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JEE Advanced 2019 · Paper 2

A full paper in the 2019 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

186maximum marks

5/33/16easy / medium / hard

Start timed mock Study with solutions

Sections and marking

Each subject has the same 3 sections, 62 marks per subject.

Section	Type	Questions	Marking
Section 1	One or more correct	8	+4 all correct, partial +3/+2/+1, -1 otherwise
Section 2	Numerical value	6	+3, no negative
Section 3	Matching lists (2 sets)	4	+3 / -1

Topics in this paper

Physics · 18 questions

AC circuits2
Ray optics2
Rotational dynamics (rolling on incline)1
Fluid mechanics (Torricelli, projectile)1
Simple harmonic motion with sticking mass1
Thermodynamic cycle with kinetic theory1
Electrostatics of conductors (concentric shells)1
Wave optics (YDSE with thin sheet)1
Bohr model with photoelectric effect and de Broglie wavelength1
Electromagnetic induction on an incline1
Collisions with pendulum and friction1
Doppler effect and beats1
Capacitors, charge sharing and energy loss1
Gravitation and elliptical orbits1

Chemistry · 18 questions

Coordination compounds3
Stereoisomerism2
Thermodynamics1
Aldehydes and Cannizzaro reaction1
p-Block oxoacids1
Electrochemistry and ionic equilibrium1
Stereochemistry1
Chemical bonding and molecular shape1
d-Block oxoanions1
Colligative properties1
Chemical kinetics1
Ionic equilibrium and buffers1
Free-radical halogenation and isomerism1
Redox titrations and mole concept1

Mathematics · 18 questions

Calculus applications2
Planes in 3D2
Matrices1
Complex numbers1
Conditional probability1
Ellipse1
Parabola1
Definite integrals1
Differential equations1
Binomial theorem1
Definite integral symmetry1
Area under curves1
Probability distributions1
Vectors1

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

n

be a positive integer. Which of the following statements is (are) correct?

A. The $(1,3)$ entry of $M^{10}$ is $180$ .
B. The $(1,3)$ entry of $M^{-1}$ is $-4$ .
C. $\det\left(M^{n}+M^{-n}\right)=8$ for every positive integer $n$ .
D. $M$ is similar to a diagonal matrix.

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=O

. Hence

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

and, since the binomial series terminates,

M^{-n}=I-nN+\binom{-n}{2}N^2

. (A) The

(1,3)

entry of

M^{n}

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

, which is

180

for

n=10

: correct. (B)

M^{-1}=I-N+N^2

has

(1,3)

entry

+4

, not

-4

: incorrect. (C) Adding, the

N

terms cancel and

\binom n2+\binom{-n}2=n^2

, so

M^n+M^{-n}=2I+n^2N^2

is upper triangular with diagonal

2,2,2

and determinant

8

: correct. (D) The only eigenvalue is

1

, and

M\neq I

, so

M

is not diagonalizable (one Jordan block): incorrect. Answer: A and C.

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