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JEE Advanced 2018 · Paper 2

A full paper in the 2018 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
180maximum marks
3/30/21easy / medium / hard
Start timed mockStudy with solutions

Sections and marking

Each subject has the same 3 sections, 60 marks per subject.

SectionTypeQuestionsMarking
Section 1One or more correct6+4 all correct, partial +3/+2/+1, -2 otherwise
Section 2Numerical value8+3, no negative
Section 3Matching lists4+3 / -1

Topics in this paper

Physics · 18 questions

  • Rotation and rolling on an incline1
  • Thermodynamic cycle of an ideal gas1
  • Motion of a charge in crossed electric and magnetic fields1
  • Reflection and transmission of waves on strings1
  • Photoelectric effect and de Broglie wavelength1
  • Geometrical optics of a silvered lens1
  • Fluid dynamics1
  • Simple harmonic motion with an inelastic collision1
  • Capacitor with dielectric connected to a battery1
  • RC charging with Thevenin equivalent1
  • Electromagnetic induction on an incline1
  • Young's double-slit experiment with a film1
  • Bohr model and photon recoil1
  • Heat conduction through composite rods1

Chemistry · 18 questions

  • Chemical kinetics2
  • Chemical bonding1
  • Coordination compounds1
  • Alcohols1
  • Chemical equilibrium1
  • p-block1
  • Real gases1
  • Nuclear chemistry1
  • Ionic equilibrium and colligative properties1
  • Solid state1
  • Isomerism1
  • Electrochemistry1
  • Thermochemistry1
  • Named reactions1

Mathematics · 18 questions

  • Conic sections3
  • Complex numbers2
  • Probability2
  • 3D geometry2
  • Definite integrals2
  • Limits, continuity and definite integral of a piecewise function1
  • Differential equations1
  • Trigonometry and algebraic identities1
  • Matrices1
  • Series1
  • Permutations and combinations1
  • Area under curves with modulus1

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}, and define α=ω+ω2+ω4\alpha=\omega+\omega^{2}+\omega^{4} and β=ω3+ω5+ω6\beta=\omega^{3}+\omega^{5}+\omega^{6}. Which of the following statements is (are) correct?
  1. A. α+β=−1\alpha+\beta=-1
  2. B. α\alpha is a root of the equation x2+x+2=0x^{2}+x+2=0
  3. C. ∣α∣=2|\alpha|=2
  4. D. Im⁡(α)=72\operatorname{Im}(\alpha)=\dfrac{\sqrt7}{2}
Show answer and solution
Answer: A, B, D
Since 1+ω+⋯+ω6=01+\omega+\dots+\omega^6=0, the six non-trivial powers add to −1-1, so α+β=−1\alpha+\beta=-1 (A true). Expanding αβ\alpha\beta gives nine terms ωa+b\omega^{a+b}; exactly three of them have a+b≡0(mod7)a+b\equiv0\pmod 7 and contribute 11 each, while the other six are the six distinct non-trivial powers, summing to −1-1. So αβ=3−1=2\alpha\beta=3-1=2. Hence α,β\alpha,\beta are roots of x2−(α+β)x+αβ=x2+x+2x^{2}-(\alpha+\beta)x+\alpha\beta=x^{2}+x+2 (B true), giving α,β=−1±i72\alpha,\beta=\frac{-1\pm i\sqrt7}{2}. Then ∣α∣2=1+74=2|\alpha|^{2}=\frac{1+7}{4}=2, so ∣α∣=2≠2|\alpha|=\sqrt2\neq2 (C false). Because sin⁡2π7+sin⁡4π7+sin⁡8π7>0\sin\frac{2\pi}{7}+\sin\frac{4\pi}{7}+\sin\frac{8\pi}{7}>0, α\alpha is the root with positive imaginary part, Im⁡α=72\operatorname{Im}\alpha=\frac{\sqrt7}{2} (D true). A numerical evaluation confirms all of this. Answer: A, B, D.

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