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JEE Advanced 2021 · Paper 1

A full paper in the 2021 Paper 1 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

5/34/18easy / 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	Single correct	4	+3 / -1
Section 2	Paragraph based, numerical (3 sets)	6	+2, no negative
Section 3	One or more correct	6	+4 all correct, partial +3/+2/+1, -2 otherwise
Section 4	Integer answer	3	+4, no negative

Topics in this paper

Physics · 19 questions

Circular motion1
Magnetic force between a current-carrying wire and a loop1
Polarisation by reflection and total internal reflection1
Radiation pressure and equilibrium of a suspended sheet1
Electrostatics of a charged ring and small oscillations1
Electrostatic potential energy of a ring and energy conservation1
Waves on strings1
Power transmitted across a string junction1
Fluid dynamics1
Fluid pressure1
Angular momentum and torque of a projectile1
Entropy change and maximum work from finite bodies1
Galvanometer conversion and loading errors of meters1
Damped oscillations1

Chemistry · 19 questions

Colligative properties (association)2
Redox titration (iodometry)2
Electrochemistry and ionic equilibrium1
Stereochemistry of addition and elimination1
Inorganic reaction sequence and coordination chemistry1
Chemical kinetics (parallel reactions)1
Chemical equilibrium (gaseous)1
Chemical thermodynamics and equilibrium1
Coordination compounds (magnetism, CFSE, isomerism)1
p-block compounds and oxoacids1
Nucleophilic substitution and elimination1
Isomerism and stereoisomer counting1
Solid state1
Carbohydrates and amino acids1

Mathematics · 19 questions

Differential equations / area2
Matrices / eigenvalues, Newton sums2
Sequences and series1
Probability / Bayes theorem1
Area under curves / parabola normal1
3D geometry / reflection in a plane1
Probability / geometric series1
Probability / expectation1
Continuity and differentiability1
Definite integrals / symmetry1
Conic sections (ellipse and hyperbola)1
Matrices / powers1
Trigonometry / solution of triangles1
Limits / Riemann sums1

Sample question from this paper

Mathematics · Continuity and differentiability · one or more options correct

Let

f(x)=x^{2}\sin\dfrac1x

for

x\ne0

and

f(0)=0

. Which of the following statements is (are) correct?

A. $f$ is differentiable at $x=0$ and $f'(0)=0$
B. $f'$ is continuous at $x=0$
C. $f'$ is bounded on the interval $(-1,1)\setminus\{0\}$
D. $f''(0)$ exists

Show answer and solution

Answer: A, C
(A) true:

\dfrac{f(h)-f(0)}{h}=h\sin\dfrac1h

and

|h\sin(1/h)|\le|h|\to0

, so

f'(0)=0

. For

x\ne0

f'(x)=2x\sin\dfrac1x-\cos\dfrac1x

. (B) false: as

x\to0

the first term tends to

0

but

\cos(1/x)

oscillates between

-1

and

1

without a limit, so

f'(x)\not\to f'(0)=0

. (C) true:

|f'(x)|\le2|x|+1<3

(-1,1)\setminus\{0\}

, and

f'(0)=0

as well. (D) false:

\dfrac{f'(h)-f'(0)}{h}=2\sin\dfrac1h-\dfrac{\cos(1/h)}{h}

is unbounded and has no limit as

h\to0

. Thus

f

is differentiable everywhere with a bounded but discontinuous derivative, so exactly (A) and (C) hold.

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