jee-main

Papers (191)
2026
session1_21jan_shift1 13 session1_21jan_shift2 9 session1_22jan_shift1 16 session1_22jan_shift2 10 session1_23jan_shift1 11 session1_23jan_shift2 7 session1_24jan_shift1 14 session1_24jan_shift2 10 session1_28jan_shift1 10 session1_28jan_shift2 9
2025
session1_22jan_shift1 25 session1_22jan_shift2 25 session1_23jan_shift1 25 session1_23jan_shift2 25 session1_24jan_shift1 25 session1_24jan_shift2 25 session1_28jan_shift1 25 session1_28jan_shift2 25 session1_29jan_shift1 29 session1_29jan_shift2 25 session2_02apr_shift1 31 session2_02apr_shift2 36 session2_03apr_shift1 35 session2_03apr_shift2 35 session2_04apr_shift1 37 session2_04apr_shift2 33 session2_07apr_shift1 32 session2_07apr_shift2 32 session2_08apr_shift1 36 session2_08apr_shift2 35
2024
session1_01feb_shift1 5 session1_01feb_shift2 21 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 28 session1_29jan_shift2 29 session1_30jan_shift1 20 session1_30jan_shift2 29 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 5 session2_04apr_shift2 28 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 21 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 29 session2_09apr_shift1 8 session2_09apr_shift2 30
2023
session1_01feb_shift1 28 session1_01feb_shift2 3 session1_24jan_shift1 11 session1_24jan_shift2 11 session1_25jan_shift1 29 session1_25jan_shift2 29 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 5 session1_30jan_shift2 27 session1_31jan_shift1 28 session1_31jan_shift2 15 session2_06apr_shift1 5 session2_06apr_shift2 16 session2_08apr_shift1 29 session2_08apr_shift2 13 session2_10apr_shift1 29 session2_10apr_shift2 16 session2_11apr_shift1 6 session2_11apr_shift2 8 session2_12apr_shift1 26 session2_13apr_shift1 24 session2_13apr_shift2 24 session2_15apr_shift1 19
2022
session1_24jun_shift1 19 session1_24jun_shift2 25 session1_25jun_shift1 14 session1_25jun_shift2 14 session1_26jun_shift1 29 session1_26jun_shift2 24 session1_27jun_shift1 4 session1_27jun_shift2 29 session1_28jun_shift1 13 session1_29jun_shift1 20 session1_29jun_shift2 4 session2_25jul_shift1 29 session2_25jul_shift2 20 session2_26jul_shift1 29 session2_26jul_shift2 23 session2_27jul_shift1 28 session2_27jul_shift2 29 session2_28jul_shift1 11 session2_28jul_shift2 29 session2_29jul_shift1 17 session2_29jul_shift2 18
2021
session1_24feb_shift1 9 session1_24feb_shift2 4 session1_25feb_shift1 29 session1_25feb_shift2 29 session1_26feb_shift2 15 session2_16mar_shift1 29 session2_16mar_shift2 18 session2_17mar_shift1 21 session2_17mar_shift2 27 session2_18mar_shift1 18 session2_18mar_shift2 9 session3_20jul_shift1 29 session3_20jul_shift2 29 session3_22jul_shift1 9 session3_25jul_shift1 8 session3_25jul_shift2 14 session3_27jul_shift1 4 session3_27jul_shift2 7 session4_01sep_shift2 14 session4_26aug_shift1 5 session4_26aug_shift2 2 session4_27aug_shift1 3 session4_27aug_shift2 29 session4_31aug_shift1 28 session4_31aug_shift2 4
2020
session1_07jan_shift1 28 session1_07jan_shift2 20 session1_08jan_shift1 5 session1_08jan_shift2 11 session1_09jan_shift1 26 session1_09jan_shift2 16 session2_02sep_shift1 18 session2_02sep_shift2 16 session2_03sep_shift1 23 session2_03sep_shift2 8 session2_04sep_shift1 14 session2_04sep_shift2 27 session2_05sep_shift1 22 session2_05sep_shift2 29 session2_06sep_shift1 11 session2_06sep_shift2 10
2019
session1_09jan_shift1 6 session1_09jan_shift2 29 session1_10jan_shift1 29 session1_10jan_shift2 14 session1_11jan_shift1 6 session1_11jan_shift2 5 session1_12jan_shift1 10 session1_12jan_shift2 29 session2_08apr_shift1 29 session2_08apr_shift2 29 session2_09apr_shift1 29 session2_09apr_shift2 29 session2_10apr_shift1 2 session2_10apr_shift2 5 session2_12apr_shift1 3 session2_12apr_shift2 9
2018
08apr 30 15apr 28 15apr_shift1 28 15apr_shift2 6 16apr 19
2017
02apr 30 08apr 30 09apr 34
2016
03apr 28 09apr 29 10apr 30
2015
04apr 29 10apr 29 11apr 8
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
2013
07apr 29 09apr 12 22apr 5 23apr 14 25apr 13
2012
07may 17 12may 21 19may 14 26may 17 offline 30
2011
jee-main_2011.pdf 18
2010
jee-main_2010.pdf 6
2009
jee-main_2009.pdf 2
2008
jee-main_2008.pdf 4
2007
jee-main_2007.pdf 38
2006
jee-main_2006.pdf 15
2005
jee-main_2005.pdf 25
2004
jee-main_2004.pdf 22
2003
jee-main_2003.pdf 8
2002
jee-main_2002.pdf 12
2019 session2_08apr_shift1

29 maths questions

Q61 Solving quadratics and applications Solving an equation via substitution to reduce to quadratic form View
The sum of the solutions of the equation $\sqrt{x} - 2 + \sqrt{x}\sqrt{x} - 4 + 2 = 0, x > 0$ is equal to
(1) 10
(2) 9
(3) 12
(4) 4
Q62 Complex Numbers Arithmetic Vieta's formulas: compute symmetric functions of roots View
If $\alpha$ and $\beta$ be the roots of the equation $x^2 - 2x + 2 = 0$, then the least value of $n$ for which $\frac{\alpha^n}{\beta} = 1$ is
(1) 5
(2) 4
(3) 2
(4) 3
Q63 Permutations & Arrangements Word Permutations with Repeated Letters View
All possible numbers are formed using the digits $1,1,2,2,2,2,3,4,4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is
(1) 175
(2) 162
(3) 180
(4) 160
Q64 Number Theory GCD, LCM, and Coprimality View
The sum of all natural numbers $n$ such that $100 < n < 200$ and H.C.F.$(91, n) > 1$ is
(1) 3203
(2) 3221
(3) 3121
(4) 3303
Q65 Binomial Theorem (positive integer n) Evaluate a Summation Involving Binomial Coefficients View
The sum of the co-efficients of all even degree terms in $x$ in the expansion of $\left(x + \sqrt{x^3 - 1}\right)^6 + \left(x - \sqrt{x^3 - 1}\right)^6$, $x > 1$ is equal to
(1) 26
(2) 32
(3) 24
(4) 29
Q66 Arithmetic Sequences and Series Summation of Derived Sequence from AP View
The sum of the series $2\cdot{}^{20}C_0 + 5\cdot{}^{20}C_1 + 8\cdot{}^{20}C_2 + 11\cdot{}^{20}C_3 + \ldots + 62\cdot{}^{20}C_{20}$ is equal to
(1) $2^{26}$
(2) $2^{25}$
(3) $2^{24}$
(4) $2^{23}$
Q67 Addition & Double Angle Formulae Addition/Subtraction Formula Evaluation View
If $\cos(\alpha + \beta) = \frac{3}{5}$, $\sin(\alpha - \beta) = \frac{5}{13}$ and $0 < \alpha, \beta < \frac{\pi}{4}$, then $\tan 2\alpha$ is equal to:
(1) $\frac{21}{16}$
(2) $\frac{63}{52}$
(3) $\frac{33}{52}$
(4) $\frac{63}{16}$
Q68 Straight Lines & Coordinate Geometry Point-to-Line Distance Computation View
A point on the straight line, $3x + 5y = 15$ which is equidistant from the coordinate axes will lie only in:
(1) $1^{\text{st}}$ and $2^{\text{nd}}$ quadrants
(2) $1^{\text{st}}$, $2^{\text{nd}}$ and $4^{\text{th}}$ quadrants
(3) $1^{\text{st}}$ quadrant
(4) $4^{\text{th}}$ quadrant
Q69 Circles Chord Length and Chord Properties View
The sum of the squares of the lengths of the chords intercepted on the circle, $x^2 + y^2 = 16$, by the lines, $x + y = n$, $n \in N$, where $N$ is the set of all natural numbers is:
(1) 210
(2) 105
(3) 320
(4) 160
Q70 Circles Circle-Related Locus Problems View
Let $O(0,0)$ and $A(0,1)$ be two fixed points. Then, the locus of a point $P$ such that the perimeter of $\triangle AOP$ is 4 is
(1) $8x^2 + 9y^2 - 9y = 18$
(2) $9x^2 - 8y^2 + 8y = 16$
(3) $8x^2 - 9y^2 + 9y = 18$
(4) $9x^2 + 8y^2 - 8y = 16$
Q71 Circles Tangent Lines and Tangent Lengths View
If the tangents on the ellipse $4x^2 + y^2 = 8$ at the points $(1,2)$ and $(a,b)$ are perpendicular to each other, then $a^2$ is equal to
(1) $\frac{2}{17}$
(2) $\frac{4}{17}$
(3) $\frac{64}{17}$
(4) $\frac{128}{17}$
Q72 Chain Rule Limit Evaluation Involving Composition or Substitution View
$\lim_{x \rightarrow 0} \frac{\sin^2 x}{\sqrt{2} - \sqrt{1 + \cos x}}$ equals
(1) $4\sqrt{2}$
(2) $2\sqrt{2}$
(3) $\sqrt{2}$
(4) 4
Q74 Measures of Location and Spread Direct Determinant Computation View
The mean and variance for seven observations are 8 and 16 respectively. If 5 of the observations are $2, 4, 10, 12, 14$, then the product of the remaining two observations is
(1) 48
(2) 45
(3) 49
(4) 40
Q75 Matrices Matrix Algebraic Properties and Abstract Reasoning View
Let $A = \begin{pmatrix} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{pmatrix}$, $\alpha \in R$ such that $A^{32} = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$. Then, a value of $\alpha$ is:
(1) 0
(2) $\frac{\pi}{16}$
(3) $\frac{\pi}{64}$
(4) $\frac{\pi}{32}$
Q76 Complex Numbers Arithmetic Inequalities and Estimates for Complex Expressions View
The greatest value of $c \in R$ for which the system of linear equations $x - cy - cz = 0$, $cx - y + cz = 0$, $cx + cy - z = 0$ has a non-trivial solution, is
(1) $-1$
(2) $2$
(3) $\frac{1}{2}$
(4) $0$
Q77 Composite & Inverse Functions Addition/Subtraction Formula Evaluation View
If $\alpha = \cos^{-1}\frac{3}{5}$, $\beta = \tan^{-1}\frac{1}{3}$, where $0 < \alpha, \beta < \frac{\pi}{2}$, then $\alpha - \beta$ is equal to
(1) $\tan^{-1}\frac{9}{14}$
(2) $\cos^{-1}\frac{9}{5\sqrt{10}}$
(3) $\sin^{-1}\frac{9}{5\sqrt{10}}$
(4) $\tan^{-1}\frac{9}{5\sqrt{10}}$
Q78 Composite & Inverse Functions Evaluate Composition from Algebraic Definitions View
If $f(x) = \log_e\frac{1-x}{1+x}$, $|x| < 1$, then $f\left(\frac{2x}{1+x^2}\right)$ is equal to
(1) $f(x^2)$
(2) $2f(x^2)$
(3) $-2f(x)$
(4) $2f(x)$
Q79 Chain Rule Compute derivative of transcendental function View
If $2y = \cot^{-1}\left(\frac{\sqrt{3}\cos x + \sin x}{\cos x - \sqrt{3}\sin x}\right)$, $\forall x \in \left(0, \frac{\pi}{2}\right)$, then $\frac{dy}{dx}$ is equal to
(1) $\frac{\pi}{6} - x$
(2) $2x - \frac{\pi}{3}$
(3) $x - \frac{\pi}{6}$
(4) None of these
Q80 Straight Lines & Coordinate Geometry Geometric or applied optimisation problem View
The shortest distance between the line $y = x$ and the curve $y^2 = x - 2$ is
(1) $\frac{7}{4\sqrt{2}}$
(2) $\frac{7}{8}$
(3) $\frac{11}{4\sqrt{2}}$
(4) 2
Q81 Stationary points and optimisation Find critical points and classify extrema of a given function View
If $S_1$ and $S_2$ are respectively the sets of local minimum and local maximum points of the function, $f(x) = 9x^4 + 12x^3 - 36x^2 + 25$, $x \in R$, then
(1) $S_1 = \{-2\}$; $S_2 = \{0, 1\}$
(2) $S_1 = \{-1\}$; $S_2 = \{0, 2\}$
(3) $S_1 = \{-2, 0\}$; $S_2 = \{1\}$
(4) $S_1 = \{-2, 1\}$; $S_2 = \{0\}$
Q82 Connected Rates of Change Qualitative Properties of Antiderivatives View
Let $f : (0,2) \rightarrow R$ be a twice differentiable function such that $f''(x) > 0$, for all $x \in (0,2)$. If $\phi(x) = f(x) + f(2-x)$, then $\phi$ is
(1) decreasing on $(0,2)$
(2) increasing on $(0,2)$
(3) increasing on $(0,1)$ and decreasing on $(1,2)$
(4) decreasing on $(0,1)$ and increasing on $(1,2)$
Q83 Standard Integrals and Reverse Chain Rule Antiderivative Verification and Construction View
$\int \frac{\sin\frac{5x}{2}}{\sin\frac{x}{2}} dx$ is equal to
(1) $x + 2\sin x + \sin 2x + c$
(2) $2x + \sin x + \sin 2x + c$
(3) $x + 2\sin x + 2\sin 2x + c$
(4) $2x + \sin x + 2\sin 2x + c$
Q84 Areas by integration Integral Equation with Symmetry or Substitution View
If $f(x) = \frac{2 - x\cos x}{2 + x\cos x}$ and $g(x) = \log_e x$, then the value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} g(f(x))\, dx$ is
(1) $\log_e e$
(2) $\log_e 2$
(3) $\log_e 1$
(4) $\log_e 3$
Q85 First order differential equations (integrating factor) View
The area (in sq. units) of the region $A = \{(x,y) \in R \times R \mid 0 \leq x \leq 3, 0 \leq y \leq 4, y \leq x^2 + 3x\}$ is
(1) $\frac{26}{3}$
(2) $8$
(3) $\frac{53}{6}$
(4) $\frac{59}{6}$
Q86 Vectors 3D & Lines Vector Algebra and Triple Product Computation View
Let $y = y(x)$ be the solution of the differential equation, $\left(x^2 + 1\right)^2 \frac{dy}{dx} + 2x\left(x^2 + 1\right)y = 1$ such that $y(0) = 0$. If $\sqrt{a}\, y(1) = \frac{\pi}{32}$, then the value of $a$ is
(1) $\frac{1}{16}$
(2) $\frac{1}{2}$
(3) $\frac{1}{4}$
(4) $1$
Q87 Vectors: Lines & Planes Normal Vector Determination View
The magnitude of the projection of the vector $2\hat{i} + 3\hat{j} + \hat{k}$ on the vector perpendicular to the plane containing the vectors $\hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + 2\hat{j} + 3\hat{k}$, is:
(1) $3\sqrt{6}$
(2) $\sqrt{\frac{3}{2}}$
(3) $\sqrt{6}$
(4) $\frac{\sqrt{3}}{2}$
Q88 Vectors: Lines & Planes Distance Computation (Point-to-Plane or Line-to-Line) View
The length of the perpendicular from the point $(2,-1,4)$ on the straight line $\frac{x+3}{10} = \frac{y-2}{-7} = \frac{z}{1}$ is
(1) greater than 3 but less than 4
(2) greater than 4
(3) less than 2
(4) greater than 2 but less than 3
Q89 Vectors: Lines & Planes Find Cartesian Equation of a Plane View
The equation of a plane containing the line of intersection of the planes $2x - y - 4 = 0$ and $y + 2z - 4 = 0$ and passing through the point $(1,1,0)$ is
(1) $x - 3y - 2z = -2$
(2) $x + 3y + z = 4$
(3) $x - y - z = 0$
(4) $2x - z = 2$
Q90 Conditional Probability Direct Conditional Probability Computation from Definitions View
Let $A$ and $B$ be two non-null events such that $A \subset B$. Then, which of the following statements is always correct?
(1) $P(A \mid B) \geq P(A)$
(2) $P(A \mid B) = P(B) - P(A)$
(3) $P(A \mid B) \leq P(A)$
(4) $P(A \mid B) = 1$