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JEE Advanced 2017 · Paper 2

A full paper in the 2017 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
183maximum marks
3/35/16easy / medium / hard
Start timed mockStudy with solutions

Sections and marking

Each subject has the same 3 sections, 61 marks per subject.

SectionTypeQuestionsMarking
Section 1Single correct7+3 / -1
Section 2One or more correct7+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

  • Rolling on a moving plank1
  • Thermodynamic process, heat capacity1
  • YDSE with thin sheet in a medium1
  • Bohr model and photoelectric effect1
  • Capacitor with dielectric slab1
  • EMI with capacitor1
  • SHM of floating body in accelerated frame1
  • Rotation of rod about hinge1
  • Black-body radiation1
  • Charged particle in a bounded magnetic field1
  • X-rays and Moseley's law1
  • Series LCR circuit1
  • Standing waves in strings and pipes1
  • Efflux and projectile motion1

Chemistry · 18 questions

  • Electrochemistry2
  • Chemical equilibrium1
  • Chemical kinetics1
  • Inorganic1
  • Pinacol rearrangement, haloform and Hofmann degradation1
  • Ionic equilibrium1
  • Polymers1
  • p-block and noble gas1
  • Coordination compounds1
  • Chemical bonding1
  • Stereoisomerism1
  • Thermodynamics1
  • Surface chemistry1
  • Nucleophilic substitution1

Mathematics · 18 questions

  • Area under curves2
  • Sequences and series2
  • Theory of equations1
  • Probability1
  • Definite integrals1
  • 3D geometry (planes)1
  • Matrices1
  • Integral equations1
  • Complex numbers1
  • Application of derivatives1
  • Circles1
  • Probability (conditional)1
  • 3D geometry (lines)1
  • Binomial theorem1

Sample question from this paper

Mathematics · Complex numbers · one or more options correct

Let zk=e2πik/7z_k=e^{2\pi i k/7} for k=1,2,…,6k=1,2,\dots,6 be the non-real seventh roots of unity. Which of the following is/are correct?
  1. A. ∑k=16∣1−zk∣2=14\displaystyle\sum_{k=1}^{6}|1-z_k|^2=14
  2. B. ∏k=16(1−zk)=7\displaystyle\prod_{k=1}^{6}(1-z_k)=7
  3. C. ∑k=1611−zk=72\displaystyle\sum_{k=1}^{6}\frac{1}{1-z_k}=\frac72
  4. D. ∑k=16(1−zk)2=7\displaystyle\sum_{k=1}^{6}(1-z_k)^2=7
Show answer and solution
Answer: A, B, D
The zkz_k are roots of 1+z+⋯+z6=01+z+\dots+z^6=0, so ∑zk=−1\sum z_k=-1, ∑zk2=−1\sum z_k^2=-1 and, since ∏(x−zk)=1+x+⋯+x6\prod(x-z_k)=1+x+\dots+x^6, putting x=1x=1 gives ∏(1−zk)=7\prod(1-z_k)=7, so (B) is true. For (A): ∣1−zk∣2=2−2cos⁡2πk7|1-z_k|^2=2-2\cos\frac{2\pi k}{7}, so the sum is 12−2(−1)=1412-2(-1)=14, true. For (C): 11−zk\frac{1}{1-z_k} has real part 12\frac12 and the imaginary parts cancel in conjugate pairs, so the sum is 6⋅12=36\cdot\frac12=3, not 72\frac72; false. For (D): ∑(1−2zk+zk2)=6+2−1=7\sum(1-2z_k+z_k^2)=6+2-1=7, true. Each statement uses a different symmetric function of the roots of unity, and none needs the explicit angles beyond the cosine sum.

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