Updated 19 Oct 2026

JEE Main important questions with answers

How "important" is decided here: the four heaviest chapters of each subject by measured weight (their share of the 29 JEE Main shift papers of 2025 and 2026 in the bank), and one recent real question from each. Every question has its answer key and worked solution in the page.

Take a 25-Q adaptive chapter test See the measured weightage table

Q1PhysicsJEE Main 2026, 22 Jan Shift 2Properties of images formed by a mirror

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

Answer key (B) & worked solution

Correct answer: Option B

Image should be real. So object should be placed beyond focus.

Q2PhysicsJEE Main 2026, 21 Jan Shift 2Angular momentum of a point particle

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Two cars A and B each of mass

1 0^{3} kg

are moving on parallel tracks separated by a distance of 10 m , in same direction with speeds

72 km / h

and

36 km / h

. The magnitude of angular momentum of car A with respect to car B is

____

J.s.

Answer key (B) & worked solution

Correct answer: Option B

L = m . V_{rel} r_{⊥}

= 1000 \times (36 \times \frac{5}{18}) \times 10 = 1 0^{5} kg m^{2} / s

Q3PhysicsJEE Main 2026, 21 Jan Shift 1Combination of errors

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In an experiment the values of two spring constants were measured as

k_{1} = (10 \pm 0.2) N / m

and

k_{2} = (20 \pm 0.3) N / m

. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

Answer key (D) & worked solution

Correct answer: Option D

For parallel combination of spring,

K_{eq} = K_{1} + K_{2} = 30 N / m

Δ K_{eq} = Δ K_{1} + Δ K_{2} = 0.2 + 0.3 = 0.5 N / m

∴

% Error in

K = \frac{0.5}{30} \times 100 = 1.67%

Q4PhysicsJEE Main 2026, 21 Jan Shift 2Maximum power transfer theorem

A battery with EMF E and internal resistance

r

is connected across a resistance

R

. The power consumption in R will be maximum when :

R = 2 r

R = \frac{r}{2}

R = 2 r

R = r

Answer key (D) & worked solution

Correct answer: Option D

For maximum power drawn across load Resistance

R_{Load} = R_{internal}

R = r

Q5ChemistryJEE Main 2026, 21 Jan Shift 2Crystal Field Theory

Given below are two statements: Statement I: Crystal Field Stabilization Energy (CFSE) of

[Cr (H_{2} O)_{6}]^{2 +}

is greater than that of

[Mn (H_{2} O)_{6}]^{2 +}

. Statement II: Potassium ferricyanide has a greater spin-only magnetic moment than sodium Ferrocyanide. In the light of the above statements, choose the correct answer from the options given below:

ABoth Statement I and Statement II are true

BBoth Statement I and Statement II are false

CStatement I is true but Statement II is false

DStatement I is false but Statement II is true

Answer key (A) & worked solution

Correct answer: Option A

[Mn (H_{2} O)_{6}]^{2 +} \Rightarrow

CFSE value is zero because of

d^{5}

configuraiton with WFL in coordination number 6

[Cr (H_{2} O)_{6}]^{2 +}

[Cr (H_{2} O)_{6}]^{2 +} \Rightarrow

CFSE value is

- 0.6 Δ_{0}

because of

d^{4}

configuraiton with WFL in coordination number 6. For :

K_{3} [Fe (CN)_{6}], μ = 1 (1 + 2) = 3

B.M. For :

Na_{4} [Fe (CN)_{6}], μ = 0

B.M.

Q6ChemistryJEE Main 2026, 21 Jan Shift 1Quantitative analysis of elements

In Carius method, 0.75 g of an organic compound gave 1.2 g of barium sulphate, find percentage of sulphur (molar mass

32 g mol^{- 1}

). Molar mass of barium sulphate is

233 g mol^{- 1}

4.55%

10.30%

21.97%

16.48%

Answer key (C) & worked solution

Correct answer: Option C

\frac{n _{BaSO_{4}} \times 32}{W _{(unknown comp.)}} \times 100

= \frac{1.2 \times 32}{233} \times \frac{100}{0.75} = 21.97%

Q7ChemistryJEE Main 2025, 22 Jan Shift 1Chemical Properties of Alkynes

Given below are two statements : Statement I : One mole of propyne reacts with excess of sodium to liberate half a mole of H

_{2}

gas. Statement II : Four g of propyne reacts with NaNH

_{2}

to liberate NH

_{3}

gas which occupies 224 mL at STP. In the light of the above statements, choose the most appropriate answer from the options given below:

AStatement I is correct but Statement II is incorrect.

BBoth Statement I and Statement II are incorrect

CStatement I is incorrect but Statement II is correct

DBoth Statement I and Statement II are correct.

Answer key (A) & worked solution

Correct answer: Option A

1 mole C H_{3} - C \equiv C H + (e x cess) N a \to C H_{3} - C ˉ \equiv C N + a + \frac{1}{2} m o l e H_{2} \frac{1}{2} H_{2} ↑

4 gm C H_{3} - C \equiv C H + N a N H_{2} \to C H_{3} C \equiv C ˉ N + a + N H_{3}

\frac{4}{40} = 0 .1 mole

0.1 m o l e = 2240 ml of ammonia

Statement I is correct but Statement II is incorrect

Q8ChemistryJEE Main 2026, 21 Jan Shift 2Differential and Integral Forms of Rate Law

Decomposition of A is a first order reaction at

T (K)

and is given by

A (g) \to B (g) + C (g)

. In a closed 1 L vessel, 1 bar

A (g)

is allowed to decompose at

T (K)

. After 100 minutes, the total pressure was 1.5 bar . What is the rate constant (in

min^{- 1}

) of the reaction ? (

lo g 2 = 0.3)

6.9 \times 1 0^{- 1}

6.9 \times 1 0^{- 3}

6.9 \times 1 0^{- 2}

6.9 \times 1 0^{- 4}

Answer key (B) & worked solution

Correct answer: Option B

_{g}

→ B

_{g}

+ C

_{g}

1, –, – 1-P, P, P

P_{total} = 1 + P

1.5 = 1 + P

P = 0.5

K = \frac{1}{100} ln \frac{1}{0.5}

= \frac{0.693}{100}

= 6.9 \times 1 0^{- 3} min^{- 1}

Q9MathematicsJEE Main 2026, 21 Jan Shift 2Shortest distance between two lines

Let the line

L_{1}

be parallel to the vector

- 3 i^+ 2 j^+ 4 k^

and pass through the point

(2, 6, 7)

and the line

L_{2}

be parallel to the vector

2 i^+ j^+ 3 k^

and pass through the point

(4, 3, 5)

. If the line

L_{3}

is parallel to the vector

- 3 i^+ 5 j^+ 16 k^

and intersects the lines

L_{1}

and

L_{2}

at the points C and D , respectively, then

∣ CD ∣^{2}

is equal to :

A171

B290

C312

D89

Answer key (B) & worked solution

Correct answer: Option B

L_{1} : \frac{x - 2}{- 3} = \frac{y - 6}{2} = \frac{z - 7}{4}

Point C on

L_{1} : (- 3 λ_{1} + 2, 2 λ_{1} + 6, 4 λ_{1} + 7)

L_{2} : \frac{x - 4}{2} = \frac{y - 3}{1} = \frac{z - 5}{3}

Point D on

L_{2} : (2 λ_{2} + 4, λ_{2} + 3, 3 λ_{2} + 5)

Dr's of line

L_{3}

L_{3} : \frac{2 λ _{2} + 3 λ _{1} + 2}{- 3} = \frac{λ _{2} - 2 λ _{1} - 3}{5} = \frac{3 λ _{2} - 4 λ _{1} - 2}{16}

λ_{1} = - 3, λ_{2} = 2

C (11, 0, -5) D (8, 5, 11)

∣ CD ∣^{2} = 3^{2} + 5^{2} + 1 6^{2} = 290

Q10MathematicsJEE Main 2026, 21 Jan Shift 2Characteristic Equation & Cayley Hamilton Theorem

For the matrices

A = [31 - 4 - 1]

and

B = [- 29 - 13 4918]

, if

(A^{15} + B) [x y] = [00]

, then among the following which one is true?

x = 5, y = 7

x = 18, y = 11

x = 11, y = 2

x = 16, y = 3

Answer key (C) & worked solution

Correct answer: Option C

Here

A^{n} = [2 n + 1 n - 4 n - 2 n + 1]

\Rightarrow A^{15} = [3115 - 60 - 29]

\Rightarrow A^{15} + B = [22 - 11 - 11]

Now

(A^{15} + B) [x y] = [00]

\Rightarrow [22 - 11 - 11] [x y] = [00]

\Rightarrow 2 x - 11 y = 0

Q11MathematicsJEE Main 2026, 21 Jan Shift 1Geometric progression

Let

a_{1}, a_{2}, a_{3}, \dots

. be a G.P. of increasing positive terms such that

a_{2} \cdot a_{3} \cdot a_{4} = 64

and

a_{1} + a_{3} + a_{5} = \frac{813}{7}

. Then

a_{3} + a_{5} + a_{7}

is equal to :

A3256

B3252

C3244

D3248

Answer key (B) & worked solution

Correct answer: Option B

. ar^{2} . ar^{3} = 64

a^{3} r^{6} = 64 \Rightarrow ar^{2} = 4

a + ar^{2} + ar^{4} = \frac{813}{7}

r^{2} = 28

ar^{2} + ar^{4} + ar^{6} =

ar^{2} (1 + r^{2} + r^{4}) = 4 (1 + 28 + 784) = 3252

Q12MathematicsJEE Main 2026, 21 Jan Shift 2Dearrangement, grid, divisor & exponent problems

The largest

n \in N

, for which

7^{n}

divides 101!, is :

A16

B18

C15

D19

Answer key (A) & worked solution

Correct answer: Option A

Exponent of 7 in 101!

= [\frac{101}{7}] + [\frac{101}{7 ^{2}}] + [\frac{101}{7 ^{3}}] + \dots\dots

= 14 + 2 = 16