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JEE Advanced 2025 Question Paper & Answers

The official JEE Advanced 2025 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 2025 - Paper 1

180 Mins 171 Marks
48Questions
171Max Marks

Sample questions from JEE Advanced 2025 - Paper 1

1Let R\mathbb{R} denote the set of all real numbers. Let ai,bi∈Ra_i, b_i \in \mathbb{R} for i∈{1,2,3}i\in\{1,2,3\}. Define the functions f:R→Rf:\mathbb{R}\to\mathbb{R}, g:R→Rg:\mathbb{R}\to\mathbb{R}, and h:R→Rh:\mathbb{R}\to\mathbb{R} by f(x)=a1+10x+a2x2+a3x3+x4,f(x)=a_1+10x+a_2x^2+a_3x^3+x^4, g(x)=b1+3x+b2x2+b3x3+x4,g(x)=b_1+3x+b_2x^2+b_3x^3+x^4, h(x)=f(x+1)−g(x+2).h(x)=f(x+1)-g(x+2). If f(x)eg(x)f(x) e g(x) for every x∈Rx\in\mathbb{R}, then the coefficient of x3x^3 in h(x)h(x) is
  • A) 8
  • B) 2
  • C) -4
  • D) -6
Answer: C
2Three students S1S_1, S2S_2, and S3S_3 are given a problem to solve. Consider the following events: UU: At least one of S1S_1, S2S_2, and S3S_3 can solve the problem,
VV: S1S_1 can solve the problem, given that neither S2S_2 nor S3S_3 can solve the problem,
WW: S2S_2 can solve the problem and S3S_3 cannot solve the problem,
TT: S3S_3 can solve the problem. For any event EE, let P(E)P(E) denote the probability of EE. If P(U)=12P(U)=\frac{1}{2}, P(V)=110P(V)=\frac{1}{10}, and P(W)=112P(W)=\frac{1}{12}, then P(T)P(T) is equal to
  • A) 1336\frac{13}{36}
  • B) 13\frac{1}{3}
  • C) 1960\frac{19}{60}
  • D) 14\frac{1}{4}
Answer: A
3Let R\mathbb{R} denote the set of all real numbers. Define the function f:R→Rf:\mathbb{R}\to\mathbb{R} by f(x)={2−2x2−x2sin⁡1xif xe0,2if x=0.f(x)=\begin{cases}2-2x^2-x^2\sin\frac{1}{x} & \text{if } x e 0, \\ 2 & \text{if } x=0.\end{cases} Then which one of the following statements is TRUE?
  • A) The function ff is NOT differentiable at x=0x=0
  • B) There is a positive real number δ\delta, such that ff is a decreasing function on the interval (0,δ)(0,\delta)
  • C) For any positive real number δ\delta, the function ff is NOT an increasing function on the interval (−δ,0)(-\delta,0)
  • D) x=0x=0 is a point of local minima of ff
Answer: C
4Consider the matrix P=(200020003).P=\begin{pmatrix}2&0&0\\0&2&0\\0&0&3\end{pmatrix}. Let the transpose of a matrix XX be denoted by XTX^T. Then the number of 3×33\times 3 invertible matrices QQ with integer entries, such that Q−1=QTQ^{-1}=Q^T and PQ=QPPQ=QP, is
  • A) 32
  • B) 8
  • C) 16
  • D) 24
Answer: C
5Let L1L_1 be the line of intersection of the planes given by the equations 2x+3y+z=42x+3y+z=4 and x+2y+z=5x+2y+z=5. Let L2L_2 be the line passing through the point P(2,−1,3)P(2,-1,3) and parallel to L1L_1. Let MM denote the plane given by the equation 2x+y−2z=62x+y-2z=6. Suppose that the line L2L_2 meets the plane MM at the point QQ. Let RR be the foot of the perpendicular drawn from PP to the plane MM. Then which of the following statements is (are) TRUE?
  • A) The length of the line segment PQPQ is 939\sqrt{3}
  • B) The length of the line segment QRQR is 15
  • C) The area of △PQR\triangle PQR is 32234\frac{3}{2}\sqrt{234}
  • D) The acute angle between the line segments PQPQ and PRPR is cos⁡−1(123)\cos^{-1}\left(\frac{1}{2\sqrt{3}}\right)
Answer: A, C

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Official PYQ

JEE Advanced 2025 - Paper 2

180 Mins 177 Marks
47Questions
177Max Marks

Sample questions from JEE Advanced 2025 - Paper 2

1Let x0x_0 be the real number such that ex0+x0=0e^{x_0}+x_0=0. For a given real number α\alpha, define g(x)=3xex+3x−αex−αx3(ex+1)g(x)=\frac{3xe^x+3x-\alpha e^x-\alpha x}{3(e^x+1)} for all real numbers xx. Then which one of the following statements is TRUE?
  • A) For α=2\alpha=2, lim⁡x→x0∣g(x)+ex0x−x0∣=0\lim_{x\to x_0}\left|\frac{g(x)+e^{x_0}}{x-x_0}\right|=0
  • B) For α=2\alpha=2, lim⁡x→x0∣g(x)+ex0x−x0∣=1\lim_{x\to x_0}\left|\frac{g(x)+e^{x_0}}{x-x_0}\right|=1
  • C) For α=3\alpha=3, lim⁡x→x0∣g(x)+ex0x−x0∣=0\lim_{x\to x_0}\left|\frac{g(x)+e^{x_0}}{x-x_0}\right|=0
  • D) For α=3\alpha=3, lim⁡x→x0∣g(x)+ex0x−x0∣=23\lim_{x\to x_0}\left|\frac{g(x)+e^{x_0}}{x-x_0}\right|=\frac{2}{3}
Answer: C
2Let R\mathbb{R} denote the set of all real numbers. Then the area of the region {(x,y)∈R×R:x>0, y>1x, 5x−4y−1>0, 4x+4y−17<0}\left\{(x,y)\in\mathbb{R}\times\mathbb{R} : x>0,\ y>\frac{1}{x},\ 5x-4y-1>0,\ 4x+4y-17<0\right\} is
  • A) 1716−log⁡e4\frac{17}{16}-\log_e 4
  • B) 338−log⁡e4\frac{33}{8}-\log_e 4
  • C) 578−log⁡e4\frac{57}{8}-\log_e 4
  • D) 172−log⁡e4\frac{17}{2}-\log_e 4
Answer: B
3The total number of real solutions of the equation θ=tan⁡−1(2tan⁡θ)−12sin⁡−1(6tan⁡θ9+tan⁡2θ)\theta=\tan^{-1}(2\tan\theta)-\frac{1}{2}\sin^{-1}\left(\frac{6\tan\theta}{9+\tan^2\theta}\right) is (Here, the inverse trigonometric functions sin⁡−1x\sin^{-1}x and tan⁡−1x\tan^{-1}x assume values in [−π2,π2]\left[-\frac{\pi}{2},\frac{\pi}{2}\right] and (−π2,π2)\left(-\frac{\pi}{2},\frac{\pi}{2}\right), respectively.)
  • A) 1
  • B) 2
  • C) 3
  • D) 5
Answer: C
4Let SS denote the locus of the point of intersection of the pair of lines 4x−3y=12α,4αx+3αy=12,4x-3y=12\alpha, \quad 4\alpha x+3\alpha y=12, where α\alpha varies over the set of non-zero real numbers. Let TT be the tangent to SS passing through the points (p,0)(p,0) and (0,q)(0,q), q>0q>0, and parallel to the line 4x−32y=04x-\frac{3}{\sqrt{2}}y=0. Then the value of pqpq is
  • A) −62-6\sqrt{2}
  • B) −32-3\sqrt{2}
  • C) −92-9\sqrt{2}
  • D) −122-12\sqrt{2}
Answer: A
5Let I=(1001)I=\begin{pmatrix}1&0\\0&1\end{pmatrix} and P=(2003)P=\begin{pmatrix}2&0\\0&3\end{pmatrix}. Let Q=(xzy4)Q=\begin{pmatrix}x&z\\y&4\end{pmatrix} for some non-zero real numbers x,y,zx,y,z, for which there is a 2×22\times2 matrix RR with all entries being non-zero real numbers, such that QR=RPQR=RP. Then which of the following statements is (are) TRUE?
  • A) The determinant of Q−2IQ-2I is zero
  • B) The determinant of Q−6IQ-6I is 12
  • C) The determinant of Q−3IQ-3I is 15
  • D) yz=2yz=2
Answer: A, B

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JEE Advanced 2025 Previous Year Question Paper with Answers (PYQ) | ClassScribe