JEE Main 2026 (Online) 22nd January Evening Shift

In an open organ pipe 3 and 6 are 3rd and 6th harmonic frequencies, respectively. If 6 - 3 = 2200 Hz then length of the pipe is mm. (Take velocity of sound in air is 330 m/s.)

1. 200
2. 225
3. 275
4. 250

Using a simple pendulum experiment g is determined by measuring its time period T. Which of the following plots represent the correct relation between the pendulum length L and time period T ?

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

A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses m and 2m are moving in opposite directions with same speed of v and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency . The ratio of v and is : [figure]

1. 33
2. 2 88
3. 32
4. 66

A laser beam has intensity of 4.0 1014 W/m2. The amplitude of magnetic field associated with beam is T. (Take 0 = 8.85 10-12 C2/Nm2 and c = 3 108 m/s)

1. 1.83
2. 2.0
3. 5.5
4. 18.3

Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The electric potential (V) and the electric field ( E) at the center O of the pentagon due to these five positive charges are : [figure]

1. V = 5q4 0 r and E = 5 3q8 0 r2 r
2. V = 5q4 0 r and E = 0
3. V = 0 and E = 0
4. V = 5q4 0 r and E = 5q4 0 r2 r

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 false
4. Both Statement I and Statement II are true

When a part of a straight capillary tube is placed vertically in a liquid, the liquid rises up to certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1% each, then the height of the liquid in the tube will change by %.

1. +3
2. +1
3. -1
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 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

Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is 32 1018 /s then collision frequency in gas A is /s.

1. 8 1018
2. 2 1018
3. 32 1018
4. 4 1018

In parallax method for the determination of focal length of a concave mirror, the object should always be placed:

1. between the focus (F) and the centre of curvature (C) of the mirror ONLY
2. between the pole (P) and the focus (F) of the concave mirror ONLY
3. at any point beyond the focus (F) of the mirror
4. beyond the centre of the curvature (C) of the mirror ONLY

The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is 4/3. The wavelength of the same light when it is passing through a transparent medium having refractive index of 3/2 is nm.

1. 540
2. 840
3. 480
4. 380

The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly nm.

1. 1784
2. 1875
3. 1217
4. 1550

An electric power line having total resistance of 2 , delivers 1 kW of power at 250 V. The percentage efficiency of transmission line is .

1. 96.9
2. 92.5
3. 86.5
4. 100

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :

1. 1 : 32/3
2. 32/3 : 1
3. 1 : 31/3
4. 1 : 22/3

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 correct truth table for the given input data of the following logic gate is : [figure]

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

If , E and t represent the free space permittivity, electric field and time respectively, then the unit of Et will be :

1. Am
2. A/m
3. A/m2
4. Am2

Which of the following are true for a single slit diffraction?

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

Figure shows the circuit that contains three resistances (9 each) and two inductors (4 mH each). The reading of ammeter at the moment switch K is turned ON, is A. [figure]

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

Light is incident on a metallic plate having work function 110 10-20 J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is rad/s. (h = 6.63 10-34 J s)

1. 1.04 1013
2. 1.66 1016
3. 1.66 1015
4. 1.04 1016

An insulated cylinder of volume 60 cm3 is filled with a gas at 27 and 2 atmospheric pressure. Then the gas is compressed making the final volume as 20 cm3 while allowing the temperature to rise to 77 . The final pressure is atmospheric pressure.

A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by 30 from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop is mm. (Take = 227)

A capacitor P with capacitance 10 10-6 F is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance 20 10-6 F. The charge on capacitor Q when equilibrium is established will be 10-5 C (assume capacitor Q does not have any charge initially), the value of is .

A cylindrical conductor of length 2 m and area of cross-section 0.2 mm2 carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is 10-3 m2/V s. The value of is : (electron concentration = 5 1028 /m3 and electron charge = 1.6 10-19 C)

Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius r = 0.1 m. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended through a height of 3.6 m is m/s. (Assume string does not slip and g = 10 m/s2)

Among H2S, H2O, NF3, NH3 and CHCl3, identify the molecule (X) with lowest dipole moment value. The number of lone pairs of electrons present on the central atom of the molecule (X) is :

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

[figure] The final product [B] is :

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

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

Consider the following reduction processes : Al3+ + 3e- Al(s), E0 = -1.66 V Fe3+ + e- Fe2+, E0 = +0.77 V Co3+ + e- Co2+, E0 = +1.81 V Cr3+ + 3e- Cr(s), E0 = -0.74 V The tendency to act as reducing agent decreases in the order :

1. Al > Fe2+ > Cr > Co2+
2. Al > Cr > Co2+ > Fe2+
3. Cr > Fe2+ > Al > Co2+
4. Al > Cr > Fe2+ > Co2+

The compound A, C8H8O2 reacts with acetophenone to form a single product via cross-Aldol condensation. The compound A on reaction with conc. NaOH forms a substituted benzyl alcohol as one of the two products. The compound A is :

1. 2-hydroxy acetophenone
2. 4-hydroxy benzaldehyde
3. 4-methyl benzoic acid
4. 4-methoxy benzaldehyde

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

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

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

Correct statements regarding Arrhenius equation among the following are : Choose the correct answer from the options given below :

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

Consider the following reaction : [figure] The product Y formed is :

1. 2-methylhex-3-yne
2. 5-methylhex-2-yne
3. Isopropylbut-1-yne
4. 2-methylhex-2-yne

[Ni(PPh3)2Cl2] is a paramagnetic complex. Identify the INCORRECT statements about this complex. Choose the correct answer from the options given below :

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

The dibromo compound [P] (molecular formula: C9H10Br2) when heated with excess sodamide followed by treatment with dilute HCl gives [Q]. On warming [Q] with mercuric sulphate and dilute sulphuric acid yields [R] which gives positive Iodoform test but negative Tollens' test. The compound [P] is :

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

Which of the following mixture gives a buffer solution with pH = 9.25 ? Given : pKb (NH4OH) = 4.75

1. 0.5 M NH4OH (0.2 L) + 0.2 M HCl (0.5 L)
2. 0.2 M NH4OH (0.5 L) + 0.1 M HCl (0.5 L)
3. 0.2 M NH4OH (0.4 L) + 0.1 M HCl (1 L)
4. 0.4 M NH4OH (1 L) + 0.1 M HCl (1 L)

When 1 g of compound (X) is subjected to Kjeldahl's method for estimation of nitrogen, 15 mL 1 M H2SO4 was neutralized by ammonia evolved. The percentage of nitrogen in compound (X) is :

1. 0.21
2. 21
3. 42
4. 0.42

The energy of first (lowest) Balmer line of H atom is x J. The energy (in J) of second Balmer line of H atom is :

1. x1.35
2. 1.35x
3. x2
4. 2x

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

At T(K), 100 g of 98\% H2SO4 (w/w) aqueous solution is mixed with 100 g of 49\% H2SO4 (w/w) aqueous solution. What is the mole fraction of H2SO4 in the resultant solution? (Given : Atomic mass H = 1 u; S = 32 u; O = 16 u). (Assume that temperature after mixing remains constant)

1. 0.9
2. 0.663
3. 0.1
4. 0.337

3,3-Dimethyl-2-butanol cannot be prepared by : Choose the correct answer from the options given below :

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

A + 2B AB2 36.0 g of 'A' (Molar mass : 60 g mol-1) and 56.0 g of 'B' (Molar mass : 80 g mol-1) are allowed to react. Which of the following statements are correct ? Choose the correct answer from the options given below :

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

The IUPAC name of the following compound is : [figure]

1. 2-bromo-5-methylhexylpropanoate
2. n-propyl-1-bromo-4-methylhexanoate
3. n-propyl-2-bromo-5-methylheptanoate
4. 2-bromo-5-methylpropanoate

Consider the following electrochemical cell : Pt | O2(g)(1 bar) | HCl(aq) || M2+(aq, 1.0 M) | M(s) The pH above which, oxygen gas would start to evolve at anode is (nearest integer). [Given : . arrayl E M2+/M = 0.994 V \ E O2/H2O = 1.23 V array \ standard reduction potential and RTF(2.303) = 0.059 V at the given condition]

The mass of benzanilide obtained from the benzoylation reaction of 5.8 g of aniline, if yield of product is 82\%, is g (nearest integer). (Given molar mass in g mol-1 H : 1, C : 12, N : 14, O : 16)

Among the following oxides of 3d elements, the number of mixed oxides are . Ti2O3, V2O4, Cr2O3, Mn3O4, Fe3O4, Fe2O3, Co3O4

If the enthalpy of sublimation of Li is 155 kJ mol-1, enthalpy of dissociation of F2 is 150 kJ mol-1, ionization enthalpy of Li is 520 kJ mol-1, electron gain enthalpy of F is -313 kJ mol-1, standard enthalpy of formation of LiF is -594 kJ mol-1. The magnitude of lattice enthalpy of LiF is kJ mol-1. (Nearest Integer)

Consider A k1 B and C k2 D are two reactions. If the rate constant (k1) of the A B reaction can be expressed by the following equation 10 k = 14.34 - 1.5 104T/K and activation energy of C D reaction (Ea2) is 15th of the A B reaction (Ea1), then the value of (Ea2) is kJ mol-1. (Nearest Integer)

Let f(x) = [x]2 - [x + 3] - 3, x R, where [.] is the greatest integer function. Then

1. f(x) = 0 for finitely many values of x
2. f(x) < 0 only for x [-1, 3)
3. 02 f(x) dx = -6
4. f(x) > 0 only for x [4, )

Let the locus of the mid-point of the chord through the origin O of the parabola y2 = 4x be the curve S. Let P be any point on S. Then the locus of the point, which internally divides OP in the ratio 3 : 1, is :

1. 2x2 = 3y
2. 2y2 = 3x
3. 3y2 = 2x
4. 3x2 = 2y

Let n be the number obtained on rolling a fair die. If the probability that the system x - ny + z = 6 x + (n - 2)y + (n + 1)z = 8 (n - 1)y + z = 1 has a unique solution is k6, then the sum of k and all possible values of n is :

1. 22
2. 20
3. 24
4. 21

Let the domain of the function f(x) = 3 5 (7 - 2 (x2 - 10x + 85 ) ) + -1 ( | 3x - 717 - x | ) be ( , ]. Then + is equal to :

1. 12
2. 8
3. 10
4. 9

Let S and S′ be the foci of the ellipse x225 + y29 = 1 and P( , ) be a point on the ellipse in the first quadrant. If (SP)2 + (S'P)2 - SP S'P = 37, then 2 + 2 is equal to :

1. 13
2. 15
3. 11
4. 17

If x 0 e(a - 1)x + 2 bx + (c - 2)e-xx x - e(1 + x) = 2, then a2 + b2 + c2 is equal to :

1. 3
2. 5
3. 9
4. 7

Let a = 2 i - j + k and b = j + 2 k, Z be two vectors. Let c = a b and d be a vector of magnitude 2 in yz-plane. If | c| = 53, then the maximum possible value of ( c d)2 is equal to :

1. 52
2. 26
3. 104
4. 208

Let [ ] denote the greatest integer function, and let f(x) = \ 2x, x2 \. Let S = \x (-2, 2) : the function g(x) = |x| [x2 ] is discontinuous at x\. Then x S f(x) equals

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

Among the statements (S1) : If A(5, -1) and B(-2, 3) are two vertices of a triangle, whose orthocentre is (0, 0), then its third vertex is (-4, -7) and (S2) : If positive numbers 2a, b, c are three consecutive terms of an A.P., then the lines ax + by + c = 0 are concurrent at (2, -2),

1. both are incorrect
2. only (S2) is correct
3. both are correct
4. only (S1) is correct

Let , be the roots of the quadratic equation 12x2 - 20x + 3 = 0, Z. If 12 | - | 32, then the sum of all possible values of is :

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

The number of elements in the relation R = \(x, y) : 4x2 + y2 < 52, x, y Z \ is

1. 86
2. 67
3. 89
4. 77

Let f and g be functions satisfying f(x + y) = f(x)f(y), f(1) = 7 and g(x + y) = g(xy), g(1) = 1, for all x, y N. If x = 1n ( f(x)g(x) ) = 19607, then n is equal to :

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

If X = bmatrix x \ y \ z bmatrix is a solution of the system of equations AX = B, where adj A = bmatrix 4 & 2 & 2 \ -5 & 0 & 5 \ 1 & -2 & 3 bmatrix and B = bmatrix 4 \ 0 \ 2 bmatrix, then |x + y + z| is equal to :

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

The area of the region A = \(x, y) : 4x2 + y2 8 and y2 4x\ is:

1. + 23
2. 2 + 2
3. + 4
4. 2 + 13

Let L be the line x+12 = y+13 = z+36 and let S be the set of all points (a, b, c) on L, whose distance from the line x+12 = y+13 = z-90 along the line L is 7. Then (a, b, c) S (a + b + c) is equal to :

1. 28
2. 6
3. 40
4. 34

If y = y(x) satisfies the differential equation 16 ( 9x + x x ) (4 + 9 + x ) y dy = (1 + 2 y) dx, x > 0 and y(256) = 2, y(49) = , then 2 is equal to :

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

Let P(10, 2 15) be a point on the hyperbola x2a2 - y2b2 = 1, whose foci are S and S'. If the length of its latus rectum is 8, then the square of the area of PSS' is equal to :

1. 4200
2. 1462
3. 900
4. 2700

If the mean deviation about the median of the numbers k, 2k, 3k, , 1000k is 500, then k2 is equal to :

1. 1
2. 16
3. 9
4. 4

Let S = \z C : 4z2 + z = 0\. Then z S |z|2 is equal to:

1. 564
2. 116
3. 764
4. 316

Let Cr denote the coefficient of xr in the binomial expansion of (1 + x)n, n N, 0 r n. If Pn = C0 - C1 + 223C2 - 234C3 + + (-2)nn+1Cn, then the value of n=125 1P2n equals

1. 675
2. 580
3. 525
4. 650

Suppose a, b, c are in A.P. and a2, 2b2, c2 are in G.P. If a < b < c and a + b + c = 1, then 9(a2 + b2 + c2) is equal to .

Let a vector a = 2 i - j + k, > 0, make an obtuse angle with the vector b = - 2 i + 4 2 j + 4 2 k and an angle , 6 < < 2, with the positive z-axis. If the set of all possible values of is ( , ) - \ \, then + + is equal to .

Let [.] be the greatest integer function. If = 064 (x1/3 - [x1/3] )dx, then 1 0 ( 2 6 + 6 )d is equal to .

Let ( + ) = - 110 and ( - ) = 38, where 0 < < 3 and 0 < < 4. If 2 = 3(1 - r 5) 11(s + 5), r, s N, then r + s is equal to .

Let S be the set of the first 11 natural numbers. Then the number of elements in A = \B S : n(B) 2 and the product of all elements of B is even\ is .