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JEE Advanced 2022 · Paper 2

A full paper in the 2022 Paper 2 pattern: Physics, Chemistry and Mathematics, 18 questions each, one 180-minute clock. Take it as a timed mock or open it in learn mode and check every answer.

54questions

180 minone clock

180maximum marks

4/36/14easy / medium / hard

Start timed mock Study with solutions

Sections and marking

Each subject has the same 3 sections, 60 marks per subject.

Section	Type	Questions	Marking
Section 1	Integer answer	8	+3 / -1
Section 2	One or more correct	6	+4 all correct, partial +3/+2/+1, -2 otherwise
Section 3	Single correct	4	+3 / -1

Topics in this paper

Physics · 18 questions

Projectile motion on an incline with elastic impacts1
Electrostatics of concentric conductors and energy loss1
Compton scattering and conservation laws1
Stretched string resonance with buoyancy1
Metre bridge and error analysis1
Massive pulley with incline friction1
LC oscillations with two capacitors1
Nuclear reaction Q-value and threshold energy1
Method of images with a grounded plane1
Prism1
Isothermal, adiabatic and free expansion1
Rotating rod in magnetic field1
Draining tank1
Circular motion with tangential acceleration and friction1

Chemistry · 18 questions

Atomic structure1
Electrochemistry1
Coordination compounds1
Ionic equilibrium1
Stereoisomerism in cyclic polyols1
Organic synthesis sequence and NMR symmetry1
Hydrides, carbides and nitrides1
Mole concept1
Gaseous state1
Electrophilic aromatic substitution1
d-block1
Organic acidity and basicity1
Chemical thermodynamics1
s-block1

Mathematics · 18 questions

Matrices2
Conics2
3D geometry2
Complex numbers1
Definite integrals (King's property)1
Conditional probability1
Trigonometric equations1
Differential equations + area1
Calculus1
Theory of equations1
Probability1
Reduction formulae and limits1
Combinatorics1
Area under curves with modulus1

Sample question from this paper

Mathematics · Calculus: functions defined by integrals · one or more options correct

Let

f(x)=\displaystyle\int_{0}^{x}t(t-1)(t-2)\,dt

for

x\in\mathbb R

. Which of the following statements is/are correct?

A. $f$ has a local maximum at $x=1$ and local minima at $x=0$ and $x=2$
B. The equation $f(x)=0$ has exactly two distinct real roots
C. $\displaystyle\int_0^2 f(x)\,dx=\frac4{15}$
D. $f(1)=\dfrac12$

Show answer and solution

Answer: A, B, C
Integrating,

f(x)=\frac{x^4}4-x^3+x^2=\frac{x^2(x-2)^2}{4}

. Option A is true:

f'(x)=x(x-1)(x-2)

changes sign from negative to positive at

0

, from positive to negative at

1

, and from negative to positive at

2

. Option B is true:

f(x)=0

only at

x=0

and

x=2

, both double roots. Option C is true:

\int_0^2\frac{x^2(x-2)^2}4dx=\frac14\cdot2^5B(3,3)=\frac14\cdot\frac{32}{30}=\frac4{15}

. Option D is false:

f(1)=\frac14-1+1=\frac14\ne\frac12

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