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JEE Advanced 2022 · Paper 1

A full paper in the 2022 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
180maximum marks
4/30/20easy / medium / hard
Start timed mockStudy with solutions

Sections and marking

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

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

Topics in this paper

Physics · 18 questions

  • Rolling motion3
  • Thermodynamics2
  • Heat engines1
  • Wave optics1
  • Atomic and photoelectric1
  • Electromagnetic induction1
  • Fluids and SHM1
  • Gravitation1
  • Capacitors1
  • Electrostatics1
  • LR circuits1
  • Ray optics1
  • Photoelectric effect1
  • Atomic physics1

Chemistry · 18 questions

  • Eudiometry and gas stoichiometry1
  • Graham's law of effusion with gas mixtures1
  • Nuclear chemistry and radioactive dating1
  • Bohr model, photoelectric effect and de Broglie wavelength1
  • Surface chemistry1
  • Structural isomerism and stereoisomerism of carbonyl compounds1
  • Thermochemistry1
  • Polymers1
  • General principles of metallurgy1
  • s-block elements and their compounds1
  • Amino acids, peptides and isoelectric points1
  • Stereochemistry of substitution and elimination1
  • Kinetic theory and real gases1
  • Phenols, anilines and diazonium salts1

Mathematics · 18 questions

  • Theory of equations1
  • Theory of equations and extrema of cubic1
  • Probability1
  • 3D geometry1
  • Area under curves, conics1
  • Triangles1
  • Limits and Riemann sums1
  • Matrices, Cayley-Hamilton1
  • Trigonometric equations1
  • Continuity and differentiability1
  • Parabola1
  • Vectors1
  • Complex numbers1
  • Binomial theorem1

Sample question from this paper

Mathematics · Trigonometric equations · one or more options correct

Consider the equation sin⁡x+sin⁡2x+sin⁡3x=cos⁡x+cos⁡2x+cos⁡3x\sin x+\sin2x+\sin3x=\cos x+\cos2x+\cos3x for x∈[0,2π]x\in[0,2\pi]. Which of the following statements is/are correct?
  1. A. The equation has exactly six solutions in [0,2π][0,2\pi].
  2. B. The sum of all solutions in [0,2π][0,2\pi] is 6π6\pi.
  3. C. Exactly three solutions lie in the open interval (0,π)(0,\pi).
  4. D. x=π2x=\dfrac{\pi}{2} is a solution.
Show answer and solution
Answer: A, C
Grouping, sin⁡2x(1+2cos⁡x)=cos⁡2x(1+2cos⁡x)\sin2x(1+2\cos x)=\cos2x(1+2\cos x), i.e. (1+2cos⁡x)(sin⁡2x−cos⁡2x)=0(1+2\cos x)(\sin2x-\cos2x)=0. Then cos⁡x=−12\cos x=-\frac12 gives x=2π3,4π3x=\frac{2\pi}3,\frac{4\pi}3, and tan⁡2x=1\tan2x=1 gives x=π8,5π8,9π8,13π8x=\frac\pi8,\frac{5\pi}8,\frac{9\pi}8,\frac{13\pi}8. (A) true: six solutions. (B) false: the sum is 2π+28π8=11π22\pi+\frac{28\pi}{8}=\frac{11\pi}2. (C) true: π8,5π8,2π3\frac\pi8,\frac{5\pi}8,\frac{2\pi}3 lie in (0,π)(0,\pi). (D) false: at x=π2x=\frac\pi2 the left side is 1+0−1=01+0-1=0 while the right side is 0−1+0=−10-1+0=-1.

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