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JEE Advanced 2019 · Paper 1

A full paper in the 2019 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
186maximum marks
3/30/21easy / medium / hard
Start timed mockStudy with solutions

Sections and marking

Each subject has the same 3 sections, 62 marks per subject.

SectionTypeQuestionsMarking
Section 1Single correct4+3 / -1
Section 2One or more correct8+4 all correct, partial +3/+2/+1, -1 otherwise
Section 3Numerical value6+3, no negative

Topics in this paper

Physics · 18 questions

  • Rotational mechanics1
  • Kinetic theory and thermodynamics1
  • Geometrical optics1
  • Atomic structure and photoelectric effect1
  • Fluid mechanics1
  • Simple harmonic motion1
  • Electrostatics1
  • Motion of charges in electric and magnetic fields1
  • Electromagnetic induction1
  • Alternating current1
  • Waves and Doppler effect1
  • Experimental physics and errors1
  • Rotational mechanics and collisions1
  • Current electricity and capacitors1

Chemistry · 18 questions

  • Electrochemistry and solubility equilibrium1
  • Stereoisomerism1
  • p-block chemistry and redox1
  • Colligative properties and chemical equilibrium1
  • Chemical bonding and molecular shape1
  • Coordination compounds1
  • Thermodynamics1
  • Solid state1
  • Electrophilic aromatic substitution1
  • Aldol condensation and carbonyl chemistry1
  • Biomolecules and polymers1
  • d-block chemistry1
  • Chemical kinetics1
  • Ionic equilibrium and complex formation1

Mathematics · 18 questions

  • Complex numbers1
  • Matrices1
  • Functional equations and area1
  • Conditional probability1
  • Trigonometry and triangles1
  • Definite integrals1
  • Theory of equations1
  • Lines and planes in 3D1
  • Permutations and combinations1
  • Binomial theorem and identities1
  • Ellipse1
  • Continuity and differentiability1
  • Maxima and minima1
  • Series1

Sample question from this paper

Mathematics · Trigonometry and triangles · one or more options correct

In an acute-angled triangle ABCABC, tan⁡A=2\tan A=2 and tan⁡B=3\tan B=3, and the circumradius is R=10R=\sqrt{10}. Let a,b,ca,b,c be the sides opposite to A,B,CA,B,C. Which of the following statements is/are correct?
  1. A. C=45∘C=45^\circ
  2. B. The area of the triangle is 1212
  3. C. The shortest side has length 44
  4. D. sin⁡2A+sin⁡2B+sin⁡2C=125\sin^2A+\sin^2B+\sin^2C=\dfrac{12}{5}
Show answer and solution
Answer: A, B
Since A+B+C=πA+B+C=\pi, tan⁡C=−tan⁡(A+B)=−2+31−6=1\tan C=-\tan(A+B)=-\frac{2+3}{1-6}=1, so C=45∘C=45^\circ and (A) is correct. With tan⁡A=2\tan A=2, sin⁡A=25\sin A=\frac2{\sqrt5}; with tan⁡B=3\tan B=3, sin⁡B=310\sin B=\frac3{\sqrt{10}}; and sin⁡C=12\sin C=\frac1{\sqrt2}. Sides are 2Rsin⁡2R\sin of the angles: a=42a=4\sqrt2, b=6b=6, c=25c=2\sqrt5. The area is 2R2sin⁡Asin⁡Bsin⁡C=2⋅10⋅35=122R^2\sin A\sin B\sin C=2\cdot10\cdot\frac35=12, so (B) is correct. The shortest side is c=25≈4.47c=2\sqrt5\approx4.47, not 44, so (C) is wrong. Finally sin⁡2A+sin⁡2B+sin⁡2C=45+910+12=115\sin^2A+\sin^2B+\sin^2C=\frac45+\frac9{10}+\frac12=\frac{11}5, not 125\frac{12}5, so (D) is wrong.

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