jee-main

Papers (169)
2025
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2024
session1_01feb_shift1 4 session1_01feb_shift2 22 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 30 session1_29jan_shift2 23 session1_30jan_shift1 17 session1_30jan_shift2 30 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 4 session2_04apr_shift2 30 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 22 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 30 session2_09apr_shift1 5 session2_09apr_shift2 30
2023
session1_01feb_shift1 24 session1_01feb_shift2 3 session1_24jan_shift1 13 session1_24jan_shift2 12 session1_25jan_shift1 28 session1_25jan_shift2 27 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 2 session1_30jan_shift2 29 session1_31jan_shift1 28 session1_31jan_shift2 17 session2_06apr_shift1 5 session2_06apr_shift2 17 session2_08apr_shift1 29 session2_08apr_shift2 14 session2_10apr_shift1 29 session2_10apr_shift2 15 session2_11apr_shift1 5 session2_11apr_shift2 4 session2_12apr_shift1 26 session2_13apr_shift1 25 session2_13apr_shift2 20 session2_15apr_shift1 20
2022
session1_24jun_shift1 20 session1_24jun_shift2 25 session1_25jun_shift1 14 session1_25jun_shift2 17 session1_26jun_shift1 26 session1_26jun_shift2 23 session1_27jun_shift1 4 session1_27jun_shift2 29 session1_28jun_shift1 13 session1_29jun_shift1 20 session1_29jun_shift2 5 session2_25jul_shift1 29 session2_25jul_shift2 22 session2_26jul_shift1 29 session2_26jul_shift2 24 session2_27jul_shift1 26 session2_27jul_shift2 29 session2_28jul_shift1 12 session2_28jul_shift2 29 session2_29jul_shift1 18 session2_29jul_shift2 17
2021
session1_24feb_shift1 10 session1_24feb_shift2 7 session1_25feb_shift1 29 session1_25feb_shift2 29 session1_26feb_shift2 17 session2_16mar_shift1 29 session2_16mar_shift2 15 session2_17mar_shift1 20 session2_17mar_shift2 24 session2_18mar_shift1 12 session2_18mar_shift2 11 session3_20jul_shift1 30 session3_20jul_shift2 29 session3_22jul_shift1 7 session3_25jul_shift1 2 session3_25jul_shift2 15 session3_27jul_shift1 3 session3_27jul_shift2 4 session4_01sep_shift2 11 session4_26aug_shift1 5 session4_26aug_shift2 2 session4_27aug_shift1 3 session4_27aug_shift2 28 session4_31aug_shift1 28 session4_31aug_shift2 4
2020
session1_07jan_shift1 26 session1_07jan_shift2 17 session1_08jan_shift1 5 session1_08jan_shift2 12 session1_09jan_shift1 22 session1_09jan_shift2 18 session2_02sep_shift1 19 session2_02sep_shift2 17 session2_03sep_shift1 21 session2_03sep_shift2 9 session2_04sep_shift1 10 session2_04sep_shift2 24 session2_05sep_shift1 23 session2_05sep_shift2 27 session2_06sep_shift1 13 session2_06sep_shift2 10
2019
session1_09jan_shift1 6 session1_09jan_shift2 29 session1_10jan_shift1 30 session1_10jan_shift2 12 session1_11jan_shift1 6 session1_11jan_shift2 5 session1_12jan_shift1 10 session1_12jan_shift2 20 session2_08apr_shift1 29 session2_08apr_shift2 29 session2_09apr_shift1 29 session2_09apr_shift2 29 session2_10apr_shift1 2 session2_10apr_shift2 3 session2_12apr_shift1 3 session2_12apr_shift2 9
2018
08apr 29 15apr 28 15apr_shift1 28 15apr_shift2 2 16apr 15
2017
02apr 28 08apr 29 09apr 30
2016
03apr 30 09apr 30 10apr 28
2015
04apr 29 10apr 30
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
2013
07apr 29 09apr 14 22apr 5 23apr 14 25apr 13
2012
07may 18 12may 22 19may 13 26may 17 offline 30
2011
jee-main_2011.pdf 13
2010
jee-main_2010.pdf 1
2009
jee-main_2009.pdf 1
2008
jee-main_2008.pdf 1
2007
jee-main_2007.pdf 38
2005
jee-main_2005.pdf 19
2004
jee-main_2004.pdf 11
2003
jee-main_2003.pdf 9
2002
jee-main_2002.pdf 8
2024 session1_31jan_shift2

15 maths questions

Q22 Projectiles Angular Momentum of a Projectile View
A body of mass $m$ is projected with a speed $u$ making an angle of $45^\circ$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $\dfrac{\sqrt{Z}\, m u^3}{X g}$. The value of $X$ is $\_\_\_\_$.
Q24 Simple Harmonic Motion View
The time period of simple harmonic motion of mass $M$ in the given figure is $\pi\sqrt{\dfrac{\alpha M}{5K}}$, where the value of $\alpha$ is $\_\_\_\_$.
Q61 Trigonometric equations in context View
The number of solutions, of the equation $e^{\sin x} - 2e^{-\sin x} = 2$ is
(1) 2
(2) more than 2
(3) 1
(4) 0
Q62 Complex Numbers Argand & Loci Solving Complex Equations with Geometric Interpretation View
Let $z_1$ and $z_2$ be two complex number 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
(3) $15\sqrt{15}$
(4) $25\sqrt{3}$
Q63 Combinations & Selection Counting Integer Solutions to Equations View
The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is
(1) 406
(2) 130
(3) 142
(4) 136
Q64 Geometric Sequences and Series Arithmetic-Geometric Sequence Interplay View
Let $2^{\text{nd}}$, $8^{\text{th}}$ and $44^{\text{th}}$ terms of a non-constant A.P. be respectively the $1^{\text{st}}$, $2^{\text{nd}}$ and $3^{\text{rd}}$ terms of G.P. If the first term of A.P. is 1 then the sum of first 20 terms is equal to-
(1) 980
(2) 960
(3) 990
(4) 970
Q65 Combinations & Selection Basic Combination Computation View
If for some $m, n$; ${}^{6}C_m + 2\,{}^{6}C_{m+1} + {}^{6}C_{m+2} > {}^{8}C_3$ and ${}^{n-1}P_3 : {}^{n}P_4 = 1 : 8$, then ${}^{n}P_{m+1} + {}^{n+1}C_m$ is equal to
(1) 380
(2) 376
(3) 384
(4) 372
Q66 Straight Lines & Coordinate Geometry Point-to-Line Distance Computation View
Let $A(a, b)$, $B(3, 4)$ and $(-6, -8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P(2a+3, 7b+5)$ from the line $2x + 3y - 4 = 0$ measured parallel to the line $x - 2y - 1 = 0$ is
(1) $\dfrac{15\sqrt{5}}{7}$
(2) $\dfrac{17\sqrt{5}}{6}$
(3) $\dfrac{17\sqrt{5}}{7}$
(4) $\dfrac{\sqrt{5}}{17}$
Q67 Circles Optimization on a Circle View
Let a variable line passing through the centre of the circle $x^2 + y^2 - 16x - 4y = 0$, meet the positive coordinate axes at the point $A$ and $B$. Then the minimum value of $OA + OB$, where $O$ is the origin, is equal to
(1) 12
(2) 18
(3) 20
(4) 24
Q68 Conic sections Equation Determination from Geometric Conditions View
Let $P$ be a parabola with vertex $(2, 3)$ and directrix $2x + y = 6$. Let an ellipse $E : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$, $a > b$ of eccentricity $\dfrac{1}{\sqrt{2}}$ pass through the focus of the parabola $P$. Then the square of the length of the latus rectum of $E$, is
(1) $\dfrac{385}{8}$
(2) $\dfrac{347}{8}$
(3) $\dfrac{512}{25}$
(4) $\dfrac{656}{25}$
Q69 Curve Sketching Limit Computation from Algebraic Expressions View
Let $f : \mathbb{R} \rightarrow (0, \infty)$ be strictly increasing function such that $\lim_{x \rightarrow \infty} \dfrac{f(7x)}{f(x)} = 1$. Then, the value of $\lim_{x \rightarrow \infty} \left(\dfrac{f(5x)}{f(x)} - 1\right)$ is equal to
(1) 4
(2) 0
(3) $\dfrac{7}{5}$
(4) 1
Q70 Measures of Location and Spread View
Let the mean and the variance of 6 observations $a, b, 68, 44, 48, 60$ be 55 and 194, respectively. If $a > b$, then $a + 3b$ is
(1) 200
(2) 190
(3) 180
(4) 210
Q71 3x3 Matrices Solving a 3×3 Linear System Explicitly View
Let $A$ be a $3 \times 3$ real matrix such that $A\begin{pmatrix}0\\1\\0\end{pmatrix} = \begin{pmatrix}2\\0\\0\end{pmatrix}$, $A\begin{pmatrix}0\\0\\1\end{pmatrix} = \begin{pmatrix}4\\0\\0\end{pmatrix}$, $A\begin{pmatrix}1\\1\\1\end{pmatrix} = \begin{pmatrix}2\\1\\1\end{pmatrix}$. Then, the system $(A - 3I)\begin{pmatrix}x\\y\\z\end{pmatrix} = \begin{pmatrix}1\\2\\3\end{pmatrix}$ has
(1) unique solution
(2) exactly two solutions
(3) no solution
(4) infinitely many solutions
Q72 Standard trigonometric equations Inverse trigonometric equation View
If $a = \sin^{-1}(\sin 5)$ and $b = \cos^{-1}(\cos 5)$, then $a^2 + b^2$ is equal to
(1) $4\pi^2 + 25$
(2) $8\pi^2 - 40\pi + 50$
(3) $4\pi^2 - 20\pi + 50$
(4) 25
Q73 Stationary points and optimisation Find absolute extrema on a closed interval or domain View
If the function $f : (-\infty, -1] \rightarrow [a, b]$ defined by $f(x) = e^{x^3 - 3x + 1}$ is one-one and onto, then the distance of the point $P(2b+4, a+2)$ from the line $x + e^{-3}y = 4$ is: