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JEE Advanced 2016 · Paper 1

A full paper in the 2016 Paper 1 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

5/35/14easy / 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	Single correct	5	+3 / -1
Section 2	One or more correct	8	+4 all correct, +1 per correct option if no wrong one, -2
Section 3	Integer answer	5	+3, no negative

Topics in this paper

Physics · 18 questions

Rotation1
Thermodynamics1
Ray optics1
Modern physics1
SHM1
Gravitation1
Electrostatics1
Electromagnetic induction1
Current electricity1
Waves1
Heat transfer1
Wave optics1
Magnetism1
Fluid mechanics1

Chemistry · 18 questions

Electrochemistry and solubility equilibrium1
Hydroboration, Grignard addition and dehydration sequence1
Iodometric redox titration1
Parallel reactions and Arrhenius equation1
Chemical equilibrium and Gibbs energy1
Coordination compounds, magnetism and hybridisation1
Aromatic substitution reactions1
Thermodynamics, entropy and expansion work1
Solid state1
Acid-base strength and substituent effects1
p-block oxoacids, shapes and Lewis acidity1
Structural and stereoisomerism counting1
Molecular orbital theory of diatomics1
Ionic equilibrium and selective precipitation1

Mathematics · 18 questions

Probability2
Complex numbers1
Definite integrals1
Conics with area by integration1
3D geometry1
Matrices1
Differential equations1
Theory of equations1
Calculus1
Conics1
Sequences1
Trigonometric equations1
Limits, continuity and differentiability1
Graphs of cubic1

Sample question from this paper

Mathematics · Matrices: nilpotent and powers · one or more options correct

Let

N=\begin{pmatrix}0&1&2\\0&0&3\\0&0&0\end{pmatrix}

and

M=I+N

. Which of the following is/are correct?

A. The $(1,3)$ entry of $M^{10}$ is $135$
B. The $(1,3)$ entry of $M^{-1}$ is $1$
C. The $(2,3)$ entry of $M^{10}$ is $20$
D. $M^n=I$ for some positive integer $n$

Show answer and solution

Answer: B
Since

N

is strictly upper triangular,

N^3=0

and

N^2

has only the

(1,3)

entry, equal to

1\cdot3=3

. Because

I

and

N

commute,

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

. For

n=10

the

(1,3)

entry is

10\cdot2+45\cdot3=155

, not

135

, so (A) is false. The

(2,3)

entry is

10\cdot3=30

, not

20

, so (C) is false. The inverse is

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

, whose

(1,3)

entry is

-2+3=1

, so (B) is true. For (D),

M^n=I

would need

nN+\binom n2N^2=0

, impossible since the

(1,2)

entry is

n\ne0

, so (D) is false.

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