JEE Main 2026 (Online) 22nd January Morning Shift

A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification m1 when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which leads to a change in magnification of total lens system to m2. The value of | m1m2 | is .

1. 2527
2. 56
3. 527
4. 32

Consider an equilateral prism (refractive index 2). A ray of light is incident on its one surface at a certain angle i. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to

1. 30
2. 20
3. 40
4. 15

A cylindrical tube AB of length l, closed at both ends contains an ideal gas of 1 mol having molecular weight M. The tube is rotated in a horizontal plane with constant angular velocity about an axis perpendicular to AB and passing through the edge at end A, as shown in the figure. If PA and PB are the pressures at A and B respectively, then (Consider the temperature is same at all points in the tube) [figure]

1. PB = PA e ( M 2 l23RT )
2. PB = PA
3. PB = PA e ( M 2 l22RT )
4. PB = PA e ( M 2 l2RT )

Electric field in a region is given by E = Ax i + By j, where A = 10 V/m2 and B = 5 V/m2. If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is V.

1. 1000
2. 0
3. 2000
4. 500

XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is l. A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L(L > l) and mass m is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is m/s. (g = acceleration due to gravity) [figure]

1. mgRB2l2
2. 2mgRB2L2
3. 2mgRB2l2
4. 8mgRB2l2

Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points A and F are maintained at 100 and 40 respectively. Given the thermal conductivity of rod x is three times of that of rod y, the temperatures at junction points B and E are (close to): [figure]

1. 60 and 45 respectively
2. 80 and 70 respectively
3. 89 and 73 respectively
4. 80 and 60 respectively

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

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

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 false
4. Both Statement I and Statement II are true

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is kg m2.

1. 0.18
2. 0.72
3. 0.36
4. 0.63

A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field E is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is .

1. mg - qE
2. m2g2 + q2E2
3. mg + qE
4. m2g2 - q2E2

A projectile is thrown upward at an angle 60 with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is 45 with the horizontal. The initial speed of the projectile is m/s.

1. 20 3
2. 20 2
3. 40
4. 40 2

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10\% of those of planet A, is m/s.

1. 1000
2. 200 5
3. 1000 2
4. 100 10

Find the correct combination of A, B, C and D inputs which can cause the LED to glow. [figure]

1. 1000
2. 0011
3. 0100
4. 1101

Three identical coils C1, C2 and C3 are closely placed such that they share a common axis. C2 is exactly midway. C1 carries current I in anti-clockwise direction while C3 carries current I in clockwise direction. An induced current flows through C2 will be in clockwise direction when

1. C1 and C3 move with equal speeds away from C2
2. C1 moves towards C2 and C3 moves away from C2
3. C1 and C3 move with equal speeds towards C2
4. C1 moves away from C2 and C3 moves towards C2

The volume of an ideal gas increases 8 times and temperature becomes (1/4)th of initial temperature during a reversible change. If there is no exchange of heat in this process ( Q = 0) then identify the gas from the following options (Assuming the gases given in the options are ideal gases) :

1. NH3
2. O2
3. CO2
4. He

The minimum frequency of photon required to break a particle of mass 15.348 amu into 4 particles is kHz. [mass of He nucleus = 4.002 amu, 1 amu = 1.66 10-27 kg, h = 6.6 10-34 J s and c = 3 108 m/s]

1. 14.94 1020
2. 9 1019
3. 9 1020
4. 14.94 1019

Six point charges are kept 60 apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is . ( 0 is permittivity of free space) [figure]

1. - ( 5Q8 0 R2 )( i - 3 j)
2. Q4 0 R2( 3 i - j)
3. - Q4 0 R2( 3 i - j)
4. - 5Q8 0 R2( i + 3 j)

A 7.9 MeV -particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) m. [ 14 0 = 9 109 N m2/C2 . and electron charge . = 1.6 10-19 C ]

1. 2.88 10-14
2. 5.76 10-14
3. 1.44 10-13
4. 1.69 10-12

Net gravitational force at the center of a square is found to be F1 when four particles having mass M, 2M, 3M and 4M are placed at the four corners of the square as shown in figure and it is F2 when the positions of 3M and 4M are interchanged. The ratio F1F2 is 5. The value of is . [figure]

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

A meter bridge with two resistances R1 and R2 as shown in figure was balanced (null point) at 40 cm from the point P. The null point changed to 50 cm from the point P, when 16 resistance is connected in parallel to R2. The values of resistances R1 and R2 are . [figure]

1. R2 = 8 , R1 = 163
2. R2 = 12 , R1 = 123
3. R2 = 4 , R1 = 43
4. R2 = 16 , R1 = 163

Inductance of a coil with 104 turns per metre is 10 mH and it is connected to a dc source of 10 V with internal resistance of 10 . The energy density in the inductor when the current reaches ( 1e ) of its maximum value is 1e2 J/m3. The value of is . ( 0 = 4 10-7 T m/A).

The electric field of a plane electromagnetic wave, travelling in an unknown nonmagnetic medium is given by, Ey = 20 (3 106 x - 4.5 1014 t ) V/m (where x, t and other values have S.I. units). The dielectric constant of the medium is (speed of light in free space is 3 108 m/s)

Two loudspeakers (L1 and L2) are placed with a separation of 10 m, as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point A, equidistant from both loudspeakers, is moved by 25 m along the line AB while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is Hz (Speed of sound in air is 324 m/s and 5 = 2.23) [figure]

A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm. Refractive index of glass is 1.5. The rays converge to a point at a distance x cm from the centre of curvature of the spherical surface. The value of x is cm.

A circular disc has radius R1 and thickness T1. Another circular disc made of the same material has radius R2 and thickness T2. If the moments of inertia of both discs are the same and R1R2 = 2 then T1T2 = 1 . The value of is .

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

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 true
3. Both Statement I and Statement II are 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 most appropriate answer from the options given below

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

In the reaction, 2Al(s) + 6HCl(aq) 2Al3+(aq) + 6Cl-(aq) + 3H2(g)

1. 12 L HCl(aq) is consumed for every 6 L H2(g) produced.
2. 11.2 L H2(g) at STP is produced for every mole of HCl consumed.
3. 33.6 L H2(g) is produced regardless of temperature and pressure for every mole of Al that reacts.
4. 67.2 L H2(g) at STP is produced for every mole of Al that reacts.

As compared with chlorocyclohexane, which of the following statements correctly apply to chlorobenzene? Choose the correct answer from the options given below :

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

The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is J mol-1. Given: RH = 2.18 10-11 ergs.

1. 9.835 1012
2. 1.635 10-11
3. 1.635 10-18
4. 9.835 105

The correct order of the rate of reaction of the following reactants with nucleophile by SN1 mechanism is : (Given : Structures I and II are rigid) [figure]

1. I < II < III < IV
2. II < I < III < IV
3. III < I < II < IV
4. IV < III < II < I

Consider the transition metal ions Mn3+, Cr3+, Fe3+ and Co3+ and all form low spin octahedral complexes. The correct decreasing order of unpaired electrons in their respective d-orbitals of the complexes is

1. Cr3+ > Mn3+ > Fe3+ > Co3+
2. Mn3+ > Fe3+ > Co3+ > Cr3+
3. Fe3+ > Co3+ > Mn3+ > Cr3+
4. Cr3+ > Fe3+ > Co3+ > Mn3+

A product (First order reaction). Three sets of experiments were performed for a reaction under similar experimental conditions: Run 1 100 mL of 10 M solution of reactant A Run 2 200 mL of 10 M solution of reactant A Run 3 100 mL of 10 M solution of reactant A + 100 mL of H2O added. The correct variation of rate of reaction is

1. Run 1 = Run 2 = Run 3
2. Run 3 < Run 1 < Run 2
3. Run 1 < Run 2 < Run 3
4. Run 3 < Run 1 = Run 2

A 'p'-block element (E) and hydrogen form a binary cation (EHx)+, while EH3 on treatment with K2HgI4 in alkaline medium gives a precipitate of basic mercury(II) amido-iodine. Given below are first ionisation enthalpy values ( kJ mol-1) for first element each from group 13, 14, 15 and 16. Identify the correct first ionisation enthalpy value for element E.

1. 1402
2. 1086
3. 801
4. 1312

Consider a solution of CO2(g) dissolved in water in a closed container. Which one of the following plots correctly represents variation of log (partial pressure of CO2 in vapour phase above water) [y-axis] with log (mole fraction of CO2 in water) [x-axis] at 25 ?

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

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

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

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

The correct order of reactivity of CH3Br in methanol with the following nucleophiles is F-, I-, C2H5O- and C6H5O-

1. I- > C2H5O- > C6H5O- > F-
2. I- > F- > C6H5O- > C2H5O-
3. I- > C6H5O- > F- > C2H5O-
4. I- > C2H5O- > F- > C6H5O-

Two p-block elements X and Y form fluorides of the type EF3. The fluoride compound XF3 is a Lewis acid and YF3 is a Lewis base. The hybridizations of the central atoms of XF3 and YF3 respectively are

1. sp2 and sp3
2. Both sp3
3. Both sp2
4. sp3 and sp2

A first row transition metal (M) does not liberate H2 gas from dilute HCl. 1 mol of aqueous solution of MSO4 is treated with excess of aqueous KCN and then H2S(g) is passed through the solution. The amount of MS (metal sulphide) formed from the above reaction is mol.

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

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

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

'A' is a neutral organic compound (M.F. : C8H9ON). On treatment with aqueous Br2/HO , 'A' forms a compound 'B' which is soluble in dilute acid. 'B' on treatment with aqueous NaNO2/HCl (0-5 C) produces a compound 'C' which on treatment with CuCN/NaCN produces 'D'. Hydrolysis of 'D' produces 'E' which is also obtainable from the hydrolysis of 'A'. 'E' on treatment with acidified KMnO4 produces 'F'. 'F' contains two different types of hydrogen atoms. The structure of 'A' is

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

The formal charges on the atoms marked as (1) to (4) in the Lewis representation of HNO3 molecule respectively are [figure]

1. 0, 0, -1, +1
2. 0, -1, 0, +1
3. 0, +1, 0, -1
4. +1, 0, 0, -1

Sodium fusion extract of an organic compound (Y) with CHCl3 and chlorine water gives violet color to the CHCl3 layer. 0.15 g of (Y) gave 0.12 g of the silver halide precipitate in Carius method. Percentage of halogen in the compound (Y) is . (Nearest integer) (Given : molar mass g mol-1 C : 12, H : 1, Cl : 35.5, Br : 80, I : 127)

The cycloalkene (X) on bromination consumes one mole of bromine per mole of (X) and gives the product (Y) in which C : Br ratio is 3:1. The percentage of bromine in the product (Y) is %. (Nearest integer) (Given : molar mass in g mol-1 H : 1, C : 12, O : 16, Br : 80)

Dissociation of a gas A2 takes place according to the following chemical reaction. At equilibrium, the total pressure is 1 bar at 300 K. A2(g) 2A(g) The standard Gibbs energy of formation of the involved substances has been provided below: arraycc Substance & Gf /kJ mol-1 \ A2 & -100.00 \ A & -50.832 array The degree of dissociation of A2(g) is given by (x 10-2)1/2 where x = . (Nearest integer). [ Given : R = 8 J mol-1 K-1, 2 = 0.3010, 3 = 0.48 ] Assume degree of dissociation is not negligible.

The temperature at which the rate constants of the given below two gaseous reactions become equal is K. (Nearest integer) X Y, k1 = 106 e -30000T P Q, k2 = 104 e -24000T Given : 10 = 2.303

Consider the following electrochemical cell at 298 K Pt | HSnO2-(aq) | Sn(OH)62-(aq) | OH-(aq) | Bi2O3(s) | Bi(s). If the reaction quotient at a given time is 106, then the cell EMF ( Ecell) is 10-1 V (Nearest integer). Given the standard half-cell reduction potential as E Bi2O3/Bi,OH- = -0.44 V and E Sn(OH)62-/HSnO2-,OH- = -0.90 V

Two distinct numbers a and b are selected at random from 1, 2, 3, , 50. The probability, that their product ab is divisible by 3, is

1. 2721225
2. 5611225
3. 6641225
4. 825

The number of solutions of -1 4x + -1 6x = 6, where - 12 6 < x < 12 6, is equal to :

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

If the line x + 2y = 1, where R, does not meet the hyperbola x2 - 9y2 = 9, then a possible value of is :

1. 0.6
2. 0.7
3. 0.8
4. 0.5

The number of distinct real solutions of the equation x|x+4| + 3|x+2| + 10 = 0 is

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

Let the relation R on the set M = \1, 2, 3, , 16\ be given by R = \(x, y) : 4y = 5x - 3, x, y M\. Then the minimum number of elements required to be added in R, in order to make the relation symmetric, is equal to

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

Let the set of all values of r, for which the circles (x+1)2 + (y+4)2 = r2 and x2 + y2 - 4x - 2y - 4 = 0 intersect at two distinct points be the interval ( , ). Then is equal to

1. 21
2. 24
3. 20
4. 25

Let the solution curve of the differential equation x dy - y dx = x2 + y2 dx, x > 0, y(1) = 0, be y = y(x). Then y(3) is equal to

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

If the chord joining the points P1(x1, y1) and P2(x2, y2) on the parabola y2 = 12x subtends a right angle at the vertex of the parabola, then x1x2 - y1y2 is equal to

1. 280
2. 288
3. 292
4. 284

If A = bmatrix 2 & 3 \ 3 & 5 bmatrix, then the determinant of the matrix (A2025 - 3 A2024 + A2023 ) is

1. 12
2. 24
3. 28
4. 16

The value of - 2 2 ( 1[x] + 4 ) dx, where [ ] denotes the greatest integer function, is

1. 160(21 - 1)
2. 160( - 7)
3. 760( - 3)
4. 760(3 - 1)

Let AB = 2 i + 4 j - 5 k and AD = i + 2 j + k, R. Let the projection of the vector v = i + j + k on the diagonal AC of the parallelogram ABCD be of length one unit. If , , where > , be the roots of the equation 2x2 - 6 x + 5 = 0, then 2 - is equal to

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

Let the line x = -1 divide the area of the region \(x, y) : 1 + x2 y 3 - x \ in the ratio m : n, (m, n) = 1. Then m + n is equal to

1. 27
2. 28
3. 25
4. 26

Let f(x) = x2025 - x2000, x [0, 1] and the minimum value of the function f(x) in the interval [0, 1] be (80)80(n)-81. Then n is equal to

1. -40
2. -41
3. -80
4. -81

If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is

1. -26
2. -20
3. -24
4. -22

If a random variable x has the probability distribution arrayccccccccc x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \ P(x) & 0 & 2k & k & 3k & 2k2 & 2k & k2 + k & 7k2 array then P(3 < x 6) is equal to

1. 0.34
2. 0.64
3. 0.22
4. 0.33

The coefficient of x48 in (1 + x) + 2(1 + x)2 + 3(1 + x)3 + + 100(1 + x)100 is equal to

1. 100 100C49 - 100C48
2. 100 101C49 - 101C50
3. 100C50 + 101C49
4. 100 100C49 - 100C50

Let P( , , ) be the point on the line x - 12 = y + 1-3 = z at a distance 4 14 from the point (1, -1, 0) and nearer to the origin. Then the shortest distance, between the lines x - 1 = y - 2 = z - 3 and x + 52 = y - 101 = z - 31, is equal to

1. 4 75
2. 7 54
3. 4 57
4. 2 74

If the domain of the function f(x) = -1 ( 5 - x3 + 2x ) + 1 e(10 - x) is (- , ] [ , ) - \ \, then 6( + + + ) is equal to

1. 66
2. 68
3. 70
4. 67

Let f : [1, ) R be a differentiable function. If 6 1x f(t) dt = 3xf(x) + x3 - 4 for all x 1, then the value of f(2) - f(3) is :

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

If the image of the point P(1, 2, a) in the line x - 63 = y - 72 = 7 - z2 is Q(5, b, c), then a2 + b2 + c2 is equal to

1. 298
2. 264
3. 293
4. 283

If 2 48 - 2 12 2 24 - 2 6 = + 52, where , N, then + is equal to

Let A be a 3 3 matrix such that A + AT = O. If A bmatrix 1 \ -1 \ 0 bmatrix = bmatrix 3 \ 3 \ 2 bmatrix, A2 bmatrix 1 \ -1 \ 0 bmatrix = bmatrix -3 \ 19 \ -24 bmatrix and (adj(2 adj(A + I))) = (2) (3) (11) , , , are non-negative integers, then + + is equal to

Let ABC be a triangle. Consider four points p1, p2, p3, p4 on the side AB, five points p5, p6, p7, p8, p9 on the side BC, and four points p10, p11, p12, p13 on the side AC. None of these points is a vertex of the triangle ABC. Then the total number of pentagons, that can be formed by taking all the vertices from the points p1, p2, , p13, is

Let = -1 + i 32 and = -1 - i 32, i = -1. If (7 - 7 + 9 )20 + (9 + 7 - 7 )20 + (-7 + 9 + 7 )20 + (14 + 7 + 7 )20 = m10, then m is

If ( x) -112( x) -52 dx = - p1q1( x) 92 - p2q2( x) 52 - p3q3( x) 12 + p4q4( x) -32 + C, where pi and qi are positive integers with (pi, qi) = 1 for i = 1, 2, 3, 4 and C is the constant of integration, then 15p1p2p3p4q1q2q3q4 is equal to