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JEE Advanced 2021 · Paper 2

A full paper in the 2021 Paper 2 pattern: Physics, Chemistry and Mathematics, 19 questions each, one 180-minute clock. Take it as a timed mock or open it in learn mode and check every answer.

57questions

180 minone clock

180maximum marks

3/31/23easy / medium / hard

Start timed mock Study with solutions

Sections and marking

Each subject has the same 4 sections, 60 marks per subject.

Section	Type	Questions	Marking
Section 1	One or more correct	6	+4 all correct, partial +3/+2/+1, -2 otherwise
Section 2	Paragraph based, numerical (3 sets)	6	+2, no negative
Section 3	Paragraph based (2 sets)	4	+3 / -1
Section 4	Integer answer	3	+4, no negative

Topics in this paper

Physics · 19 questions

Waves and the Doppler effect2
Simple harmonic motion with collision2
RC circuits2
Rotational dynamics1
Thermodynamics and kinetic theory1
Capacitors and dielectrics1
Electromagnetic induction1
Wave optics (YDSE)1
Modern physics1
Fluid mechanics (Bernoulli, Torricelli)1
Fluid mechanics (draining tank)1
Magnetic force on moving charges1
Charged particle in combined E and B fields1
Experimental physics and error analysis1

Chemistry · 19 questions

Gas-phase first-order kinetics2
Coordination compounds1
Electrochemistry and solubility equilibrium1
Chemical kinetics (parallel reactions)1
Stereochemistry of alkene addition1
p-block halides1
Thermodynamics (entropy and work)1
Solubility product1
Solubility product with weak-acid anion1
Colligative properties with association1
Equilibrium and association in solution1
Haloform reaction and carbonyl identification1
Hofmann bromamide degradation1
Redox titration and qualitative analysis1

Mathematics · 19 questions

Matrices3
Probability3
Circle2
Complex numbers1
Limits and continuity1
Conic sections1
Three-dimensional geometry1
Differential equations1
Application of derivatives1
Area under curves1
Volume of revolution1
Trigonometric equations1
Polynomials and curve tracing1
Binomial theorem1

Sample question from this paper

Mathematics · Matrices · one or more options correct

Let

M=\begin{pmatrix}1&2&0\\0&1&2\\0&0&1\end{pmatrix}

and let

I

be the identity matrix of order 3. Which of the following statements is/are correct?

A. The $(1,3)$ entry of $M^{10}$ is $180$
B. $M$ is diagonalizable over $\mathbb{R}$
C. The $(1,3)$ entry of $M^{-1}$ is $4$
D. The sum of all nine entries of $M^{-1}$ equals $1$

Show answer and solution

Answer: A, C
Write

M=I+N

with

N=\begin{pmatrix}0&2&0\\0&0&2\\0&0&0\end{pmatrix}

, so

N^2

has the single nonzero entry

4

at position

(1,3)

and

N^3=0

. Then

M^n=I+nN+\binom n2N^2

, whose

(1,3)

entry is

4\binom n2=2n(n-1)

; for

n=10

this is

180

, so (A) is true.

M

has the single eigenvalue

1

but

M\neq I

(equivalently

N\neq0

), so it is not diagonalizable and (B) is false.

M^{-1}=I-N+N^2=\begin{pmatrix}1&-2&4\\0&1&-2\\0&0&1\end{pmatrix}

, whose

(1,3)

entry is

4

, so (C) is true. The entries of

M^{-1}

add to

3-2-2+4=3

, not

1

, so (D) is false. Answer: A and C.

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