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JEE Advanced 2017 · Paper 1

A full paper in the 2017 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
183maximum marks
9/31/14easy / medium / hard
Start timed mockStudy with solutions

Sections and marking

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

SectionTypeQuestionsMarking
Section 1One or more correct7+4 all correct, +1 per correct option if no wrong one, -2
Section 2Integer answer5+3, no negative
Section 3Matching lists (2 sets)6+3 / -1

Topics in this paper

Physics · 18 questions

  • Rolling motion combined with SHM1
  • Physical pendulum / SHM with spring1
  • Electrostatics of conducting shells1
  • Electromagnetic induction on inclined rails1
  • Fluid dynamics1
  • Bohr model and photoelectric effect1
  • Doppler effect with wind and reflection1
  • Rolling motion1
  • Experimental errors1
  • DC circuits with capacitor1
  • Heat conduction and calorimetry1
  • Gravitation with cavity1
  • Thermodynamic processes (polytropic)1
  • Adiabatic process1

Chemistry · 18 questions

  • Thermodynamics3
  • Chemical bonding2
  • Carbonyl compounds2
  • Ionic equilibrium1
  • Stereochemistry of alkene addition1
  • p-block1
  • Electrophilic aromatic substitution1
  • Chemical kinetics with total pressure1
  • Electrochemistry1
  • Electrolysis and Faraday's laws1
  • Free-radical halogenation and stereoisomerism1
  • Chemical equilibrium1
  • Redox titration with permanganate1
  • Alkyne hydration and haloform reaction1

Mathematics · 18 questions

  • Maxima and minima3
  • Hyperbola2
  • Complex numbers1
  • Matrices and determinants1
  • Application of derivatives1
  • Probability1
  • Parabola1
  • Three-dimensional geometry1
  • Differential equations1
  • Trigonometric equations1
  • Sequences and series1
  • Permutations and combinations1
  • Definite integrals1
  • Ellipse1

Sample question from this paper

Mathematics · Complex numbers: roots of unity · one or more options correct

Let ω=e2πi/7\omega=e^{2\pi i/7}. Which of the following statements is (are) correct?
  1. A. ∑k=1611−ωk=3\displaystyle\sum_{k=1}^{6}\frac{1}{1-\omega^{k}}=3
  2. B. ∏k=16(2−ωk)=127\displaystyle\prod_{k=1}^{6}\left(2-\omega^{k}\right)=127
  3. C. ∣1+ω+ω3∣2=3\left|1+\omega+\omega^{3}\right|^{2}=3
  4. D. ∑k=16∣1−ωk∣2=14\displaystyle\sum_{k=1}^{6}\left|1-\omega^{k}\right|^{2}=14
Show answer and solution
Answer: A, B, D
The numbers ωk\omega^k (k=1,…,6k=1,\dots,6) are the roots of P(z)=1+z+⋯+z6P(z)=1+z+\dots+z^6. (A) Pairing kk with 7−k7-k gives 11−ωk+11−ω−k=1\frac1{1-\omega^k}+\frac1{1-\omega^{-k}}=1, so the sum over six terms is 33; correct. (B) ∏(2−ωk)=P(2)=27−1=127\prod(2-\omega^k)=P(2)=2^7-1=127; correct. (C) Expanding ∣1+ω+ω3∣2|1+\omega+\omega^3|^2, the cross terms are ω±1,ω±3,ω±2\omega^{\pm1},\omega^{\pm3},\omega^{\pm2}, so it equals 3+2(cos⁡2π7+cos⁡4π7+cos⁡6π7)=3+2(−12)=23+2(\cos\tfrac{2\pi}7+\cos\tfrac{4\pi}7+\cos\tfrac{6\pi}7)=3+2(-\tfrac12)=2, not 33; incorrect. (D) ∣1−ωk∣2=2−2cos⁡2πk7|1-\omega^k|^2=2-2\cos\tfrac{2\pi k}{7}, so the sum is 12−2(−1)=1412-2(-1)=14; correct. Hence A, B and D. Each of these facts follows from the polynomial identity ∏k=16(z−ωk)=1+z+⋯+z6\prod_{k=1}^{6}(z-\omega^k)=1+z+\dots+z^6 and from ∑k=16ωk=−1\sum_{k=1}^{6}\omega^k=-1.

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