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JEE Advanced 2016 · Paper 2

A full paper in the 2016 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
1/37/16easy / medium / hard
Start timed mockStudy with solutions

Sections and marking

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

SectionTypeQuestionsMarking
Section 1Single correct6+3 / -1
Section 2One or more correct8+4 all correct, +1 per correct option if no wrong one, -2
Section 3Paragraph based (2 sets)4+3, no negative

Topics in this paper

Physics · 18 questions

  • Modern physics3
  • Rotation2
  • Thermodynamics1
  • Wave optics1
  • Electromagnetic induction1
  • SHM1
  • Waves1
  • Electrostatics1
  • Magnetism1
  • Heat transfer1
  • Nuclear physics1
  • Ray optics1
  • AC circuits1
  • Circular motion1

Chemistry · 18 questions

  • Electrochemistry and solubility equilibrium1
  • Isomerism and free-radical halogenation1
  • Oxoacids of phosphorus1
  • Parallel first-order reactions1
  • Pinacol rearrangement and haloform reaction1
  • Coordination compounds1
  • Thermodynamics1
  • Acidity and basicity1
  • p-block1
  • Colligative properties and association1
  • Cannizzaro reaction1
  • Redox stoichiometry of permanganate1
  • Bohr model of hydrogen-like ions1
  • Chemical equilibrium1

Mathematics · 18 questions

  • Parabola2
  • Limits and Riemann sums2
  • Complex numbers and roots of unity1
  • Circles1
  • Conditional probability and Bayes theorem1
  • Permutations and combinations1
  • Three-dimensional geometry1
  • Matrices and nilpotent powers1
  • Continuity and differentiability1
  • Trigonometric equations1
  • Ellipse1
  • Differential equations1
  • Sequences1
  • Theory of equations1

Sample question from this paper

Mathematics · Continuity and differentiability · one or more options correct

Let f(x)={x2sin⁡1x,x≠00,x=0f(x)=\begin{cases}x^{2}\sin\dfrac1x,&x\neq0\\[2mm]0,&x=0\end{cases}, g(x)=f(x)+∣x∣g(x)=f(x)+|x| and F(x)=∫0xf(t) dtF(x)=\displaystyle\int_{0}^{x}f(t)\,dt. Then
  1. A. ff is differentiable at x=0x=0 and f′(0)=0f'(0)=0
  2. B. f′f' is continuous at x=0x=0
  3. C. gg is not differentiable at x=0x=0
  4. D. FF is twice differentiable at x=0x=0
Show answer and solution
Answer: A, C, D
(A) True: f(h)−f(0)h=hsin⁡1h→0\frac{f(h)-f(0)}{h}=h\sin\frac1h\to0, so f′(0)=0f'(0)=0. (B) False: for x≠0x\ne0, f′(x)=2xsin⁡1x−cos⁡1xf'(x)=2x\sin\frac1x-\cos\frac1x, and cos⁡1x\cos\frac1x has no limit as x→0x\to0, so f′f' is discontinuous at 00. (C) True: g′(0+)=f′(0)+1=1g'(0^+)=f'(0)+1=1 while g′(0−)=f′(0)−1=−1g'(0^-)=f'(0)-1=-1; since ∣x∣|x| has a corner and ff is differentiable, the sum has the corner. (D) True: ff is continuous, so F′(x)=f(x)F'(x)=f(x) by the fundamental theorem, and F′′(0)=f′(0)=0F''(0)=f'(0)=0 exists. (F would fail to be thrice differentiable at 0, since f′f' is discontinuous there, but that is not asked.) Hence the correct options are (A), (C) and (D).

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