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
2023 session2_13apr_shift1

24 maths questions

Q1 Constant acceleration (SUVAT) Relative velocity and observed length/time View
Two trains $A$ and $B$ of length $l$ and $4l$ are travelling into a tunnel of length $L$ in parallel tracks from opposite directions with velocities $108 \mathrm{~km~h}^{-1}$ and $72 \mathrm{~km~h}^{-1}$, respectively. If train $A$ takes 35 s less time than train $B$ to cross the tunnel then, length $L$ of tunnel is: (Given $L = 60l$)
(1) 1200 m
(2) 900 m
(3) 1800 m
(4) 2700 m
Q2 Variable acceleration (vectors) View
A disc is rolling without slipping on a surface. The radius of the disc is $R$. At $t = 0$, the top most point on the disc is $A$ as shown in figure. When the disc completes half of its rotation, the displacement of point $A$ from its initial position is
(1) $2R$
(2) $R\sqrt{\left(\pi^2 + 4\right)}$
(3) $R\sqrt{\left(\pi^2 + 1\right)}$
(4) $2R\sqrt{\left(1 + 4\pi^2\right)}$
Q3 Power and driving force View
The ratio of powers of two motors is $\frac{3\sqrt{x}}{\sqrt{x+1}}$, that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of $x$ will be
(1) 16
(2) 2
(3) 2.4
(4) 4
Q5 Momentum and Collisions Velocity of Centre of Mass View
Two bodies are having kinetic energies in the ratio $16:9$. If they have same linear momentum, the ratio of their masses respectively is:
(1) $3:4$
(2) $9:16$
(3) $16:9$
(4) $4:3$
Q6 Impulse and momentum (advanced) View
A bullet of 10 g leaves the barrel of gun with a velocity of $600 \mathrm{~m~s}^{-1}$. If the barrel of gun is 50 cm long and mass of gun is 3 kg, then value of impulse supplied to the gun will be:
(1) 6 N s
(2) 3 N s
(3) 36 N s
(4) 12 N s
Q61 First order differential equations (integrating factor) Solving Separable DEs with Initial Conditions View
If $\sin\left(\frac{y}{x}\right) = \log_e|x| + \frac{\alpha}{2}$ is the solution of the differential equation $x\cos\left(\frac{y}{x}\right)\frac{dy}{dx} = y\cos\left(\frac{y}{x}\right) + x$ and $y(1) = \frac{\pi}{3}$, then $\alpha^2$ is equal to
(1) 12
(2) 3
(3) 4
(4) 9
Q62 Stationary points and optimisation Injectivity, Surjectivity, or Bijectivity Classification View
Let $f: \mathbb{R} \to \mathbb{R}$ be a function defined by $f(x) = \frac{x^2 + 2}{x^2 + 1}$. Then which of the following is NOT true?
(1) $f(x)$ has a minimum at $x = 0$
(2) $f(x)$ is an even function
(3) $f(x)$ is strictly increasing for $x > 0$
(4) $f(x)$ is onto
Q64 Solving quadratics and applications Solving an equation via substitution to reduce to quadratic form View
The number of real solutions of the equation $3\left(x^2 + \frac{1}{x^2}\right) - 2\left(x + \frac{1}{x}\right) + 5 = 0$ is
(1) 4
(2) 0
(3) 3
(4) 2
Q65 Vectors 3D & Lines Vector Algebra and Triple Product Computation View
Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$, $\vec{b} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{c} = \hat{i} + \hat{j} - \hat{k}$. A vector in the plane of $\vec{a}$ and $\vec{b}$ whose projection on $\vec{c}$ is $\frac{1}{\sqrt{3}}$ is
(1) $4\hat{i} - \hat{j} + 4\hat{k}$
(2) $3\hat{i} + \hat{j} - 3\hat{k}$
(3) $2\hat{i} + \hat{j} - 2\hat{k}$
(4) $4\hat{i} + \hat{j} - 4\hat{k}$
Q66 Standard Integrals and Reverse Chain Rule Definite Integral Evaluation (Computational) View
The value of $\int_0^1 \frac{d}{dx}\left[\tan^{-1}\left(\frac{1}{1-x+x^2}\right)\right]dx$ is
(1) $\frac{\pi}{4}$
(2) $\tan^{-1}(2)$
(3) $\frac{\pi}{2} - \tan^{-1}(2)$
(4) $\frac{\pi}{4} - \tan^{-1}(2)$
Q67 Vectors: Lines & Planes Coplanarity and Relative Position of Planes View
Let $P$ be the plane passing through the intersection of the planes $\vec{r}\cdot(\hat{i}+3\hat{j}-\hat{k}) = 5$ and $\vec{r}\cdot(2\hat{i}-\hat{j}+\hat{k}) = 3$, and the point $(2, 1, -2)$. Let the position vectors of the points $X$ and $Y$ be $\hat{i} - 2\hat{j} + 4\hat{k}$ and $5\hat{i} - \hat{j} + 2\hat{k}$ respectively. Then the points $X$ and $Y$ with respect to the plane $P$ are
(1) on the same side
(2) on opposite sides
(3) $X$ lies on $P$
(4) $Y$ lies on $P$
Q68 3x3 Matrices Matrix Power Computation and Application View
Let $A = \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}$. If $M = \sum_{k=1}^{20} (A^k + B^k)$, then $\det(M)$ is equal to
(1) 100
(2) 200
(3) 0
(4) 400
Q69 Permutations & Arrangements Linear Arrangement with Constraints View
The number of 9-digit numbers, that can be formed using all the digits of the number 123456789, such that the even digits occupy only even places, is
(1) 2880
(2) 2520
(3) 2160
(4) 2400
Q70 Stationary points and optimisation Variation Table and Monotonicity from Sign of Derivative View
Let $f(x) = \begin{cases} x^3 - x^2 + 10x - 7, & x \leq 1 \\ -2x + \log_2(b^2 - 4), & x > 1 \end{cases}$. Then the set of all values of $b$, for which $f(x)$ has maximum value at $x = 1$, is
(1) $(-2, -1]$
(2) $[-2, -1) \cup (1, 2]$
(3) $(-2, 2)$
(4) $(-\infty, -2) \cup (2, \infty)$
Q71 Measures of Location and Spread View
The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then the correct mean and variance are
(1) 14 and 13.5
(2) 14 and 12.5
(3) 15 and 14.5
(4) 14 and 11.5
Q72 Areas by integration Area Involving Piecewise or Composite Functions View
The area of the region $\{(x, y): x^2 \leq y \leq |x^2 - 4|, y \geq 1\}$ is
(1) $\frac{4(\sqrt{5}-1)}{3} + 4$
(2) $\frac{4(\sqrt{5}-1)}{3} + 2$
(3) $\frac{2(\sqrt{5}-1)}{3} + 4$
(4) $\frac{2(\sqrt{5}-1)}{3} + 2$
Q73 Complex Numbers Arithmetic Powers of i or Complex Number Integer Powers View
Let $z_1$ and $z_2$ be two complex numbers such that $z_1 + z_2 = 5$ and $z_1^3 + z_2^3 = 20 + 15i$. Then $|z_1^4 + z_2^4|$ equals
(1) $30\sqrt{3}$
(2) $75\sqrt{2}$
(3) $15\sqrt{15}$
(4) $25\sqrt{3}$
Q74 Stationary points and optimisation Find critical points and classify extrema of a given function View
Let $f(x) = \int_0^x t(t-1)(t-2)\,dt$, $x > 0$. Then the number of points in the interval $(0, 3)$ at which $f(x)$ has a local maximum is $\_\_\_\_$.
Q75 Sequences and series, recurrence and convergence Vieta's formulas: compute symmetric functions of roots View
Let $\alpha$ and $\beta$ be the roots of $x^2 - \sqrt{6}x + 3 = 0$. If $\alpha^n + \beta^n$ is an integer for $n \geq 1$, then the greatest value of $n$ for which $\alpha^n + \beta^n$ is NOT an integer is $\_\_\_\_$.
Q76 Standard trigonometric equations Solve trigonometric equation for solutions in an interval View
Let $S = \{\theta \in [0, 2\pi): \tan(\pi\cos\theta) + \tan(\pi\sin\theta) = 0\}$. Then $\sum_{\theta \in S} \sin\left(\theta + \frac{\pi}{4}\right)$ is equal to $\_\_\_\_$.
Q77 3x3 Matrices Determinant of Parametric or Structured Matrix View
Let $A$ be a $3 \times 3$ matrix and $\det(A) = 2$. If $n = \det(\text{adj}(\text{adj}(\cdots(\text{adj}(A))\cdots)))$ where adj is applied 6 times, then the remainder when $n$ is divided by 9 is $\_\_\_\_$.
Q78 Circles Circle-Line Intersection and Point Conditions View
The number of integral values of $k$ for which the line $3x + 4y = k$ intersects the circle $x^2 + y^2 - 2x - 4y + 4 = 0$ at two distinct points is $\_\_\_\_$.
Q79 Indefinite & Definite Integrals Chain Rule Combined with Fundamental Theorem of Calculus View
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $f\left(\frac{\pi}{4}\right) = \sqrt{2}$, $f\left(\frac{\pi}{2}\right) = 0$ and $f'\left(\frac{\pi}{2}\right) = 1$ and let $g(x) = \int_x^{\pi/4} (f'(t)\sec t + \tan t \cdot f(t)\sec t)\,dt$. Then $\lim_{x \to \pi/2} \frac{g(x)}{(x - \pi/2)^2}$ is equal to $\_\_\_\_$.
Q80 Arithmetic Sequences and Series Evaluation of a Finite or Infinite Sum View
The sum of the series $\frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \cdots + \frac{1}{(2n-1)(2n+1)}$ is $\_\_\_\_$.