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JEE Advanced 2024 · Paper 1

A full paper in the 2024 Paper 1 pattern: Physics, Chemistry and Mathematics, 17 questions each, one 180-minute clock. Take it as a timed mock or open it in learn mode and check every answer.

51questions
180 minone clock
180maximum marks
5/31/15easy / medium / hard
Start timed mockStudy with solutions

Sections and marking

Each subject has the same 4 sections, 60 marks per subject.

SectionTypeQuestionsMarking
Section 1Single correct4+3 / -1
Section 2One or more correct3+4 all correct, partial +3/+2/+1, -2 otherwise
Section 3Integer answer6+4, no negative
Section 4Matching lists4+3 / -1

Topics in this paper

Physics · 17 questions

  • Thermodynamics2
  • Rolling motion + SHM1
  • Geometrical optics1
  • Radioactive decay chain1
  • Doppler effect and reflection1
  • Electromagnetic induction with capacitor1
  • Fluid mechanics1
  • Rotation1
  • Electrostatics1
  • Current electricity1
  • Heat conduction in cylindrical layers1
  • Gravitation1
  • Charged particle in crossed E and B fields1
  • AC circuits1

Chemistry · 17 questions

  • Electrochemistry and solubility equilibrium1
  • Stereochemistry of alkene additions1
  • Molecular orbital theory1
  • Chemical kinetics1
  • p-block compounds1
  • Thermodynamics of ideal gas1
  • Organic reaction selectivity1
  • Stereoisomerism1
  • Solid state1
  • Redox titration1
  • Ozonolysis and carbonyl compounds1
  • Ionic equilibrium1
  • Chemical bonding and shapes1
  • Coordination compounds1

Mathematics · 17 questions

  • Theory of equations1
  • Conditional probability and Bayes1
  • Circles1
  • 3D geometry1
  • Matrices1
  • Parabola1
  • Applications of derivatives (integral functions)1
  • Permutations and combinations1
  • Trigonometric equations1
  • Differential equations1
  • Inverse trigonometric functions1
  • Probability1
  • Limits as Riemann sums1
  • Conic sections1

Sample question from this paper

Mathematics · Matrices: powers and adjoint · one or more options correct

Let A=(210021002)A=\begin{pmatrix}2&1&0\\0&2&1\\0&0&2\end{pmatrix}. Which of the following statements is/are correct?
  1. A. The (1,3)(1,3) entry of A6A^6 is 120120
  2. B. tr⁡(A5)=80\operatorname{tr}(A^5)=80
  3. C. det⁡(adj⁡(adj⁡A))=4096\det\big(\operatorname{adj}(\operatorname{adj}A)\big)=4096
  4. D. The (1,3)(1,3) entry of A−1A^{-1} is 116\dfrac1{16}
Show answer and solution
Answer: C
Write A=2I+NA=2I+N with N=(010001000)N=\begin{pmatrix}0&1&0\\0&0&1\\0&0&0\end{pmatrix}, N3=0N^3=0, and 2I2I commuting with NN. Then An=2nI+n2n−1N+(n2)2n−2N2A^n=2^nI+n2^{n-1}N+\binom n2 2^{n-2}N^2, and N2N^2 has a single 11 in position (1,3)(1,3). (A) For n=6n=6 the (1,3)(1,3) entry is (62)24=15⋅16=240\binom62 2^4=15\cdot16=240, not 120120, so false. (B) tr⁡(A5)=3⋅25=96\operatorname{tr}(A^5)=3\cdot2^5=96 because NN and N2N^2 have zero diagonals, so false. (C) For a 3×33\times3 matrix adj⁡(adj⁡A)=(det⁡A)3−2A=8A\operatorname{adj}(\operatorname{adj}A)=(\det A)^{3-2}A=8A, and det⁡(8A)=83det⁡A=512⋅8=4096\det(8A)=8^3\det A=512\cdot8=4096, so true. (D) A−1=12(I+N/2)−1=12(I−N2+N24)A^{-1}=\tfrac12(I+N/2)^{-1}=\tfrac12\left(I-\tfrac N2+\tfrac{N^2}{4}\right), whose (1,3)(1,3) entry is 18\tfrac18, not 116\tfrac1{16}, so false. Only (C) is correct.

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