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JEE Advanced 2020 · Paper 2

A full paper in the 2020 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
198maximum marks
3/37/14easy / medium / hard
Start timed mockStudy with solutions

Sections and marking

Each subject has the same 3 sections, 66 marks per subject.

SectionTypeQuestionsMarking
Section 1Integer answer6+3 / -1
Section 2One or more correct6+4 all correct, partial +3/+2/+1, -2 otherwise
Section 3Numerical value6+4, no negative

Topics in this paper

Physics · 18 questions

  • Rolling motion and energy1
  • Thermodynamics of mixtures1
  • Bohr model and photoelectric effect1
  • Capacitors with dielectrics1
  • DC circuits, infinite networks1
  • Wave optics, interference1
  • Standing waves, resonance1
  • Electromagnetic induction, sliding rod1
  • Projectile motion on an inclined plane1
  • Thermodynamic cycles1
  • AC circuits, LCR1
  • Gravitation, orbits1
  • Collisions, work-energy with spring and friction1
  • Fluid statics and SHM1

Chemistry · 18 questions

  • Stereochemistry2
  • Electrochemistry2
  • Chemical kinetics2
  • Coordination compounds1
  • Ionic equilibrium1
  • Oxoacids of P and S1
  • Chemical equilibrium1
  • Amines1
  • Nitrogen and phosphorus compounds1
  • Carbonyl compounds1
  • d-block elements1
  • Thermodynamics1
  • Colligative properties1
  • Organic analysis1

Mathematics · 18 questions

  • Probability3
  • Complex numbers2
  • Matrices2
  • 3D geometry2
  • Differential equations2
  • Limits1
  • Conics1
  • Calculus1
  • Inverse trigonometry1
  • Trigonometry1
  • Area under curves1
  • Series1

Sample question from this paper

Mathematics · Calculus: functions defined by integrals · one or more options correct

Let f(x)=∫0x2(t−1)(t−4) dtf(x)=\displaystyle\int_{0}^{x^{2}}(t-1)(t-4)\,dt for real xx. Which of the following statements is/are correct?
  1. A. ff has exactly three points of local minimum and two points of local maximum
  2. B. The least value of ff on R\mathbb R is −83-\dfrac83
  3. C. The equation f(x)=0f(x)=0 has exactly three distinct real roots
  4. D. ff is strictly increasing on (1,2)(1,2) and its local maximum value is 116\dfrac{11}{6}
Show answer and solution
Answer: A, B
Here f(x)=x63−5x42+4x2f(x)=\frac{x^6}{3}-\frac{5x^4}{2}+4x^2 and f′(x)=2x(x2−1)(x2−4)f'(x)=2x(x^2-1)(x^2-4), which changes sign at x=0,±1,±2x=0,\pm1,\pm2. Signs: negative for x<−2x<-2, positive on (−2,−1)(-2,-1), negative on (−1,0)(-1,0), positive on (0,1)(0,1), negative on (1,2)(1,2), positive for x>2x>2. So minima occur at −2,0,2-2,0,2 and maxima at ±1\pm1: (A) is true. f(±2)=−83f(\pm2)=-\frac83 and f→∞f\to\infty, and the other local minimum f(0)=0f(0)=0 is larger, so the global minimum is −83-\frac83: (B) is true. f(x)=x2(2x4−15x2+24)/6f(x)=x^2(2x^4-15x^2+24)/6 has the double root 00 and four more roots from 2u2−15u+24=02u^2-15u+24=0 (u=x2>0u=x^2>0, discriminant 33>033>0, both roots positive), so there are 55 distinct real zeros, not 33: (C) is false. On (1,2)(1,2) we found f′<0f'<0, so ff is decreasing there: (D) is false.

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