JEE Main 2026 (Online) 24th January Evening Shift

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x. The value of x is

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

In case of vertical circular motion of a particle by a thread of length r, if the tension in the thread is zero at an angle 30 shown in figure, the velocity at the bottom point (A) of the circular path is (g = gravitational acceleration) [figure]

1. 72gr
2. 4gr
3. 52gr
4. 5gr

The velocity (v) – distance (x) graph is shown in figure. Which graph represents acceleration (a) versus distance (x) variation of this system? [figure]

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

In the Young's double slit experiment the intensity produced by each one of the individual slits is Io. The distance between two slits is 2 mm. The distance of screen from slits is 10 m. The wavelength of light is 6000 . The intensity of light on the screen in front of one of the slits is

1. Io2
2. Io
3. 2Io
4. 4Io

The reading of the ammeter (A) in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is A. [figure]

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

Identify the correct truth table of the given logic circuit. [figure]

1. arrayccc A & B & Y \ 0 & 0 & 0 \ 0 & 1 & 0 \ 1 & 0 & 1 \ 1 & 1 & 0 array
2. arrayccc A & B & Y \ 0 & 0 & 0 \ 0 & 1 & 1 \ 1 & 0 & 1 \ 1 & 1 & 0 array
3. arrayccc A & B & Y \ 0 & 0 & 1 \ 0 & 1 & 1 \ 1 & 0 & 1 \ 1 & 1 & 0 array
4. arrayccc A & B & Y \ 0 & 0 & 1 \ 0 & 1 & 0 \ 1 & 0 & 1 \ 1 & 1 & 0 array

Three parallel plate capacitors each with area A and separation d are filled with two dielectrics (k1 and k2) in the following fashion. Which of the following is true? (k1 > k2) [figure]

1. CC > CB > CA
2. CB > CC > CA
3. CA > CC > CB
4. CC > CA > CB

A moving coil galvanometer of resistance 100 shows a full scale deflection for a current of 1 mA. The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of 5 mA, is

1. 25
2. 2.5
3. 0.5
4. 10

Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used is cm.

1. -20
2. -15/2
3. -10
4. -15

A cubical block of density b = 600 kg/m3 floats in a liquid of density l = 900 kg/m3. If the height of block is H = 8.0 cm, then height of the submerged part is cm.

1. 6.3
2. 4.3
3. 7.3
4. 5.3

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from P1 to P2 is Joule (P1 = 21.7 Pa and P2 = 30 Pa, Cv = 21 J/K mol, R = 8.3 J/mol K). The value of is . [figure]

1. 21
2. 28
3. 24
4. 15

In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division = 0.05 mm, then the least count of the vernier callipers is mm.

1. 0.002
2. 0.02
3. 0.05
4. 0.005

Five persons P1, P2, P3, P4 and P5 recorded object distance (u) and image distance (v) using same convex lens having power +5 D as (25, 96), (30, 62), (35, 37), (45, 35) and (50, 32) respectively. Identify correct statement

1. Readings recorded by P3 and P2 persons are incorrect
2. Readings recorded by all persons are correct
3. Readings recorded by P3 person are incorrect
4. Readings recorded by P4 and P5 persons are incorrect

The binding energies for the following nuclear reactions are expressed in MeV. 2He3 + 0n1 2He4 + 20 MeV 2He4 + 0n1 2He5 - 0.9 MeV If X3, X4, X5 denote the stability of 2He3, 2He4 and 2He5, respectively, then the correct order is :

1. X4 > X5 > X3
2. X4 < X5 < X3
3. X4 > X5 < X3
4. X4 = X5 = X3

A thin uniform rod (X) of mass M and length L is pivoted at a height ( L3 ) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top, is . (g = gravitational acceleration) [figure]

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

A point source is kept at the center of a spherically enclosed detector. If the volume of the detector is increased by 8 times, the intensity will

1. increase by 64 times
2. decrease by 4 times
3. decrease by 8 times
4. increase by 8 times

A regular hexagon is formed by six wires each of resistance r and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be

1. 35r
2. 45r
3. 58r
4. 34r

A flexible chain of mass m hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is 30 . Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is .

1. mg
2. 32mg
3. 12mg
4. 3mg

Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have common axis. The currents through P and Q are I and 4I respectively in clockwise direction as seen from O. The net magnetic field at O is : [figure]

1. 0 I4 2r towards Q
2. 3 0 I4 2r towards Q
3. 3 0 I4 2r towards P
4. 0 I4 2r towards P

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V. If a second light having wavelength twice of first light is used, the stopping potential drops to 0.7 V. The wavelength of first light is m. (h = 6.63 10-34 J s, e = 1.6 10-19 C, c = 3 108 m/s)

1. 2.9 10-8
2. 2.5 10-7
3. 3.1 10-7
4. 2.2 10-8

In a meter bridge experiment to determine the value of unknown resistance, first the resistances 2 and 3 are connected in the left and right gaps of the bridge and the null point is obtained at a distance l cm from the left. Now when an unknown resistance x is connected in parallel to 3 resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance x is .

A point charge q = 1 is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q = 24 , distributed uniformly along its length, as shown in figure. Force between q and wire is N. (Use : 14 0 = 9 109 N m2/C2) [figure]

A soap bubble of surface tension 0.04 N/m is blown to a diameter of 7 cm. If (15000 - x) of work is done in blowing it further to make its diameter 14 cm, then the value of x is . ( = 22/7)

When 300 J of heat is given to an ideal gas with Cp = 72R, its temperature rises from 20 to 50 keeping its volume constant. The amount of the gas is (approximately) 10-3 mol. (R = 8.314 J/mol K)

A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to I1. A small concentric cylinder of length L/2 and radius R/3 carved from this cylinder has moment of inertia about its axis equal to I2. The ratio I1/I2 is .

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

In the Group analysis of cations, Ba2+ & Ca2+ are precipitated respectively as

1. sulphide & sulphide
2. hydroxide & carbonate
3. chromate & sulphide
4. carbonate & carbonate

"X" is an oxoanion of the lightest element of group 7 (in the periodic table). The metal is in +6 oxidation state in "X". The color of the potassium salt of X is

1. purple
2. orange
3. yellow
4. green

At 298 K, the mole percentage of N2(g) in air is 80\%. Water is in equilibrium with air at a pressure of 10 atm. What is the mole fraction of N2(g) in water at 298 K? (KH for N2 is 6.5 107 mmHg)

1. 9.35 10-5
2. 9.35 105
3. 1.23 10-7
4. 1.17 10-4

The heats of atomisation of methane and ethane are 'x' kJ mol-1 and 'y' kJ mol-1 respectively. The longest wavelength ( ) of light capable of breaking the C-C bond can be expressed in SI unit as :

1. NA hc250(y - 6x)
2. NA hc (y - 6x4 )-1
3. hc1000 ( y - 6x4 )-1
4. NA hc250(4y - 6x)

Pair of species among the following having same bond order as well as paramagnetic character will be-

1. O2-, N2+
2. O2+, N22-
3. O2-, N2-
4. O2+, N2-

The unsaturated ether on acidic hydrolysis produces carbonyl compounds as shown below :- [figure] Based on this, predict the solution/reagent that will help to distinguish "P" and "Q" obtained in the following reaction :- CH3-CH=CH-O- CH3 |C=CH2 [ ]H3O P + Q

1. Saturated NaHSO3 solution
2. Fehling solution
3. Lucas reagent
4. 2,4-DNP reagent

Consider the following gaseous equilibrium in a closed container of volume 'V' at T(K). P2(g) + Q2(g) 2PQ(g) 2 moles each of P2(g), Q2(g) and PQ(g) are present at equilibrium. Now one mole each of 'P2' and 'Q2' are added to the equilibrium keeping the temperature at T(K). The number of moles of P2, Q2 and PQ at the new equilibrium, respectively, are

1. 2.56, 1.62, 2.24
2. 2.67, 2.67, 2.67
3. 1.21, 2.24, 1.56
4. 1.66, 1.66, 1.66

The correct order of C, N, O and F in terms of second ionisation potential is

1. C < N < F < O
2. C < F < N < O
3. F < N < C < O
4. C < O < N < F

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

Choose the INCORRECT statement

1. Carbon exhibits negative oxidation states along with +4 and +2.
2. Carbon cannot exceed its covalency more than four.
3. Among the isotopes of carbon, 13C is a radioactive isotope.
4. CO2 is the most acidic oxide among the dioxides of group 14 elements.

The wavelength of spectral line obtained in the spectrum of Li2+ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is

1. 1.14 10-6 cm
2. 2.28 10-6 cm
3. 1.14 10-7 cm
4. 2.28 10-7 cm

Two liquids A and B form an ideal solution at temperature T K. At T K, the vapour pressures of pure A and B are 55 and 15 kN m-2 respectively. What is the mole fraction of A in solution of A and B in equilibrium with a vapour in which the mole fraction of A is 0.8?

1. 0.5217
2. 0.480
3. 0.340
4. 0.663

From the following, how many compounds contain at least one secondary alcohol? [figure] Choose the correct answer from the options given below :

1. Three
2. Two
3. Four
4. Five

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

The number of possible tripeptides formed involving alanine (ala), glycine (gly) and valine (val), where no amino acid has been used more than once is:

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

One mole of Cl2(g) was passed into 2 L of cold 2 M KOH solution. After the reaction, the concentrations of Cl-, ClO- and OH- are respectively (assume volume remains constant)

1. 0.5 M, 0.5 M, 0.5 M
2. 1 M, 1 M, 1 M
3. 0.5 M, 0.5 M, 1 M
4. 0.75 M, 0.75 M, 1 M

A student has planned to prepare acetanilide from aniline using acetic anhydride. The student has started from 9.3 g of aniline. However, the student has managed to obtain 11 g of dry acetanilide. The % yield of this reaction is :-

1. 59.5\%
2. 72.5\%
3. 97.5\%
4. 81.5\%

The wavelengths of light absorbed for the following complexes are in the order (I) [Co(NH3)6]3+ ; (II) [Co(H2O)6]3+ ; (III) [Co(CN)6]3- ; (IV) [Co(NH3)5(H2O)]3+ ; (V) [CoF6]3-

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

Find out the statements which are not true. Choose the correct answer from the options given below :

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

Grignard reagent RMgBr (P) reacts with water and forms a gas (Q). One gram of Q occupies 1.4 dm3 at STP. (P) on reaction with dry ice in dry ether followed by H3O+ forms a compound (Z). 0.1 mole of (Z) will weigh g. (Nearest integer)

Molar conductivity of a weak acid HQ of concentration 0.18 M was found to be 130 of the molar conductivity of another weak acid HZ with concentration of 0.02 M. If Q- happened to be equal to Z-, then the difference of the pKa values of the two weak acids (pKa(HQ) - pKa(HZ)) is (Nearest integer). [Given: degree of dissociation ( ) 1 for both weak acids, : limiting molar conductivity of ions]

A chromium complex with a formula CrCl3 6H2O has a spin only magnetic moment value of 3.87 BM and its solution conductivity corresponds to 1 : 2 electrolyte. 2.75 g of the complex solution was initially passed through a cation exchanger. The solution obtained after the process was reacted with excess of AgNO3. The amount of AgCl formed in the above process is g. (Nearest integer) [Given: Molar mass in g mol-1 Cr : 52, Cl : 35.5, Ag : 108, O : 16, H : 1]

The half-life of 65Zn is 245 days. After x days, 75\% of original activity remained. The value of x in days is . (Nearest integer) (Given: 3 = 0.4771 and 2 = 0.3010)

0.25 g of an organic compound "A" containing carbon, hydrogen and oxygen was analysed using the combustion method. There was an increase in mass of CaCl2 tube and potash tube at the end of the experiment. The amount was found to be 0.15 g and 0.1837 g, respectively. The percentage of oxygen in compound A is %. (Nearest integer) (Given: molar mass in g mol-1 H : 1, C : 12, O : 16)

The smallest positive integral value of a, for which all the roots of x4 - ax2 + 9 = 0 are real and distinct, is equal to

1. 7
2. 3
3. 4
4. 9

The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is

1. 1579
2. 1578
3. 1580
4. 1581

Let a1, a2, a3, a4 be an A.P. of four terms such that each term of the A.P. and its common difference l are integers. If a1 + a2 + a3 + a4 = 48 and a1a2a3a4 + l4 = 361, then the largest term of the A.P. is equal to

1. 27
2. 24
3. 23
4. 21

Consider the following three statements for the function f : (0, ) R defined by f(x) = | e x| - |x - 1| : (I) f is differentiable at all x > 0. (II) f is increasing in (0, 1). (III) f is decreasing in (1, ). Then

1. Only (I) is TRUE.
2. Only (I) and (III) are TRUE.
3. Only (II) and (III) are TRUE.
4. All (I), (II) and (III) are TRUE.

Let P = [pij] and Q = [qij] be two square matrices of order 3 such that qij = 2(i+j-1)pij and (Q) = 210. Then the value of ( adj( adj P)) is:

1. 81
2. 16
3. 124
4. 32

Let y = y(x) be a differentiable function in the interval (0, ) such that y(1) = 2, and t x ( t2y(x) - x2y(t)x - t ) = 3 for each x > 0. Then 2y(2) is equal to :

1. 27
2. 18
3. 23
4. 12

The sum of all values of , for which the shortest distance between the lines x+1 = y-2-1 = z-4- and x = y-12 = z-12 is 2, is

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

Let [t] denote the greatest integer less than or equal to t. If the function f(x) = cases b2 ( 2 [ 2( x + x) x ] ), & x < 0 \ x - 12 2xx3, & x > 0 \ a, & x = 0 cases is continuous at x = 0, then a2 + b2 is equal to :

1. 12
2. 58
3. 34
4. 916

Let X = \x N : 1 x 19\ and for some a, b R, Y = \ax + b : x X\. If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of b is

1. 20
2. 100
3. 80
4. 60

The largest value of n, for which 40n divides 60!, is

1. 14
2. 13
3. 11
4. 12

Let f( ) denote the area of the region in the first quadrant bounded by x = 0, x = 1, y2 = x and y = | x - 5| - |1 - x| + x2. Then (f(0) + f(1)) is equal to

1. 12
2. 14
3. 9
4. 7

Let the image of parabola x2 = 4y, in the line x - y = 1 be (y + a)2 = b(x - c), a, b, c N. Then a + b + c is equal to

1. 12
2. 8
3. 6
4. 4

Let the angles made with the positive x-axis by two straight lines drawn from the point P(2, 3) and meeting the line x + y = 6 at a distance 23 from the point P be 1 and 2. Then the value of ( 1 + 2) is:

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

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

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

Let f(x) = 7x10 + 9x8(1 + x2 + 2x9)2 dx, x > 0, x 0 f(x) = 0 and f(1) = 14. If A = bmatrix 0 & 0 & 1 \ 14 & f'(1) & 1 \ 2 & 4 & 1 bmatrix and B = adj(adj A) be such that |B| = 81, then 2 is equal to

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

Let the length of the latus rectum of an ellipse x2a2 + y2b2 = 1, (a > b), be 30. If its eccentricity is the maximum value of the function f(t) = - 34 + 2t - t2, then (a2 + b2) is equal to

1. 276
2. 516
3. 256
4. 496

Let f be a function such that 3f(x) + 2f ( m19x ) = 5x, x 0, where m = i=19 (i)2. Then f(5) - f(2) is equal to

1. 36
2. 9
3. -9
4. 18

Let a = 2 i - j - k, b = i + 3 j - k and c = 2 i + j + 3 k. Let v = a + b, R, be the vector in the plane of the vectors a and b, such that the length of its projection on the vector c is 1 14. Then | v| is equal to

1. 352
2. 13
3. 212
4. 7

Let a = 2 i - 5 j + 5 k and b = i - j + 3 k. If c is a vector such that 2( a c) + 3( b c) = 0 and ( a - b) c = -97, then | c k|2 is equal to

1. 193
2. 205
3. 218
4. 233

( 13 + 47 ) + ( 132 + 13 47 + 4272 ) + ( 133 + 132 47 + 13 4272 + 4373 ) + up to infinite terms, is equal to

1. 74
2. 43
3. 65
4. 52

Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of choosing an ordered pair (A, B) from the set P(S) P(S) such that A B = . If the probability of the event E is 3p2q, where p, q N, then p + q is equal to .

Let z = (1 + i)(1 + 2i)(1 + 3i) (1 + ni), where i = -1. If |z|2 = 44200, then n is equal to .

The number of elements in the set \x [0, 180 ] : (x + 100 ) = (x + 50 ) x (x - 50 )\ is .

Let (h, k) lie on the circle C : x2 + y2 = 4 and the point (2h + 1, 3k + 2) lie on an ellipse with eccentricity e. Then the value of 5e2 is equal to .

If f(x) satisfies the relation f(x) = ex + 01 (y + xex) f(y) dy, then e + f(0) is equal to .