JEE Main 2026 April 06, Shift 2 Question Paper with Solutions

All 74 questions from the JEE Main 2026 (April 06, Shift 2) shift — Physics (24), Chemistry (25) and Mathematics (25) — each with the correct answer (answer key) and a step-by-step solution. Read it free online, or attempt the full paper as a timed mock test.

Physics PYQs 2026 Chemistry PYQs 2026 Mathematics PYQs 2026

Physics24 questions

Q26Single correctUnits and Measurements

The percentage error in the calculated volume of a sphere, if there is

2

% error in its diameter measurement, is _____ .

(A)

1

(B)

2

(C)

6

(D)

8

Q27Single correctUnits and Measurements

Match List - I with List - II.

List - I	List - II
A. Boltzmann constant	I. $[M^{- 1} L^{3} T^{- 2}]$
B. Stefan's constant	II. $[M L^{2} T^{- 1}]$
C. Planck's constant	III. $[M L^{2} T^{- 2} K^{- 1}]$
D. Gravitational constant	IV. $[M L^{0} T^{- 3} K^{- 4}]$

(A)

A-I, B-II, C-III, D-IV

(B)

A-IV, B-III, C-II, D-I

(C)

A-III, B-IV, C-II, D-I

(D)

A-II, B-I, C-IV, D-III

Q28Single correctRotational Motion

A solid sphere (A) of mass

5 m

and a spherical shell (B) of mass m, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B, they start rolling without slipping with an acceleration of

a_{A}

and

a_{B}

, respectively. The ratio of

a_{A}

and

a_{B}

is _____ .

(A)

5 : 21

(B)

6 : 10

(C)

21 : 25

(D)

1 : 5

Q29Single correctWork, Energy and Power

A body of mass

1

kg moves along a straight line with a velocity

v = 2 x^{2}

. The work done by the body during displacement from

x = 0

5

m is ___ J.

(A)

0

(B)

250

(C)

1250

(D)

1000

Q30Single correctThermodynamics

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same P, V, T. Heating is started from left side until pressure changes to

27 P /8

. If initial volume of each compartment was

9

litres then the final volume in right-hand side compartment is _____ litres. (for this ideal gas

C_{P} / C_{V} = 1.5

)

(A)

3

(B)

4

(C)

14

(D)

9

Q31Single correctElectromagnetic Waves

For an electromagnetic wave propagating through vacuum,

k, E

and

ω

represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by :

(A)

\frac{E \times k}{ω}

(B)

\frac{k \times E}{ω}

(C)

ω (E \times k)

(D)

ω (k \times E)

Q32Single correctKinematics

Two identical bodies A and B of equal masses have initial velocities

v_{1} = 4 \hat{i} m/s

and

v_{2} = 4 \hat{j} m/s

respectively. The body A has acceleration

a_{1} = 6 \hat{i} + 6 \hat{j} m/s^{2}

while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in ____ path.

(A)

circular

(B)

parabolic

(C)

straight line

(D)

elliptical

Q33Single correctProperties of Solids and Liquids

Figure represents the extension (

Δ l

) of a wire of length 1 meter, suspended from the ceiling of the room at one end with a load W connected to the other end. If the cross-sectional area of the wire is

1 0^{- 5} m^{2}

then the Young's modulus of the wire is ______

N/m^{2}

Graph showing the extension Δl (×10⁻⁴ m) of the wire on the vertical axis versus the load W (N) on the horizontal axis as a straight line.

(A)

1.0 \times 1 0^{11}

(B)

2.0 \times 1 0^{10}

(C)

1.0 \times 1 0^{10}

(D)

2.0 \times 1 0^{11}

Q34Single correctProperties of Solids and Liquids

A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 d

m^{3}

(dm : decimeter) The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is ______ cm.

(A)

1202

(B)

1402

(C)

1403

(D)

1203

Q35Single correctKinetic Theory of Gases

If 2 mole of an ideal monoatomic gas at temperature

T

, is mixed with 6 mole of another ideal monoatomic gas at temperature

2 T

then the temperature of mixture is :

(A)

\frac{5}{2} T

(B)

\frac{5}{4} T

(C)

\frac{7}{2} T

(D)

\frac{7}{4} T

Q36Single correctOscillations and Waves

A spring stretches by 2 mm when it is loaded with a mass of 200 g . From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maxmimum energy in the spring are ______ Hz and ______ J, respectively. (Take g = 10 m/

s^{2}

)

(A)

\frac{5 50}{π}

and

8 \times 1 0^{- 3}

(B)

\frac{5 50}{π}

and 8

(C)

1050

and

2 \times 1 0^{- 3}

(D)

\frac{5 50}{π}

and

16 \times 1 0^{- 3}

Q37Single correctElectrostatics

The electric potential as a function of x, y is given by

V = 5 (x^{2} - y^{2})

V. The electric field at a point (2,3) m is ______ V/m.

(A)

(- 20 \hat{i} + 30 \hat{j})

(B)

(20 \hat{i} - 30 \hat{j})

(C)

(20 \hat{i} + 45 \hat{j})

(D)

(- 4 \hat{i} + 6 \hat{j})

Q38Single correctMagnetic Effects of Current and Magnetism

A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm. The magnetic field at the mid point between the two wires is ______

μ

(\frac{μ _{0}}{4 π} = 1 0^{- 7} N/A^{2})

(A)

(B)

300

(C)

150

(D)

0.0

Q39Single correctElectromagnetic Induction and Alternating Currents

A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as

B = 0.4 sin (300 t)

Tesla. The normal to the plane of loop makes an angle of

6 0^{\circ}

with the field. The maximum induced emf produced in the loop is ______ mV.

(A)

(B)

(C)

(D)

Q40Single correctElectrostatics

A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is

α \times 1 0^{- 7}

J. The value of

α

is ______. (combined capacitance of spheres is 200 pF)

(A)

(B)

\frac{5}{2}

(C)

\frac{7}{2}

(D)

\frac{9}{2}

Q41Single correctAtoms and Nuclei

The energy released if hydrogen atoms are combined to form

_{2}^{4} He

is ____ MeV. (Take binding energies per nucleon of

_{1}^{2} H

and

_{2}^{4} He

as 1.1 MeV and 7.2 MeV, respectively)

(A)

6.1

(B)

24.4

(C)

26.6

(D)

Q42Single correctOptics

Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is ______.

(A)

1.5

(B)

3

(C)

2

(D)

1.65

Q43Single correctElectronic Devices

Refer to the logic circuit given below. For two inputs (

A = 1

B = 1

) and (

A = 0

B = 1

), output (Y) will

b e

Logic circuit with inputs A and B feeding a network of gates producing output Y.

(A)

1, 0

respectively

(B)

0, 1

respectively

(C)

0, 0

respectively

(D)

1, 1

respectively

Q44Single correctLaws of Motion

The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is ____ m/s. Assume pulley is massless and string is light and inextensible. (Take

g = 10 m/s^{2}

)

A 6 kg mass held at a height of 6 m connected over a pulley to a 2 kg mass resting on the ground.

(A)

7.74

(B)

7.20

(C)

6.55

(D)

4.50

Q46NumericalLaws of Motion

A block takes t time to slide down a plane inclined at

4 5^{\circ}

to the horizontal. If the surface is made smooth (frictionless), the block takes time

\frac{t}{2}

to slide down the plane. The coefficient of friction between the block and the inclined plane is

(\frac{α}{100})

. The value of

α

is _____.

Q47NumericalDual Nature of Matter and Radiation

The de Broglie wavelength for an electron accelerated through the potential difference of

V_{1}

volt is

λ_{1}

. When the potential difference is changed to

V_{2}

volt, the associated de Broglie wavelength is increased by 50%. If

(V_{1} / V_{2}) = (9/ α)

, then the value of

α

is _______.

Q48NumericalMagnetic Effects of Current and Magnetism

A moving coil galvanometer when shunted with

2 Ω

resistance gives a full scale deflection for a current of 500 mA. When a resistance of

470 Ω

is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is _____

Ω

Q49NumericalCurrent Electricity

Two cells of emfs 1 V and 2 V and internal resistance

2 Ω

and

1 Ω

, respectively connected in parallel, gave a current of 1 A through an external resistance. If the polarity of one cell is reversed, then value of current through the external resistance will be

\frac{α}{5}

A. The value of

α

is _____.

Q50NumericalOptics

A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is _____ cm.

Chemistry25 questions

Q51Single correctSome Basic Concepts in Chemistry

Which of the following contain the same number of atoms? (Given : Molar mass in

gmo l^{- 1}

of H, He, O and S are 1, 4, 16 and 32 respectively) A. 2 g of

O_{2}

gas; B. 4 g of

S O_{2}

gas; C. 1400 mL of

O_{2}

at STP; D.

0.05 L

of He at STP; E. 0.0625 mol of

H_{2}

gas. Choose the correct answer from the options given below :

(A)

A and B only

(B)

B and C only

(C)

C and D only

(D)

A, C and E only

Q52Single correctAtomic Structure

The Bohr radius of a hydrogen like species is 70.53 pm. The species and the stationary state (

n

) are respectively (Given : Hydrogen atom Bohr radius is 52.9 pm)

(A)

L i^{2 +}, 3

(B)

H e^{+}, 3

(C)

H e^{+}, 2

(D)

L i^{2 +}, 2

Q53Single correctChemical Bonding and Molecular Structure

Given below are two statements :
Statement I : The number of compounds among

S O_{2}, S O_{3}, S F_{4}, S F_{6}

and

H_{2} S

in which sulphur does not obey the Octet rule is 3.
Statement II : Among

[H_{2} O, ClF_{3}, S F_{4}]

[N H_{3}, BrF_{5}, S F_{4}]

[BrF_{5}, ClF_{3}, XeF_{4}]

and

[XeF_{4}, ClF_{3}, H_{2} O]

, the number of sets in which all the molecules have one lone pair of electrons on the central atom is 1.
In the light of the above statements, choose the correct answer from the options given below :

(A)

Both Statement I and Statement II are true

(B)

Both Statement I and Statement II are false

(C)

Statement I is true but Statement II is false

(D)

Statement I is false but Statement II is true

Q54Single correctChemical Thermodynamics

Match List - I with List - II. Given

V_{1}

and

V_{2}

are initial and final volumes respectively. Choose the correct answer from the options given below :

List - I (Isothermal process)	List - II (Expression)
A. Reversible expansion	I. $q = 0$
B. Free expansion	II. $q = nRT ln \frac{V _{2}}{V _{1}}$
C. Irreversible Compression	III. $w = - p_{e x t} (V_{1} - V_{2})$
D. Cyclic reversible	IV. $\frac{q _{re v}}{T} = 0$

(A)

A-II, B-III, C-I, D-IV

(B)

A-II, B-I, C-IV, D-III

(C)

A-II, B-I, C-III, D-IV

(D)

A-I, B-II, C-III, D-IV

Q55Single correctSolutions

Given below are two statements :
Statement I:

H_{2} O

molecules move from the chamber 1 to chamber 2.
Statement II: The osmotic pressure of a solution prepared by dissolving 50 mg of potassium sulphate (molar mass = 174 g/mol) in 2 L of water (at

2 7^{\circ}

C) is 0.0107 bar. (Given :

R = 0.083 d m^{3}

bar

K^{- 1} mol^{- 1}

and assume complete dissociation of electrolyte).
In the light of the above statements, choose the correct answer from the options given below :

Two chambers separated by a semipermeable membrane: Chamber I with 18 g glucose in 100 mL solution and Chamber II with 30 g glucose in 250 mL solution.

(A)

Both Statement I and Statement II are true

(B)

Both Statement I and Statement II are false

(C)

Statement I is true but Statement II is false

(D)

Statement I is false but Statement II is true

Q56Single correctEquilibrium

Given is a concentrated solution of a weak electrolyte

A_{x} B_{y}

of concentration 'c' and dissociation constant 'K'. The degree of dissociation is given by :

(A)

[K \times c^{x + y - 1} x^{x} y^{y}]^{x + y}

(B)

(\frac{K}{c ^{x + y - 1} x ^{x} y ^{y}})^{\frac{1}{x + y}}

(C)

(\frac{c ^{x + y - 1} x ^{x} y ^{y}}{K})^{x + y}

(D)

(\frac{c ^{x + y - 1} x ^{x} y ^{y}}{K})^{\frac{1}{x + y}}

Q57Single correctRedox Reactions and Electrochemistry

For a general redox reaction
Anode :

Red_{1} \to O_{1}^{n_{1}^{+}} + n_{1} e^{-}

Cathode :

O x_{2} + n_{2} e^{-} \to Red_{2}^{n_{2} -}

Which of the following statement is incorrect?

Graph of (E−E°)/(RT/F) versus log₁₀Q showing three straight lines for n=1, 2 and 3, with slope proportional to 1/n.

(A)

The overall reaction can be written as

n_{2} Red_{1} + n_{1} O x_{2} ⇌ n_{2} O_{1}^{n_{1}^{+}} + n_{1} Red_{2}^{n_{2} -}

(B)

The electrons do not appear in the overall reaction because electrons produced at the anode are consumed at the cathode.

(C)

A plot of

\frac{( E - E ^{\circ} )}{RT / F}

versus

lo g_{10} Q

for n = 1, 2, 3 with Slope

α \frac{1}{n}

(D)

If the reaction is carried out reversibly, the electrical work done is equal to the ratio of charge and potential difference through which charge is moved.

Q58Single correctClassification of Elements and Periodicity in Properties

In a period, the first ionisation enthalpy of the element at extreme left and the negative electron gain enthalpy of the extreme right element, except noble gases, are respectively.

(A)

lowest and lowest

(B)

highest and lowest

(C)

lowest and highest

(D)

highest and highest

Q59Single correctp-Block Elements

Given below are two statements :
Statement I:

F_{2} O < H_{2} O < C l_{2} O

is the correct trend in terms of bond angle.
Statement II:

SiF_{4}, SnF_{4}

and

PbF_{4}

are ionic in nature.
In the light of the above statements, choose the correct answer from the options given below :

(A)

Both Statement I and Statement II are true

(B)

Both Statement I and Statement II are false

(C)

Statement I is true but Statement II is false

(D)

Statement I is false but Statement II is true

Q60Single correctd- and f-Block Elements

The correct order of first

(Δ_{i} H_{1})

and second

(Δ_{i} H_{2})

ionisation enthalpy values of Cr and Mn are :
A.

Δ_{i} H_{1} : Cr > Mn

Δ_{i} H_{2} : Cr > Mn

Δ_{i} H_{1} : Mn > Cr

Δ_{i} H_{2} : Mn > Cr

Choose the correct answer from the options given below :

(A)

A and B only

(B)

B and C only

(C)

A and D only

(D)

C and D only

Q61Single correctCoordination Compounds

Which of the following sequences of hybridisation, geometry and magnetic nature are correct for the given coordination compounds ?
A.

[NiCl_{4}]^{2 -} - s p^{3}

, tetrahedral, paramagnetic
B.

[Ni (NH_{3})_{6}]^{2 +} - s p^{3} d^{2}

, octahedral, paramagnetic
C.

[Ni (CO)_{4}] - s p^{3}

, tetrahedral, paramagnetic
D.

[Ni (CN)_{4}]^{2 -} - dsp^{2}

, square planar, diamagnetic
Choose the correct answer from the options given below :

(A)

A, B, C and D

(B)

B, C and D only

(C)

A, C and D only

(D)

A, B and D only

Q62Single correctPurification and Characterisation of Organic Compounds

Given below are two statements :
Statement I: A mixture of

C_{12} H_{22} O_{11}

(sugar) and NaCl can be separated by dissolving sugar in alcohol, due to differential solubility.
Statement II: Rose essence from rose petals is seperated by steam distillation due to its high volatility and insolubility in

H_{2} O

.
In the light of the above statements, choose the correct answer from the options given below :

(A)

Both Statement I and Statement II are true

(B)

Both Statement I and Statement II are false

(C)

Statement I is true but Statement II is false

(D)

Statement I is false but Statement II is true

Q63Single correctSome Basic Principles of Organic Chemistry

Shown below is the structure of methyl acetate with three different

α, β

and

γ

carbon - oxygen bonds. The correct order of bond lengths of these bonds is :

Structure of methyl acetate (CH₃–C(=O)–O–CH₃) with the three bonds labelled α, β and γ.

(A)

α > β > γ

(B)

α < β < γ

(C)

α = β = γ

(D)

α < β = γ

Q64Single correctOrganic Compounds Containing Oxygen

x

' is the product which is obtained by the hydrolysis of prop-1-yne in the presence of mercuric sulphate under dilute acidic medium at 333 K. '

y

' is the product which is obtained by the reaction of ethane nitrile with methyl magnesium bromide in dry ether followed by hydrolysis. IUPAC name of product obtained from '

x

' and '

y

' in the presence of barium hydroxide followed by heating is :

(A)

2 - Methylpent-4-en-3-one

(B)

4 - Methylpent-3-en-2-one

(C)

4 - Methylpent-1-ene

(D)

2 - Methylpent-3-one

Q65Single correctOrganic Compounds Containing Halogens

An optically active alkyl bromide

C_{4} H_{9} Br

, reacts with ethanolic KOH to form major compound [A] which reacts with bromine to give compound [B]. Compound [B] reacts with ethanolic KOH and sodamide to give compound [C]. One molecule of water adds to compound [C] on warming with mercuric sulphate and dilute sulphuric acid at 333 K to form compound [D]. The functional group in compound D will be confirmed by :

(A)

Haloform test

(B)

Lucas test

(C)

Silver mirror test

(D)

Benedict test

Q66Single correctOrganic Compounds Containing Oxygen

Consider the following reaction.

Benzyl phenyl ether: a benzene ring linked through -O-CH2- to a second benzene ring, reacting with HI to give the product.

(A)

Both Statement I and Statement II are true

(B)

Both Statement I and Statement II are false

(C)

Statement I is true but Statement II is false

(D)

Statement I is false but Statement II is true

Q67Single correctOrganic Compounds Containing Nitrogen

Propanoic acid undergoing the reagent sequence (i) NH3/Delta, (ii) NaOH/Br2, (iii) HNO2/H2O 0 deg C, (iv) C6H5N2Cl 0 deg C to give major product X.

(A)

Benzene

(B)

Phenol

(C)

Propanol

(D)

Chlorobenzene

Q68Single correctOrganic Compounds Containing Nitrogen

The number of compounds from the following which can undergo reaction with

B r_{2} /KOH

(alcoholic) to give respective products and these respective products can also be obtained separately by Gabriel phthalimide reaction is :

A set of six amide structures provided as the candidate compounds to be counted.

(A)

(B)

(C)

(D)

Q69Single correctBiomolecules

Consider the following reactions. Total number of electrons in the

π

bonds and lone pair of electrons in the product (X) is :

Glucose (CHO-(CHOH)4-CH2OH) undergoing (i) HI, Delta, (ii) V2O5/10-20 atm/773 K, (iii) benzoyl chloride/anhydrous AlCl3 to give major product X.

(A)

(B)

(C)

(D)

Q70Single correctp-Block Elements

Treatment of a gas 'X' with a freshly prepared ferrous sulphate solution gives a compound 'Y' as a brown ring. The compounds X and Y are.

(A)

NO

and

[Fe (NO)] S O_{4}

(B)

N O_{2}

and

[Fe (N O_{2})] S O_{4}

(C)

N_{2} O

and

[Fe (N_{2} O)] S O_{4}

(D)

N_{2} O_{4}

and

[Fe (N_{2} O_{4})] S O_{4}

Q71NumericalCoordination Compounds

An excess of

AgN O_{3}

is added to 100 mL of a 0.05 M solution of tetraaquadichloridochromium (III) chloride. The number of moles of AgCl precipitated will be ______

\times 1 0^{- 3}

. (Nearest integer)

Q72NumericalHydrocarbons

An alkane

(Y)

requires 8 moles of oxygen for complete combustion and on chlorination with

C l_{2} /h ν

(Y)

gives only one monochlorinated product (Z). The total number of primary carbon atoms in (Y) is ______.

Q73NumericalRedox Reactions and Electrochemistry

500 mL of

0.2 M Mn O_{4}^{-}

solution in basic medium when mixed with 500 mL of 1.5 M KI solution, oxidises iodide ions to liberate molecular iodine. This liberated iodine is then titrated with a standard

x M

thiosulphate solution in presence of starch till the end point. If 300 mL of thiosulphate was consumed, then the value of x is ______.

Q74NumericalEquilibrium

In a closed flask at 600 K, one mole of

X_{2} Y_{4} (g)

attains equilibrium as given below :

X_{2} Y_{4} (g) ⇌ 2X Y_{2} (g)

. At equilibrium,

75% X_{2} Y_{4} (g)

was dissociated and the total pressure is 1 atm. The magnitude of

Δ_{r} G^{⊖}

(in

kJ mo l^{- 1}

) at this temperature is ______. (Nearest Integer) (Given:

R = 8.3 J mo l^{- 1} K^{- 1}

;

ln 10 = 2.3, lo g 2 = 0.3, lo g 3 = 0.48, lo g 5 = 0.69, lo g 7 = 0.84

)

Q75NumericalChemical Kinetics

Decomposition of a hydrocarbon follows the equation

k = (5.5 \times 1 0^{11} s^{- 1}) e^{\frac{- 28000 K}{T}}

. The activation energy of reaction is ______

kJ mo l^{- 1}

. (Nearest Integer) Given:

R = 8.3 J K^{- 1} mo l^{- 1}

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