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JEE Main & Advanced Mathematics PYQs with solutions

Chapter-wise Mathematics previous year questions for JEE Main & Advanced: 14,870 questions in 39 chapters. Largest chapters: Application of Derivatives (795), Three Dimensional Geometry (756) and Sequences and Series (748). Open any question for options, correct answer and solution.

14,870 questions39 chapters

JEE Mathematics PYQs · Year-wise Maths PYQs

JEE Mathematics chapters

Application of Derivatives

795 PYQs

Three Dimensional Geometry

756 PYQs

Sequences and Series

748 PYQs

Functions

700 PYQs

Definite Integration

692 PYQs

Vector Algebra

616 PYQs

Differential Equations

586 PYQs

Continuity and Differentiability

576 PYQs

Probability

561 PYQs

Complex Number

551 PYQs

Binomial Theorem

550 PYQs

Quadratic Equation

517 PYQs

Determinants

508 PYQs

Circle

506 PYQs

Matrices

506 PYQs

Permutation and Combination

503 PYQs

Limits

497 PYQs

Straight Lines

497 PYQs

Area Under Curves

435 PYQs

Parabola

411 PYQs

Statistics

323 PYQs

Ellipse

313 PYQs

Indefinite Integration

297 PYQs

Hyperbola

276 PYQs

Quadratic Equation

269 PYQs

Inverse Trigonometric Functions

266 PYQs

Sets and Relations

242 PYQs

Trigonometric Equations

236 PYQs

Mathematical Reasoning

204 PYQs

Differentiation

190 PYQs

Trigonometric Ratios & Identities

189 PYQs

Indefinite and Definite Integration

182 PYQs

Heights and Distances

137 PYQs

Basics of Mathematics

90 PYQs

Trigonometry

66 PYQs

Properties of Triangles

61 PYQs

Sequences and Series

10 PYQs

Mathematical Induction

6 PYQs

Pair of Lines

2 PYQs

Sample Mathematics questions

Consider the function f: (0, ∞) arrow (-∞, ∞) given by f(x) = x \, _e(x) - x + 1 . Then which one of the following statements is TRUE?

JEE Advanced 2026 Solution View → 2

Let P be the point on the parabola y = x^2 such that the slope of the tangent to the parabola at the point P is 4 . Let Q be the point in the first quadrant lying on the circle

JEE Advanced 2026 Solution View → 3

Let f: ℝ arrow ℝ be a differentiable function such that f((x+y)/(3)) = (f(x) + f(y))/(3) for all x, y ∈ ℝ , and f'(0) = 3 . Then the minimum value of the function g(x) = 3 + e^x

JEE Main 2026 Solution View → 4

Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π] , and the curve C_2 given by y = e^ -x ( x + x) for x ∈ [0, 10π] . Let n be the total number of points of

JEE Advanced 2026 Solution View → 5

Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: If α is the area of the common region that lies inside both the given ellipses, then the

JEE Advanced 2026 Solution View → 6

The area of the region \ (x, y) : x^2 - 8x ≤ y ≤ -x\ is :

JEE Main 2026 Solution View → 7

The sum of squares of all the real solutions of the equation _ (x+1) (2x^2+5x+3) = 4 - _ (2x+3) (x^2+2x+1) is equal to ________.

JEE Main 2026 Solution View → 8

If the set of all solutions of |x^2 + x - 9| = |x| + |x^2 - 9| is [α, β] ∪ [γ, ∞) , then (α^2 + β^2 + γ^2) is equal to:

JEE Main 2026 Solution View → 9

The number of the real solutions of the equation: x|x+3|+|x-1|-2=0 is

JEE Main 2026 Solution View → 10

If 26((2^3)/(3) 12 2 + (2^5)/(5) 12 4 + (2^7)/(7) 12 6 + … + 2^ 13 13 12 12 ) = 3^ 13 - α , then α is equal to:

JEE Main 2026 Solution View → 11

If (1 - x^3)^ 10 = ∑ _ r=0 ^ 10 a_r x^r (1-x)^ 30-2r , then 9a_9 a_ 10 is equal to __________.

JEE Main 2026 Solution View → 12

If the coefficients of the middle terms in the binomial expansions of (1 + α x)^ 26 and (1 - α x)^ 28 , α ≠ 0 , are equal, then the value of α is:

JEE Main 2026 Solution View → 13

Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) The circle with centre (1, 2) and touching the straight line 3x + 4y =

JEE Advanced 2026 Solution View → 14

Consider the circle C: x^2+y^2-6x-8y-11=0 . Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from

JEE Main 2026 Solution View → 15

Let C be a circle having centre in the first quadrant and touching the x -axis at a distance of 3 units from the origin. If the circle C has an intercept of length 6 3 on y -axis

JEE Main 2026 Solution View → 16

The number of values of z ∈ ℂ , satisfying the equations |z-(4+8i)|= 10 and |z-(3+5i)|+|z-(5+11i)|=4 5 , is:

JEE Main 2026 Solution View → 17

Let S = \ z ∈ ℂ : z^2 + 6 \,iz - 3 = 0\ . Then ∑ _ z ∈ S z^8 is equal to :

JEE Main 2026 Solution View → 18

Let the set of all values of k ∈ ℝ such that the equation z( z + 2 + i) + k(2 + 3i) = 0 , z ∈ ℂ , has at least one solution, be the interval [α, β] . Then 9(α + β) is equal to:

JEE Main 2026 Solution View → 19

Let ℝ denote the set of all real numbers. Let f : ℝ arrow ℝ be an arbitrary function and let g : ℝ arrow ℝ be the function defined by g(x) = x f(x) , for all x ∈ ℝ . Then which of

JEE Advanced 2026 Solution View → 20

Consider the function f : (-(π)/(2), (π)/(2)) arrow (-∞, ∞) defined by f(x) = (|x| + |x - 1|) x + [x x] , where [x x] is the greatest integer less than or equal to x x . Let α be

JEE Advanced 2026 Solution View → 21

For a real number α , let [α] denote the greatest integer less than or equal to α . For a finite set S , let |S| denote the number of elements in the set S . Consider the

JEE Advanced 2026 Solution View → 22

The value of the definite integral ∫_ 0 ^ 2 1 3^ (x+3)/(2) \, dx is

JEE Advanced 2026 Solution View → 23

The value of the integral ∫_ 0 ^ 2 x(x^2+x+1) ( x+1 )( x^4+x^2+1 ) \, dx is equal to:

JEE Main 2026 Solution View → 24

If ∫_ π/6 ^ π/4 ( (x-(π)/(3)) (x+(π)/(3))+1)dx = α _e( 3 -1) , then 9α^2 is equal to ________.

JEE Main 2026 Solution View → 25

If the system of linear equations: x+y+z=6 , x+2y+5z=10 , 2x+3y+λ z=μ has infinitely many solutions, then the value of λ+μ equals:

JEE Main 2026 Solution View → 26

The sum of all possible values of θ ∈ [0, 2π] , for which the system of equations : x 3θ - 8y - 12z = 0 x 2θ + 3y + 3z = 0 x + y + 3z = 0 has a non-trivial solution, is equal to :

JEE Main 2026 Solution View → 27

If f: N arrow Z is defined by f(n) = vmatrix n & -1 & -5 -2n^2 & 3(2k+1) & 2k+1 -3n^3 & 3k(2k+1) & 3k(k+2)+1 vmatrix , k ∈ N , and ∑_ n=1 ^ k f(n) = 98 , then k is equal to :

JEE Main 2026 Solution View → 28

Let y : (-∞, ∞) arrow (0, ∞) be the solution of the differential equation (dy)/(dx) = e^ 5x y^3 + y^3 e^x + e^x y^4 , satisfying y(0) = 1 2 . Then the value of y( _e 2) is

JEE Advanced 2026 Solution View → 29

Let y = f(x) be the real valued function defined on the interval (0, ∞) , satisfying y(1) = 0 and the differential equation x(dy)/(dx) = y - x^3 . Then which of the following

JEE Advanced 2026 Solution View → 30

Let y=y(x) be the solution of the differential equation x 1-x^2 \,dy + (y 1-x^2 - x ^ -1 x)dx = 0 , x ∈ (0, 1) , _ x→ 1^- y(x) = 1 . Then y((1)/(2)) equals:

JEE Main 2026 Solution View → 31

Let ℝ denote the set of all real numbers. Consider the polynomial function f: ℝ arrow ℝ defined by f(x) = d^ 10 dx^ 10 ((x^2 - 1)^ 10 ) , for all x ∈ ℝ . Here d^ 10 dx^ 10 ((x^2

JEE Advanced 2026 Solution View → 32

Let f(x) and g(x) be twice differentiable functions satisfying f''(x) = g''(x) for all x ∈ R , f'(1) = 2g'(1) = 4 and g(2) = 3f(2) = 9 . Then f(25) - g(25) is equal to :

JEE Main 2026 Solution View → 33

Let f be a real polynomial of degree n such that f(x) = f'(x) f''(x) , for all x ∈ ℝ . If f(0) = 0 , then 36(f'(2) + f''(2) + ∫_0^2 f(x)\,dx) is equal to:

JEE Main 2026 Solution View → 34

Consider the ellipse E given by (x^2)/(18) + (y^2)/(12) = 1 . Let H be the hyperbola whose eccentricity is the reciprocal of the eccentricity of E and whose foci are the same as

JEE Advanced 2026 Solution View → 35

Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: Let P be the point in the first quadrant where the given ellipses intersect. If θ is the

JEE Advanced 2026 Solution View → 36

Let (x^2)/(f(a^2+7a+3)) + (y^2)/(f(3a+15)) = 1 represent an ellipse with major axis along y -axis, where f is a strictly decreasing positive function on ℝ . If the set of all

JEE Main 2026 Solution View → 37

Let ℕ denote the set of all positive integers. Consider the sets A = \ 1, 2, 3, 4, 5\ and B = \ 1, 2, 3, 4, 5, 6, 7\ . Let S be the set of all functions f: A arrow B such that

JEE Advanced 2026 Solution View → 38

Let f:(1,∞)→ℝ be a function defined as f(x) = (x-1)/(x+1) . Let f^ i+1 (x) = f(f^i(x)) , i=1, 2, …, 25 , where f^1(x)=f(x) . If g(x) + f^ 26 (x) = 0 , x ∈ (1, ∞) , then the area

JEE Main 2026 Solution View → 39

Let f be a polynomial function such that _2(f(x)) = ( _2(2+(2)/(3)+(2)/(9)+…∞))· _3(1+(f(x))/(f(1/x))) , x>0 and f(6)=37 . Then ∑_ n=1 ^ 10 f(n) is equal to ________.

JEE Main 2026 Solution View → 40

If the eccentricity e of the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = 1 , passing through (6, 4 3 ) , satisfies 15(e^2 + 1) = 34e , then the length of the latus rectum of the

JEE Main 2026 Solution View →

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