JEE Main 2026 (Online) 28th January Evening Shift

Which one of the following is not a measurable quantity?

1. Resistance
2. Voltage difference
3. Displacement current
4. Voltage

The mean free path of a molecule of diameter 5 10-10 m at the temperature 41 C and pressure 1.38 105 Pa, is given as m. (Given kB = 1.38 10-23 J/K).

1. 2 2 10-10
2. 10 2 10-8
3. 2 2 10-8
4. 2 10-8

The time period of a simple harmonic oscillator is T = 2 mk. Measured value of mass (m) of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant (k) is %.

1. 3.43
2. 7.60
3. 3.35
4. 6.76

A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is: Choose the correct answer from the options given below:

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

The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1%, respectively then the speed of the wave is changed approximately to m/s.

1. 398
2. 402
3. 401
4. 399

When the position vector r = x i + y j + z k changes sign as - r, which one of the following vector will not flip under sign change?

1. Velocity
2. Linear momentum
3. Acceleration
4. Angular momentum

A small block of mass m slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration a0. The angle between the inclined plane and ground is and its base length is L. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is . [figure]

1. 2Lg - a0
2. 4Lg 2 - a0(1 + 2 )
3. 2Lg 2 - a0(1 + 2 )
4. 4Lg 2 - a0

A plane electromagnetic wave is moving in free space with velocity c = 3 108 m/s and its electric field is given as E = 54 (kz - t) j V/m, where j is the unit vector along y-axis. The magnetic field vector B of the wave is :

1. -1.8 10-7 (kz - t) i T
2. +1.8 10-7 (kz - t) i T
3. 1.4 10-7 (kz - t) k T
4. 1.4 10-7 (kz - t) i T

Two p-n junction diodes D1 and D2 are connected as shown in figure. A and B are input signals and C is the output. The given circuit will function as a . [figure]

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

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

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

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

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

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

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

A biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in figure. When an object is placed on the left side of lens at a distance of 30 cm from the biconvex lens, the magnification of the image will be : [figure]

1. −2
2. −2.5
3. +2.5
4. +2

A nucleus has mass number and radius R . Another nucleus has mass number and radius R . If = 8 then R /R is :

1. 1
2. 2
3. 8
4. 0.5

A particle starts moving from time t = 0 and its coordinate is given as x(t) = 4t3 - 3t Choose the correct answer from the options given below :

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

For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies.

1. n 2
2. 2 < n < 2
3. 1 < n < 2
4. 2 < n < 2 2

As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is : [figure]

1. 20
2. 5
3. 30
4. 27

In an experiment, a set of readings are obtained as follows: 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is mm.

1. 0.01
2. 0.05
3. 0.001
4. 0.1

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is . (Given : h = 6.63 10-34 J s and c = 3 108 m/s)

1. 10 1015
2. 5 1016
3. 5 1015
4. 2 1016

A Wheatstone bridge is initially at room temperature and all arms of the bridge have same value of resistances (R1 = R2 = R3 = R4). When R3 resistance is heated to some temperature, its resistance value has gone up by 10%. The potential difference (Va - Vb) (after R3 is heated) is V. [figure]

1. 1.05
2. 0.95
3. 0
4. 2

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is . ( = 3.14)

A thermodynamic system is taken through the cyclic process ABC as shown in the figure. The total work done by the system during the cycle ABC is J. [figure]

A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young's double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum, where the bright fringes due to both the wavelengths coincide, is 10-5 m.

A flywheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is J. (g = 10 m/s2)

Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz then original frequency of tuning fork A is Hz.

A student performed analysis of an aliphatic organic compound 'X' which on analysis gave C = 61.01%, H = 15.25%, N = 23.74%. This compound, on treatment with HNO2/H2O, produced another compound 'Y' which did not contain any nitrogen atom. However, the compound 'Y' upon controlled oxidation produced another compound 'Z' that responded to iodoform test. The structure of 'X' is :

1. CH3-CH2CH(NH2)-CH3
2. CH3CH2CH2NH2
3. Ph-CH(CH3)-NH2
4. [figure]

The plot of 10 K vs 1T gives a straight line. The intercept and slope respectively are (where K is the equilibrium constant).

1. - S R2.303, H R2.303
2. - H 2.303R, S 2.303R
3. S 2.303R, - H 2.303R
4. 2.303R H , 2.303R S

Total number of alkali-insoluble solid sulphonamides obtained by reaction of given amines with Hinsberg's reagent is . Aniline, N-Methylaniline, Methanamine, N,N-Dimethylmethanamine, N-Methylmethanamine, Phenylmethanamine, N-Propylaniline, N-Phenylaniline, N,N-Dimethylaniline, Allylamine, Isopropylamine

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

Match List-I with List-II according to shape. Choose the correct answer from the options given below :

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

Consider the following reactions Na2B4O7 2X + Y CuSO4 + Y Non-luminous flame Z + SO3 2Z + 2X + Carbon Luminous flame 2Q + Na2B4O7 + CO The oxidation states of Cu in Z and Q, respectively are :

1. +2 and +1
2. +1 and +1
3. +1 and +2
4. +2 and +2

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

Structures of four disaccharides are given below. Among the given disaccharides, the non-reducing sugar is :

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

Consider the following statements about manganate and permanganate ions. Identify the correct statements. Choose the correct answer from the options given below :

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

The wavelength of photon 'A' is 400 nm. The frequency of photon 'B' is 1016 s-1. The wave number of photon 'C' is 104 cm-1. The correct order of energy of these photons is :

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

The reactions which produce alcohol as the product are : Choose the correct answer from the options given below :

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

For the given reaction; CaCO3 + 2HCl CaCl2 + H2O + CO2 If 90 g CaCO3 is added to 300 mL of HCl which contains 38.55% HCl by mass and has density 1.13 g mL-1, then which of the following option is correct? Given molar mass of H, Cl, Ca and O are 1, 35.5, 40 and 16 g mol-1 respectively.

1. 64.97 g of HCl remains unreacted
2. 60.32 g of HCl remains unreacted
3. 32.85 g of CaCO3 remains unreacted
4. 97.30 g of HCl reacted

Consider the elements N, P, O, S, Cl and F. The number of valence electrons present in the elements with most and least metallic character from the above list is respectively.

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

Observe the following equilibrium in a 1 L flask. A(g) B(g) At T(K), the equilibrium concentrations of A and B are 0.5 M and 0.375 M respectively. 0.1 moles of A is added into the flask and heated to T(K) to establish the equilibrium again. The new equilibrium concentrations (in M) of A and B are respectively

1. 0.742, 0.557
2. 0.367, 0.275
3. 0.53, 0.4
4. 0.557, 0.418

The correct increasing order of spin-only magnetic moment values of the complex ions [MnBr4]2- (A), [Cu(H2O)6]2+ (B), [Ni(CN)4]2- (C) and [Ni(H2O)6]2+ (D) is :

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

The correct order of acidic strength of the major products formed in the given reactions, is : Choose the correct answer from the options given below :

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

Consider the following aqueous solutions. I. 2.2 g glucose in 125 mL of solution. II. 1.9 g calcium chloride in 250 mL of solution. III. 9.0 g urea in 500 mL of solution. IV. 20.5 g aluminium sulphate in 750 mL of solution. The correct increasing order of boiling point of these solutions will be : [Given : Molar mass in g mol-1 : H = 1, C = 12, N = 14, O = 16, Cl = 35.5, Ca = 40, Al = 27 and S = 32]

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

A student has been given 0.314 g of an organic compound and asked to estimate sulphur. During the experiment, the student has obtained 0.4813 g of barium sulphate. The percentage of sulphur present in the compound is . (Given molar mass in g mol-1 S : 32, BaSO4 : 233)

1. 63.15%
2. 21.05%
3. 48.24%
4. 42.10%

Which of the following reactions is NOT correctly represented?

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

Identify the correct statements : The presence of -NO2 group in benzene ring Choose the correct answer from the options given below :

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

The cyclic cations having the same number of hyperconjugation are : Choose the correct answer from the options given below :

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

The number of isoelectronic species among Sc3+, Cr2+, Mn3+, Co3+ and Fe3+ is ‘n’. If ‘n’ moles of AgCl is formed during the reaction of complex with formula CoCl3(en)2NH3 with excess of AgNO3 solution, then the number of electrons present in the t2g orbital of the complex is .

A volume of x mL of 5 M NaHCO3 solution was mixed with 10 mL of 2 M H2CO3 solution to make an electrolytic buffer. If the same buffer was used in the following electrochemical cell to record a cell potential of 235.3 mV, then the value of x = mL (nearest integer). Sn(s) | Sn(OH)62- (0.5 M) | HSnO2- (0.05 M) | OH- | Bi2O3(s) | Bi(s) Consider up to one place of decimal for intermediate calculations [ arrayllGiven: & E Sn(OH)62-|HSnO2- = -0.9 V \ & E Bi2O3|Bi = -0.44 V \ & pKa(H2CO3) = 6.11 \ & 2.303RTF = 0.059 V \ & Antilog (1.29) = 19.5 array ]

For strong electrolyte m increases slowly with dilution and can be represented by the equation m = m - Ac1/2 Molar conductivity values of the solutions of strong electrolyte AB at 18°C are given below : array|l|c|c|c|c| c [mol L-1] & 0.04 & 0.09 & 0.16 & 0.25 \ m [S cm2 mol-1] & 96.1 & 95.7 & 95.3 & 94.9 \ array The value of constant A based on the above data [in S cm2 mol-1/(mol/L)1/2] unit is .

Two positively charged particles m1 and m2 have been accelerated across the same potential difference of 200 kV as shown below. [figure] [Given mass of m1 = 1 amu and m2 = 4 amu] The de Broglie wavelength of m1 will be x times of m2. The value of x is (nearest integer)

A → B (first reaction) C → D (second reaction) Consider the above two first-order reactions. The rate constant for first reaction at 500 K is double of the same at 300 K. At 500 K, 50% of the reaction becomes complete in 2 hours. The activation energy of the second reaction is half of that of first reaction. If the rate constant at 500 K of the second reaction becomes double of the rate constant of first reaction at the same temperature; then rate constant for the second reaction at 300 K is 10-1 hour-1 (nearest integer).

Let the circle x2 + y2 = 4 intersect x-axis at the points A(a, 0), a > 0 and B(b, 0). Let P(2 , 2 ), 0 < < 2 and Q(2 , 2 ) be two points such that ( - ) = 2. Then the point of intersection of AQ and BP lies on :

1. x2 + y2 - 4x - 4 = 0
2. x2 + y2 - 4x - 4y = 0
3. x2 + y2 - 4x - 4y - 4 = 0
4. x2 + y2 - 4y - 4 = 0

Let y = y(x) be the solution of the differential equation x dydx - y = x2 x, x (0, ). If y ( 2 ) = 2, then 6y ( 6 ) - 8y ( 4 ) is equal to :

1. -3
2. 3
3. -

Let Q(a, b, c) be the image of the point P(3, 2, 1) in the line x - 11 = y2 = z - 11. Then the distance of Q from the line x - 93 = y - 92 = z - 5-2 is

1. 8
2. 7
3. 6
4. 5

Considering the principal values of inverse trigonometric functions, the value of the expression (2 -1 ( 2 13 ) - 2 -1 ( 3 10 ) ) is equal to :

1. 3356
2. - 3356
3. - 1663
4. 1663

Let the arithmetic mean of 1a and 1b be 516, a > 2. If is such that a, 4, , b are in A.P., then the equation x2 - ax + 2( - 2b) = 0 has :

1. one root in (1, 4) and another in (-2, 0)
2. one root in (0, 2) and another in (-4, -2)
3. both roots in the interval (-2, 0)
4. complex roots of magnitude less than 2

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

Let P be a point in the plane of the vectors AB = 3 i + j - k and AC = i - j + 3 k such that P is equidistant from the lines AB and AC. If | AP| = 52, then the area of the triangle ABP is :

1. 32
2. 304
3. 264
4. 2

Let f(x) = dxx2/3 + 2x1/2, be such that f(0) = -26 + 24 e(2). If f(1) = a + b e(3), where a, b Z, then a + b is equal to :

1. -5
2. -11
3. -18
4. -26

An ellipse has its center at (1, -2), one focus at (3, -2) and one vertex at (5, -2). Then the length of its latus rectum is :

1. 6
2. 6 3
3. 16 3
4. 4 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 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

Let A = \z C : |z - 2| 4\ and B = \z C : |z - 2| + |z + 2| = 5\. Then the \|z1 - z2| : z1 A and z2 B\ is :

1. 172
2. 8
3. 9
4. 152

Let A be the focus of the parabola y2 = 8x. Let the line y = mx + c intersect the parabola at two distinct points B and C. If the centroid of the triangle ABC is ( 73, 43 ), then (BC)2 is equal to :

1. 89
2. 80
3. 32
4. 41

Let f(x) = 0 ( x - x ( 2 ) (x - 1)1 + x ( 2 )(x - 1) ), x R. Consider the following two statements : (I) f(x) is discontinuous at x = 1. (II) f(x) is continuous at x = -1. Then,

1. Neither (I) nor (II) is True
2. Only (II) is True
3. Only (I) is True
4. Both (I) and (II) are True

6326 + 10 1325 + 10 2324 + 10 22323 + + 10 2243 is equal to :

1. 226
2. 325
3. 326
4. 225

Let [.] denote the greatest integer function. Then - 2 2 ( 12(3 + [x])3 + [ x] + [ x] ) dx is equal to :

1. 12 + 5
2. 11 + 2
3. 15 + 4
4. 13 + 1

Let the ellipse E : x2144 + y2169 = 1 and the hyperbola H : x216 - y2 2 = -1 have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of H, then the value of 24(e + L) is :

1. 296
2. 126
3. 67
4. 148

The probability distribution of a random variable X is given below : array|c|c|c|c|c|c|c|c|c| X & 4k & 307k & 327k & 347k & 367k & 387k & 407k & 6k \ P(X) & 215 & 115 & 215 & 15 & 115 & 215 & 15 & 115 \ array If E(X) = 26315, then P(X < 20) is equal to :

1. 35
2. 1415
3. 815
4. 1115

Let P1 : y = 4x2 and P2 : y = x2 + 27 be two parabolas. If the area of the bounded region enclosed between P1 and P2 is six times the area of the bounded region enclosed between the line y = x, > 0 and P1, then is equal to :

1. 12
2. 15
3. 8
4. 6

The sum of all the elements in the range of f(x) = Sgn( x) + Sgn( x) + Sgn( x) + Sgn( x), x n 2, n Z, where Sgn(t) = cases 1, & if t > 0 \ -1, & if t < 0 cases is :

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

The sum of the coefficients of x499 and x500 in (1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + + x1000 is :

1. 1002C501
2. 1001C501
3. 1000C501
4. 1002C500

If r=125 ( rr4 + r2 + 1 ) = pq, where p and q are positive integers such that (p, q) = 1, then p + q is equal to .

Three persons enter in a lift at the ground floor. The lift will go up to 10th floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to .

If the distance of the point P(43, , ), < 0, from the line r = 4 i - k + (2 i + 3 k), R along a line with direction ratios 3, -1, 0 is 13 10, then 2 + 2 is equal to

Let A = bmatrix 3 & -4 \ 1 & -1 bmatrix and B be two matrices such that A100 = 100B + I. Then the sum of all the elements of B100 is

Let f be a differentiable function satisfying f(x) = 1 - 2x + 0x e(x-t) f(t) dt, x R and let g(x) = 0x (f(t) + 2)15(t - 4)6(t + 12)17 dt, x R. If p and q are respectively the points of local minima and local maxima of g, then the value of |p + q| is equal to .