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JEE Advanced 2026 Question Paper & Answers

The official JEE Advanced 2026 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 2026 - Paper 1

180 Mins 165 Marks
47Questions
165Max Marks

Sample questions from JEE Advanced 2026 - Paper 1

1Consider the function f:(0,∞)β†’(βˆ’βˆž,∞)f:(0,\infty)\to(-\infty,\infty) given by f(x)=x ln⁑(x)βˆ’x+1f(x)=\sqrt{x}\,\ln(x)-x+1. Then which one of the following statements is TRUE?
  • A) The derivative of the function ff is decreasing in the interval (0,1)(0,1)
  • B) The function ff has a local maximum at some point a∈(0,∞)a\in(0,\infty)
  • C) The function ff has a local minimum at some point b∈(0,∞)b\in(0,\infty)
  • D) The function ff has NEITHER a point of local maximum NOR a point of local minimum in the interval (0,∞)(0,\infty)
Answer: D
2Let PP be the point on the parabola y=x2y=x^2 such that the slope of the tangent to the parabola at PP is 44. Let QQ be the point in the first quadrant lying on the circle x2+y2=2x^2+y^2=2 such that the slope of the tangent to the circle at QQ is βˆ’1-1. Let RR be the point in the first quadrant lying on the ellipse x2+4y2=8x^2+4y^2=8 such that the slope of the tangent to the ellipse at RR is βˆ’12-\frac{1}{2}. Then the radius of the circle passing through the points PP, QQ and RR is
  • A) 10\sqrt{10}
  • B) 5\sqrt{5}
  • C) 52\frac{\sqrt{5}}{2}
  • D) 252\sqrt{5}
Answer: C
3Which one of the following matrices can be obtained by performing elementary row transformations on the 3Γ—33\times 3 identity matrix?
  • A) [111111111]\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}
  • B) [111234121]\begin{bmatrix}1&1&1\\2&3&4\\1&2&1\end{bmatrix}
  • C) [111234258]\begin{bmatrix}1&1&1\\2&3&4\\2&5&8\end{bmatrix}
  • D) [111βˆ’112023]\begin{bmatrix}1&1&1\\-1&1&2\\0&2&3\end{bmatrix}
Answer: B
4Considering only the principal values of the inverse trigonometric functions, the value of cotβ‘βˆ’1(cot⁑(βˆ’11))+10sin⁑(2cosβ‘βˆ’1(12))+10sin⁑(2tanβ‘βˆ’1(2))\cot^{-1}(\cot(-11)) + 10\sin\left(2\cos^{-1}\left(\frac{1}{\sqrt{2}}\right)\right) + 10\sin(2\tan^{-1}(2)) is
  • A) 3Ο€+73\pi+7
  • B) 77
  • C) 4Ο€+74\pi+7
  • D) 3Ο€βˆ’53\pi-5
Answer: C
5Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red balls and 12 green balls. All the balls of Box I and Box II are mixed together and a ball is chosen at random from them. Let E1E_1 be the event that the ball chosen belonged to Box I and let E2E_2 be the event that the ball chosen belonged to Box II. Let F1F_1 be the event that the ball chosen is red and let F2F_2 be the event that the ball chosen is green. Then which of the following statements is (are) TRUE?
  • A) The events E1E_1 and F1F_1 are independent
  • B) The events E2E_2 and F2F_2 are dependent
  • C) The conditional probability P(F1∣E1)P(F_1 \mid E_1) is equal to the conditional probability P(F1∣E2)P(F_1 \mid E_2)
  • D) The conditional probability P(F1∣E1)P(F_1 \mid E_1) is greater than the conditional probability P(F2∣E2)P(F_2 \mid E_2)
Answer: A, C

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Official PYQ

JEE Advanced 2026 - Paper 2

180 Mins 176 Marks
53Questions
176Max Marks

Sample questions from JEE Advanced 2026 - Paper 2

1Let aβƒ—,bβƒ—\vec{a}, \vec{b} be two vectors, and let PP, QQ and RR be the points with position vectors aβƒ—\vec{a}, bβƒ—\vec{b} and aβƒ—+bβƒ—\vec{a}+\vec{b}, respectively, with respect to the origin OO. If ∣aβƒ—+bβƒ—βˆ£=21|\vec{a}+\vec{b}|=\sqrt{21}, ∣aβƒ—βˆ’bβƒ—βˆ£=3|\vec{a}-\vec{b}|=3, and aβƒ—\vec{a} and (aβƒ—βˆ’bβƒ—)(\vec{a}-\vec{b}) are perpendicular to each other, then the area of the triangle OPROPR is
  • A) 3\sqrt{3}
  • B) 32\frac{\sqrt{3}}{2}
  • C) 332\frac{3\sqrt{3}}{2}
  • D) 32\frac{3}{2}
Answer: C
2Let TT be the tangent to the parabola y2=16xy^2=16x at the point (64,32)(64,32). Let LL be the tangent to the same parabola at another point (x1,y1)(x_1,y_1) on the parabola. If LL and TT are perpendicular to each other, then the distance between the point (x1,y1)(x_1,y_1) and the focus of the parabola, is
  • A) 154\frac{15}{4}
  • B) 44
  • C) 174\frac{17}{4}
  • D) 55
Answer: C
3Let y:(βˆ’βˆž,∞)β†’(0,∞)y:(-\infty,\infty)\to(0,\infty) be the solution of the differential equation dydx=e5xy3+y3ex+exy4,\frac{dy}{dx}=\frac{e^{5x}y^3+y^3}{e^x+e^xy^4}, satisfying y(0)=12y(0)=\frac{1}{\sqrt{2}}. Then the value of y(log⁑e2)y(\log_e 2) is
  • A) 5+352\frac{\sqrt{5}+\sqrt{35}}{2}
  • B) 7+532\frac{\sqrt{7}+\sqrt{53}}{2}
  • C) 7+532\frac{7+\sqrt{53}}{2}
  • D) 5+352\frac{5+\sqrt{35}}{2}
Answer: B
4The value of the definite integral ∫0213x+3 dx\int_0^2 \frac{1}{3^{x+3}}\,dx is
  • A) 12\frac{1}{2}
  • B) 13\frac{1}{3}
  • C) log⁑e33\frac{\log_e 3}{3}
  • D) log⁑e32\frac{\log_e 3}{2}
Answer: B
5Let R\mathbb{R} denote the set of all real numbers. Consider the polynomial function f:Rβ†’Rf:\mathbb{R}\to\mathbb{R} defined by f(x)=d10dx10((x2βˆ’1)10),Β forΒ allΒ x∈R.f(x)=\frac{d^{10}}{dx^{10}}\left((x^2-1)^{10}\right), \text{ for all } x\in\mathbb{R}. Here d10dx10((x2βˆ’1)10)\frac{d^{10}}{dx^{10}}((x^2-1)^{10}) is the 10th order derivative of the function (x2βˆ’1)10(x^2-1)^{10}. Then which of the following statements is (are) TRUE?
  • A) The coefficient of x8x^8 in the polynomial f(x)f(x) is (βˆ’10)(18!8!)(-10)\left(\frac{18!}{8!}\right)
  • B) The value of f(1)+f(βˆ’1)f(1)+f(-1) is equal to 10! 21110!\,2^{11}
  • C) The degree of the polynomial f(x)f(x) is 10
  • D) The constant term of the polynomial f(x)f(x) is βˆ’(10!5!)-\left(\frac{10!}{5!}\right)
Answer: A, B, C

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JEE Advanced 2026 Previous Year Question Paper with Answers (PYQ) | ClassScribe