E = 60 [ (3 1015 t ) + (12 1015 t ) ] (in SI units) falls on a metal surface of work function 2.8 eV. The maximum kinetic energy of ejected photoelectron is (approximately) eV. (h = 6.6 10-34 J s and e = 1.6 10-19 C)

1. 3.8
2. 7.8
3. 6.0
4. 5.1

Initially a satellite of 100 kg is in a circular orbit of radius 1.5RE. This satellite can be moved to a circular orbit of radius 3RE by supplying 106 J of energy. The value of is . (Take Radius of Earth RE = 6 106 m and g = 10 m/s2)

1. 500
2. 1000
3. 100
4. 150

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27 to 87 . The rate of consumption of the gas is g/s. (Take heat of combustion of gas = 5.0 104 J/g, specific heat capacity of water = 4200 J/kg C)

1. 4.2
2. 2.1
3. 0.21
4. 0.42

Potential energy (V) versus distance (x) is given by the graph. Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low. [figure]

1. FBC > FAB > FDE > FCD
2. FBC > FCD > FDE > FAB
3. FCD > FAB > FBC > FDE
4. FCD > FDE > FAB > FBC

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is m. (Atomic number of gold = 79 and 14 0 = 9 109 in SI units)

1. 2.95 10-16
2. 3.85 10-14
3. 2.95 10-14
4. 3.85 10-16

A current carrying solenoid is placed vertically and a particle of mass m with charge Q is released from rest. The particle moves along the axis of solenoid. If g is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy :

1. a > g
2. a = 0
3. 0 < a < g
4. a = g

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 cm2 and 3 cm2 respectively. The rate of flow will be cm3/s. (take g = 10 m/s2) [figure]

1. 100 3
2. 200 3
3. 200 6
4. 200 3

In a double slit experiment the distance between the slits is 0.1 cm and the screen is placed at 50 cm from the slits plane. When one slit is covered with a transparent sheet having thickness t and refractive index n (= 1.5), the central fringe shifts by 0.2 cm. The value of t is cm.

1. 6.0 10-3
2. 8 10-4
3. 5.0 10-3
4. 5.6 10-4

A uniform rod of mass m and length l is suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is . (g acceleration due to gravity) [figure]

1. mg/3
2. mg/4
3. mg
4. mg/2

A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is 2 then the force needed to move the rod towards right with constant speed (v) of 1.5 m/s is N. [figure]

1. 5.7 10-2
2. 7.5 10-3
3. 5.7 10-3
4. 7.5 10-2

10 mole of oxygen is heated at constant volume from 30 to 40 . The change in the internal energy of the gas is cal. (The molecular specific heat of oxygen at constant pressure, CP = 7 cal/mol C and R = 2 cal/mol C.)

In a microscope the objective is having focal length fo = 2 cm and eye-piece is having focal length fe = 4 cm. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is .

Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is x12ML2 kg m2. The value of x is . [figure]

A collimated beam of light of diameter 2 mm is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm, then the focal length of second lens is mm.

The heat generated in 1 minute between points A and B in the given circuit, when a battery of 9 V with internal resistance of 1 is connected across these points is J. [figure]

Consider the following reactions. (Hot solution)PbCl2 + K2CrO4 A + 2KCl A + NaOH B + Na2CrO4 PbSO4 + 4CH3COONH4 (NH4)2SO4 + X In the above reactions, A, B and X are respectively.

1. Na2[Pb(OH)2], PbCrO4 and [Pb(NH3)4]SO4
2. Na2[Pb(OH)2], PbCrO4 and (NH4)2[Pb(CH3COO)4]
3. PbCrO4, Na2[Pb(OH)4] and (NH4)2[Pb(CH3COO)4]
4. PbCrO4, Na2[Pb(OH)4] and [Pb(NH3)4]SO4

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

An organic compound (P) on treatment with aqueous ammonia under hot condition forms compound (Q) which on heating with Br2 and KOH forms compound (R) having molecular formula C6H7N. Names of P, Q and R respectively are.

1. Toluic acid, methylbenzamide, 2-methylaniline
2. Benzoic acid, benzamide, aniline
3. Benzoic acid, 4-methylbenzamide, 4-methylaniline
4. Phenylethanoic acid, phenylethanamide, benzamine

From the following, the least stable structure is :

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

Identify the correct statements. Choose the correct answer from the options given below :

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

A hydrocarbon 'P' (C4H8) on reaction with HCl gives an optically active compound 'Q' (C4H9Cl) which on reaction with one mole of ammonia gives compound 'R' ( C4H11N). 'R' on diazotization followed by hydrolysis gives 'S'. Identify P, Q, R and S.

1. P=CH3-CH=CH-CH3, Q=CH3-CH2-CH2-CH2-Cl, R=CH3-CH2-CH2- NH2 |CH2, S=CH3-CH2- OH |CH2 |CH2
2. P=CH3-CH=CH-CH3, Q=CH3-CH2- Cl |CH-CH3, R=CH3-CH2- NH2 |CH-CH3, S=CH3-CH2- OH |CH-CH3
3. P = [figure] , Q = [figure] , R = [figure] , S = [figure]
4. P=CH3-CH2-CH=CH2, Q=CH3-CH2-CH2- Cl |CH2, R=CH3-CH2-CH2- CH3 |NH, S=CH3-CH2- OH | CH3 |CH

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

An organic compound "P" of molecular formula C6H12O3 gives positive iodoform test but negative Tollens' test. When "P" is treated with dilute acid, it produces "Q". "Q" gives positive Tollens' test and also iodoform test. The structure of "P" is :

1. H- O \|C-CH2-CH2- OCH3 |CH-OCH3
2. CH3- O \|C- OCH3 |CH- OCH3 |CH2
3. CH3- O \|C-CH2- OCH3 |CH-OCH3
4. CH3- O \|C- OCH3 | OCH3 |C-CH3

Which of the following graphs between pressure 'p' versus volume 'V' represents the maximum work done?

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

For the reaction, N2O4 2NO2, graph is plotted as shown below. Identify correct statements. [figure] Choose the correct answer from the options given below :

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

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

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

Identify A in the following reaction. [figure]

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

14.0 g of calcium metal is allowed to react with excess HCl at 1.0 atm pressure and 273 K. Which of the following statements is incorrect? [Given : Molar mass in g mol-1 of Ca – 40, Cl – 35.5, H – 1]

1. The limiting reagent is calcium metal.
2. 33.3 g of CaCl2 is produced.
3. 7.84 L of H2 gas is evolved.
4. 0.35 mol of H2 gas is evolved.

Which of the following represents the correct trend for the mentioned property? Choose the correct answer from the options given below :

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

80 mL of a hydrocarbon on mixing with 264 mL of oxygen in a closed U-tube undergoes complete combustion. The residual gases after cooling to 273 K occupy 224 mL. When the system is treated with KOH solution, the volume decreases to 64 mL. The formula of the hydrocarbon is :

1. C2H2
2. C2H4
3. C4H10
4. C2H6

MnO42-, in acidic medium, disproportionates to :

1. MnO4- and MnO
2. MnO4- and MnO2
3. Mn2O7 and MnO2
4. Mn2O7 and MnO

In Carius method, 0.75 g of an organic compound gave 1.2 g of barium sulphate, find percentage of sulphur (molar mass 32 g mol-1). Molar mass of barium sulphate is 233 g mol-1.

1. 4.55%
2. 16.48%
3. 10.30%
4. 21.97%

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

Elements P and Q form two types of non-volatile, non-ionizable compounds PQ and PQ2. When 1 g of PQ is dissolved in 50 g of solvent 'A', Tb was 1.176 K while when 1 g of PQ2 is dissolved in 50 g of solvent 'A', Tb was 0.689 K. (Kb of 'A' = 5 K kg mol-1). The molar masses of elements P and Q (in g mol-1) respectively, are :

1. 25, 60
2. 60, 25
3. 65, 145
4. 70, 110

Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceed the activation energy of second reaction by 20 kJ mol-1. If k1 and k2 are the rate constants of first and second reaction respectively at 300 K, then k2k1 will be . (nearest integer) [R = 8.3 J K-1 mol-1]

Use the following data : array|c|c|c| Substance & f H (500 K) kJ mol-1 & S (500 K) J K-1 mol-1 \ AB(g) & 32 & 222 \ A2(g) & 6 & 146 \ B2(g) & x & 280 \ array One mole each of A2(g) and B2(g) are taken in a 1 L closed flask and allowed to establish the equilibrium at 500 K. A2(g) + B2(g) 2AB(g) The value of x (in kJ mol-1) is . (Nearest integer) (Given : K = 2.2, R = 8.3 J K-1 mol-1)

Consider the following reactions : NaCl + K2Cr2O7 + H2SO4 A + KHSO4 + NaHSO4 + H2O A + NaOH B + NaCl + H2O B + H2SO4 + H2O2 C + Na2SO4 + H2O In the product 'C', 'X' is the number of O22- units, 'Y' is the total number of oxygen atoms present and 'Z' is the oxidation state of Cr. The value of X + Y + Z is .

The pH and conductance of a weak acid (HX) were found to be 5 and 4 10-5 S, respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of 1 cm2 were at a distance of 15 cm apart. The value of the limiting molar conductivity is S m2 mol-1. (nearest integer) (Given : degree of dissociation of the weak acid ( ) 1)

Consider the following reaction sequence [figure] The percentage of nitrogen in product 'T' formed is %. (Nearest integer) (Given molar mass in g mol-1 H : 1, C : 12, N : 14, O : 16)

Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, x > y, be 8 and 16 respectively. Two numbers are chosen from \1, 2, 3, x - 4, y, 5\ one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is :

1. 45
2. 35
3. 25
4. 13

If x2 + x + 1 = 0, then the value of (x + 1x )4 + (x2 + 1x2 )4 + (x3 + 1x3 )4 + + (x25 + 1x25 )4 is:

1. 162
2. 145
3. 128
4. 175

Let a point A lie between the parallel lines L1 and L2 such that its distances from L1 and L2 are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC, where the points B and C lie on the lines L1 and L2, respectively, is :

1. 21 3
2. 12 2
3. 15 6
4. 27

The value of cosec 10 - 3 10 is equal to :

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

Let a = - i + 2 j + 2 k, b = 8 i + 7 j - 3 k and c be a vector such that a c = b. If c ( i + j + k) = 4, then | a + c|2 is equal to :

1. 30
2. 33
3. 27
4. 35

The value of - /6 /6 ( + 4x111 - (|x| + /6) )dx is equal to:

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

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

1. 4e /4 - 2 - 1
2. 2e /4 + 4 - 1
3. 4e /4 + 2 - 1
4. 2e /4 - 4 - 1

The number of strictly increasing functions f from the set \1, 2, 3, 4, 5, 6\ to the set \1, 2, 3, , 9\ such that f(i) i for 1 i 6, is equal to :

1. 21
2. 28
3. 27
4. 22

Let ( , , ) be the co-ordinates of the foot of the perpendicular drawn from the point (5, 4, 2) on the line r = (- i + 3 j + k) + (2 i + 3 j - k). Then the length of the projection of the vector i + j + k on the vector 6 i + 2 j + 3 k is :

1. 187
2. 157
3. 4
4. 3

Let a1, a2, a3, be a G.P. of increasing positive terms such that a2 a3 a4 = 64 and a1 + a3 + a5 = 8137. Then a3 + a5 + a7 is equal to :

1. 3256
2. 3252
3. 3248
4. 3244

Let PQ and MN be two straight lines touching the circle x2 + y2 - 4x - 6y - 3 = 0 at the points A and B respectively. Let O be the centre of the circle and AOB = /3. Then the locus of the point of intersection of the lines PQ and MN is :

1. x2 + y2 - 18x - 12y - 25 = 0
2. x2 + y2 - 12x - 18y - 25 = 0
3. 3(x2 + y2) - 12x - 18y - 25 = 0
4. 3(x2 + y2) - 18x - 12y + 25 = 0

The area of the region, inside the ellipse x2 + 4y2 = 4 and outside the region bounded by the curves y = |x| - 1 and y = 1 - |x|, is :

1. 2 - 1
2. 3( - 1)
3. 2( - 1)
4. 2 - 12

The sum of all the roots of the equation (x - 1)2 - 5|x - 1| + 6 = 0, is :

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

If the coefficient of x in the expansion of (ax2 + bx + c)(1 - 2x)26 is -56 and the coefficients of x2 and x3 are both zero, then a + b + c is equal to :

1. 1483
2. 1300
3. 1500
4. 1403

The number of relations, defined on the set \a, b, c, d\, which are both reflexive and symmetric, is equal to:

1. 16
2. 64
3. 256
4. 1024

Let the foci of a hyperbola coincide with the foci of the ellipse x236 + y216 = 1. If the eccentricity of the hyperbola is 5, then the length of its latus rectum is :

1. 96 5
2. 24 5
3. 12
4. 16

If the domain of the function f(x) = -1 ( 2x - 511 - 3x ) + -1(2x2 - 3x + 1) is the interval [ , ], then + 2 is equal to :

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

Let O be the vertex of the parabola x2 = 4y and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2 : 3 be the conic C. Then the equation of the chord of C, which is bisected at the point (1, 2), is :

1. 5x - 4y + 3 = 0
2. x - 2y + 3 = 0
3. 4x - 5y + 6 = 0
4. 5x - y - 3 = 0

Let c and d be vectors such that | c + d| = 29 and c (2 i + 3 j + 4 k) = (2 i + 3 j + 4 k) d. If 1, 2 ( 1 > 2) are the possible values of ( c + d) (-7 i + 2 j + 3 k), then the equation K2x2 + (K2 - 5K + 1)xy + (3K + 22 )y2 - 8x + 12y + 2 = 0 represents a circle, for K equal to :

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

Let f : R (0, ) be a twice differentiable function such that f(3) = 18, f'(3) = 0 and f''(3) = 4. Then x 1 e ( f(2 + x)f(3) ) 18(x - 1)2 is equal to :

1. 9
2. 18
3. 1
4. 2

Let f : R R be a twice differentiable function such that the quadratic equation f(x)m2 - 2f'(x)m + f''(x) = 0 in m, has two equal roots for every x R. If f(0) = 1, f'(0) = 2, and ( , ) is the largest interval in which the function f( e x - x) is increasing, then + is equal to .

Let S = \(m, n) : m, n \1, 2, 3, , 50\\. If the number of elements (m, n) in S such that 6m + 9n is a multiple of 5 is p and the number of elements (m, n) in S such that m + n is a square of a prime number is q, then p + q is equal to .

Let a1 = 1 and for n 1, an+1 = 12an + n2 - 2n - 1n2(n + 1)2. Then | n=1 (an - 2n2 ) | is equal to .

6 0 |( 3x + 2x + x)| dx is equal to .

For some , R, let A = bmatrix & 2 \ 1 & 2 bmatrix and B = bmatrix 1 & 1 \ 1 & bmatrix be such that A2 - 4A + 2I = B2 - 3B + I = O. Then ( ( adj(A3 - B3)))2 is equal to .