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JEE Advanced 2024 Question Paper & Answers

The official JEE Advanced 2024 question papers, with the official answer key. Attempt as a real timed exam (with negative marking) or switch to practice mode for instant per-question answers and explanations.

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Official PYQ

JEE Advanced 2024 - Paper 1

180 Mins 180 Marks
51Questions
180Max Marks

Sample questions from JEE Advanced 2024 - Paper 1

1Let f(x)f(x) be a continuously differentiable function on the interval (0,∞)(0,\infty) such that f(1)=2f(1)=2 and lim⁡t→xt10f(x)−x10f(t)t9−x9=1\lim_{t\to x}\frac{t^{10}f(x)-x^{10}f(t)}{t^9-x^9}=1 for each x>0x>0. Then, for all x>0x>0, f(x)f(x) is equal to
  • A) 3111x−911x10\dfrac{31}{11x}-\dfrac{9}{11}x^{10}
  • B) 911x+1311x10\dfrac{9}{11x}+\dfrac{13}{11}x^{10}
  • C) −911x+3111x10\dfrac{-9}{11x}+\dfrac{31}{11}x^{10}
  • D) 1311x+911x10\dfrac{13}{11x}+\dfrac{9}{11}x^{10}
Answer: B
2A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question, he gives the correct answer. Assume that the probability of the student giving the correct answer for a question, given that he has guessed it, is 12\frac12. Also assume that the probability of the answer for a question being guessed, given that the student's answer is correct, is 16\frac16. Then the probability that the student knows the answer of a randomly chosen question is
  • A) 112\dfrac{1}{12}
  • B) 17\dfrac{1}{7}
  • C) 57\dfrac{5}{7}
  • D) 512\dfrac{5}{12}
Answer: C
3Let π2<x<π\frac{\pi}{2}<x<\pi be such that cot⁡x=−511\cot x=\dfrac{-5}{\sqrt{11}}. Then (sin⁡11x2)(sin⁡6x−cos⁡6x)+(cos⁡11x2)(sin⁡6x+cos⁡6x)\left(\sin\frac{11x}{2}\right)(\sin 6x-\cos 6x)+\left(\cos\frac{11x}{2}\right)(\sin 6x+\cos 6x) is equal to
  • A) 11−123\dfrac{\sqrt{11}-1}{2\sqrt3}
  • B) 11+123\dfrac{\sqrt{11}+1}{2\sqrt3}
  • C) 11+132\dfrac{\sqrt{11}+1}{3\sqrt2}
  • D) 11−132\dfrac{\sqrt{11}-1}{3\sqrt2}
Answer: B
4Consider the ellipse x29+y24=1\dfrac{x^2}{9}+\dfrac{y^2}{4}=1. Let S(p,q)S(p,q) be a point in the first quadrant such that p29+q24>1\dfrac{p^2}{9}+\dfrac{q^2}{4}>1. Two tangents are drawn from SS to the ellipse, of which one meets the ellipse at one end point of the minor axis and the other meets the ellipse at a point TT in the fourth quadrant. Let RR be the vertex of the ellipse with positive xx-coordinate and OO be the center of the ellipse. If the area of the triangle △ORT\triangle ORT is 32\dfrac32, then which of the following options is correct?
  • A) q=2, p=33q=2,\ p=3\sqrt3
  • B) q=2, p=43q=2,\ p=4\sqrt3
  • C) q=1, p=53q=1,\ p=5\sqrt3
  • D) q=1, p=63q=1,\ p=6\sqrt3
Answer: A
5Let S={a+b2:a,b∈Z}S=\{a+b\sqrt2 : a,b\in\mathbb{Z}\}, T1={(−1+2)n:n∈N}T_1=\{(-1+\sqrt2)^n : n\in\mathbb{N}\}, and T2={(1+2)n:n∈N}T_2=\{(1+\sqrt2)^n : n\in\mathbb{N}\}. Then which of the following statements is (are) TRUE?
  • A) Z∪T1∪T2⊂S\mathbb{Z}\cup T_1\cup T_2\subset S
  • B) T1∩(0,12024)=ϕT_1\cap\left(0,\dfrac{1}{2024}\right)=\phi, where ϕ\phi denotes the empty set.
  • C) T2∩(2024,∞)≠ϕT_2\cap(2024,\infty)\ne\phi
  • D) For any given a,b∈Za,b\in\mathbb{Z}, cos⁡(π(a+b2))+isin⁡(π(a+b2))∈Z\cos(\pi(a+b\sqrt2))+i\sin(\pi(a+b\sqrt2))\in\mathbb{Z} if and only if b=0b=0, where i=−1i=\sqrt{-1}.
Answer: A, C, D

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Official PYQ

JEE Advanced 2024 - Paper 2

180 Mins 173 Marks
49Questions
173Max Marks

Sample questions from JEE Advanced 2024 - Paper 2

1Considering only the principal values of the inverse trigonometric functions, the value of tan⁡(sin⁡−1(35)−2cos⁡−1(25))\tan\left(\sin^{-1}\left(\frac{3}{5}\right)-2\cos^{-1}\left(\frac{2}{\sqrt5}\right)\right) is
  • A) 724\dfrac{7}{24}
  • B) −724\dfrac{-7}{24}
  • C) −524\dfrac{-5}{24}
  • D) 524\dfrac{5}{24}
Answer: B
2Let S={(x,y)∈R×R:x≥0, y≥0, y2≤4x, y2≤12−2x and 3y+8 x≤58}.S=\{(x,y)\in\mathbb{R}\times\mathbb{R} : x\ge0,\ y\ge0,\ y^2\le4x,\ y^2\le12-2x\ \text{and}\ 3y+\sqrt8\,x\le5\sqrt8\}. If the area of the region SS is α2\alpha\sqrt2, then α\alpha is equal to
  • A) 172\dfrac{17}{2}
  • B) 173\dfrac{17}{3}
  • C) 174\dfrac{17}{4}
  • D) 175\dfrac{17}{5}
Answer: B
3Let k∈Rk\in\mathbb{R}. If lim⁡x→0+(sin⁡(sin⁡kx)+cos⁡x+x)2/x=e6,\lim_{x\to0+}\left(\sin(\sin kx)+\cos x+x\right)^{2/x}=e^6, then the value of kk is
  • A) 1
  • B) 2
  • C) 3
  • D) 4
Answer: B
4Let f:R→Rf:\mathbb{R}\to\mathbb{R} be a function defined by f(x)={x2sin⁡(πx2),if x≠0,0,if x=0.f(x)=\begin{cases}x^2\sin\left(\dfrac{\pi}{x^2}\right), & \text{if }x\ne0,\\0, & \text{if }x=0.\end{cases} Then which of the following statements is TRUE?
  • A) f(x)=0f(x)=0 has infinitely many solutions in the interval [11010, ∞)\left[\dfrac{1}{10^{10}},\ \infty\right).
  • B) f(x)=0f(x)=0 has no solutions in the interval [1π, ∞)\left[\dfrac{1}{\pi},\ \infty\right).
  • C) The set of solutions of f(x)=0f(x)=0 in the interval (0, 11010)\left(0,\ \dfrac{1}{10^{10}}\right) is finite.
  • D) f(x)=0f(x)=0 has more than 25 solutions in the interval (1π2, 1π)\left(\dfrac{1}{\pi^2},\ \dfrac{1}{\pi}\right).
Answer: D
5Let SS be the set of all (α,β)∈R×R(\alpha,\beta)\in\mathbb{R}\times\mathbb{R} such that lim⁡x→∞sin⁡(x2)(log⁡ex)αsin⁡(1x2)xαβ(log⁡e(1+x))β=0.\lim_{x\to\infty}\frac{\sin(x^2)(\log_e x)^\alpha\sin\left(\dfrac{1}{x^2}\right)}{x^{\alpha\beta}\left(\log_e(1+x)\right)^\beta}=0. Then which of the following is (are) correct?
  • A) (−1,3)∈S(-1,3)\in S
  • B) (−1,1)∈S(-1,1)\in S
  • C) (1,−1)∈S(1,-1)\in S
  • D) (1,−2)∈S(1,-2)\in S
Answer: B, C

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JEE Advanced 2024 Previous Year Question Paper with Answers (PYQ) | ClassScribe