Updated 19 Oct 2026

JEE Advanced PYQ chapterwise and year papers

JEE Advanced tests multi-concept depth across Paper 1 and Paper 2 in the TCS iON interface, featuring single-choice, multiple-correct (with +4 / +3 / +2 / +1 / 0 / −2 partial marking), non-negative integer, and paragraph/matching sections. Below are real JEE Advanced past questions with worked solutions, year links, and the highest-weight chapters.

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On multiple-correct questions (SEC 2), ticking any wrong option deducts −2 marks. When no wrong option is ticked: ticking all correct options awards +4; ticking 3 of 4 correct options awards +3; ticking 2 of 3 or 4 awards +2; ticking 1 of 2, 3 or 4 awards +1. In the ViJEEta Scorecard, partial credit earned is highlighted in amber so you can separate partial hits from full solutions.

Real JEE Advanced PYQs with worked solutions

Q1ChemistryJEE Advanced 2025 Paper 1Crystal Field Theory

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The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region for the given complexes is

Answer key (A) & worked solution

Correct answer: Option A

Δ_{0} \propto \frac{1}{λ}

According to the spectrochemical series, the strength of ligands is

C l^{-} < H_{2} O < N H_{3} < C N^{-}

. Since

Δ_{0}

is inversely proportional to wavelength, the order of

λ_{ma x}

is:

[C o (C N)_{6}]^{3 -} < [C o (N H_{3})_{6}]^{3 +} < [C o (N H_{3})_{5} H_{2} O]^{3 +} < [C o (N H_{3})_{5} C l]^{2 +}

Q2ChemistryJEE Advanced 2025 Paper 1Potassium Permanganate

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One of the products formed from the reaction of permanganate ion with iodide ion in neutral aqueous medium is

Answer key (B) & worked solution

Correct answer: Option B

In neutral or faintly alkaline medium, permanganate ion oxidizes iodide to iodate:

2 M n O_{4}^{-} + H_{2} O + I^{-} \to 2 M n O_{2} + 2 O H^{-} + I O_{3}^{-}

Q3MathematicsJEE Advanced 2025 Paper 1Maxima and Minima at a point

Let

R

denote the set of all real numbers. Define the function

f : R \to R

f (x) = {2 - 2 x^{2} - x^{2} sin \frac{1}{x} 2 if x \neq = 0 if x = 0

Then which one of the following statements is TRUE?

AThe function

f

is NOT differentiable at

x = 0

BThere is a positive real number

δ

, such that

f

is a decreasing function on the interval

(0, δ)

CFor any positive real number

δ

, the function

f

is NOT an increasing function on the interval

(- δ, 0)

x = 0

is a point of local minima of

f

Answer key (C) & worked solution

Correct answer: Option C

(a) RHD at

x = 0 : lim_{h \to 0} \frac{( 2 - 2 h ^{2} - h ^{2} s i n \frac{1}{h} ) - 2}{h} = 0

. LHD is also 0. So

f

is differentiable at

x = 0

. (b)

f^{'} (x) = - 4 x - 2 x sin \frac{1}{x} - x^{2} (cos \frac{1}{x}) (- \frac{1}{x ^{2}}) = - (2 x (4 - sin \frac{1}{x})) + cos \frac{1}{x}

. As

cos \frac{1}{x}

oscillates, we can't say it's decreasing on

(0, δ)

. (d)

f (0) = 2, f (0 + h) 0

Q4MathematicsJEE Advanced 2025 Paper 1Some Special type of Matrices

Consider the matrix

P = 200020003

. Let the transpose of a matrix

X

be denoted by

X^{T}

. Then the number of

3 \times 3

invertible matrices

Q

with integer entries, such that

P Q = QP

and

Q^{T} Q = I

is:

A32

C16

D24

Answer key (C) & worked solution

Correct answer: Option C

Let

Q = a_{1} a_{2} a_{3} b_{1} b_{2} b_{3} c_{1} c_{2} c_{3}

. From

P Q = QP

, we find

c_{1} = 0, c_{2} = 0, a_{3} = 0, b_{3} = 0

Q = a_{1} a_{2} 0 b_{1} b_{2} 0 00 c_{3}

. From

Q^{T} Q = I

and integer entries:

a_{1}^{2} + b_{1}^{2} = 1, a_{2}^{2} + b_{2}^{2} = 1, c_{3}^{2} = 1

and

a_{1} a_{2} + b_{1} b_{2} = 0

. Possible values:

c_{3} \in {1, - 1}

. The

2 \times 2

block yields 8 integer combinations for

(a_{1}, b_{1}, a_{2}, b_{2})

. Total matrices

= 8 \times 2 = 16

Q5PhysicsJEE Advanced 2025 Paper 2Other problems involving circular orbits

Consider a star of mass

m_{2}

kg revolving in a circular orbit around another start of mass

m_{1} k g

with

m_{1} >> m_{2} .

The heavier start slowly acquires mass from the lighter star at a constant rate of

γ

kg/s. In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is r, then its relative rate of change

\frac{1}{r} \frac{d r}{d t} (in s^{- 1})

is given by:

- \frac{3 γ}{2 m _{2}}

- \frac{2 γ}{m _{2}}

- \frac{2 γ}{m _{1}}

- \frac{3 γ}{2 m _{1}}

Answer key (B) & worked solution

Correct answer: Option B

m_{2} ω^{2} r = \frac{G m _{1} m _{2}}{r ^{2}}

ω = \frac{G m _{1}}{r ^{3}}

L = m_{2} ω r^{2}

= m_{2} \frac{G m _{1}}{r ^{3}} r^{2}

L = m_{2} G m_{1} r

= const.

ℓ n L = ℓ n m_{2} + ℓ n G + \frac{1}{2} ℓ n m_{1} + \frac{1}{2} ℓ n r

0 = \frac{d m _{2}}{m _{2}} + \frac{1}{2} \frac{d m _{1}}{m _{1}} + \frac{1}{2} \frac{d r}{r}

\frac{d r}{r d t} = - \frac{2 d m _{2}}{m _{2} d t} - \frac{d m _{1}}{m _{1} d t} \approx - \frac{2 γ}{m _{2}}

Here

(\frac{d m}{d t} = γ)

Q6PhysicsJEE Advanced 2025 Paper 2Dimensional analysis

A temperature difference can generate e.m.f. in some materials. Let S be the e.m.f. produced per unit temperature difference between the ends of a wire,

σ

the electrical conductivity and

k

the thermal conductivity of the material of the wire. Taking

M, L, T, I

and

K

as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity

Z = \frac{S ^{2} σ}{k}

is:

[M^{0} L^{0} T^{0} I^{0} K^{0}]

[M^{0} L^{0} T^{0} I^{0} K^{- 1}]

[M^{1} L^{2} T^{- 2} I^{- 1} K^{- 1}]

[M^{1} L^{2} T^{- 4} I^{- 1} K^{- 1}]

Answer key (B) & worked solution

Correct answer: Option B

S = emf per unit temperature difference

σ =

Electrical conductivity k = Thermal conductivity

[S] = [M L^{2} T^{- 3} I^{- 1} K^{- 1}]

[σ] = [M^{- 1} L^{- 3} T^{3} I^{2}]

[K] = [M^{1} L^{1} T^{- 3} K^{- 1}]

[Z] = \frac{S ^{2} σ}{K} = \frac{[ M ^{1} L ^{1} T ^{- 3} K ^{- 2} ]}{[ M ^{1} L ^{1} T ^{- 3} K ^{- 1} ]}

[Z] = [K^{- 1}]

Start chapter-wise JEE Advanced practice

Chapter	Subject	Weight (/100)	Tagged PYQs	Action
Coordination Compounds	Chemistry	8.1	54	Open chapter →
Ray Optics	Physics	7.9	55	Open chapter →
3D Geometry	Mathematics	6.6	47	Open chapter →
Matrices and Determinants	Mathematics	6.6	47	Open chapter →
Practical Chemistry	Chemistry	6.5	43	Open chapter →
Sequence and Series	Mathematics	6.4	45	Open chapter →
Rotational Motion	Physics	6.2	43	Open chapter →
Units and Measurements	Physics	5.9	41	Open chapter →
Hydrocarbons	Chemistry	5.7	38	Open chapter →
Current Electricity	Physics	5.4	38	Open chapter →
Chemical Kinetics	Chemistry	5.4	36	Open chapter →
Solutions	Chemistry	5.3	35	Open chapter →
Permutations and Combinations	Mathematics	5.2	37	Open chapter →
Chemical Bonding	Chemistry	5.1	34	Open chapter →
Mole and Equivalent Concept	Chemistry	5.1	34	Open chapter →
Vectors	Mathematics	5.1	36	Open chapter →
Aldehydes and Ketones	Chemistry	5.0	33	Open chapter →
Electrochemistry	Chemistry	5.0	33	Open chapter →
Electrostatics	Physics	4.9	34	Open chapter →
Thermodynamics and Thermochemistry	Chemistry	4.8	32	Open chapter →
Definite Integrals	Mathematics	4.7	33	Open chapter →
Fluid Mechanics	Physics	4.6	32	Open chapter →
Relation and Functions	Mathematics	4.5	32	Open chapter →
Thermodynamics	Physics	4.4	31	Open chapter →