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
2012 12may

21 maths questions

Q2 Constant acceleration (SUVAT) Find acceleration from position or velocity View
The distance travelled by a body moving along a line in time $t$ is proportional to $t^{3}$. The acceleration-time $(a, t)$ graph for the motion of the body will be
(1) [graph 1] (2) [graph 2] (3) [graph 3] (4) [graph 4]
Q3 Forces, equilibrium and resultants Friction on Curved Surface (Limiting Angle) View
An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ so that the insect does not slip is given by
(1) $\cot \alpha = 3$
(2) $\sec \alpha = 3$
(3) $\operatorname{cosec} \alpha = 3$
(4) $\cos \alpha = 3$
Q4 Projectiles Projectile with Mid-Flight Event (Breakup or Bounce) View
A projectile moving vertically upwards with a velocity of $200 \mathrm{~ms}^{-1}$ breaks into two equal parts at a height of 490 m. One part starts moving vertically upwards with a velocity of $400 \mathrm{~ms}^{-1}$. How much time it will take, after the break up with the other part to hit the ground?
(1) $2\sqrt{10} \mathrm{~s}$
(2) 5 s
(3) 10 s
(4) $\sqrt{10} \mathrm{~s}$
Q5 Momentum and Collisions Collision with Spring System View
Two bodies $A$ and $B$ of mass $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. A third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_{0}$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision it is found that the instantaneous velocities of $A$ and $B$ are same and the compression of the spring is $x_{0}$. The spring constant $k$ will be
(1) $m\frac{v_{0}^{2}}{x_{0}^{2}}$
(2) $m\frac{v_{0}}{2x_{0}}$
(3) $2m\frac{v_{0}}{x_{0}}$
(4) $\frac{2}{3}m\left(\frac{v_{0}}{x_{0}}\right)^{2}$
Q6 Work done and energy Explosion or Breakup – Fragment Velocities or Energies View
A spring is compressed between two blocks of masses $m_{1}$ and $m_{2}$ placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of $v_{1}$ and $v_{2}$ as shown. The blocks travel distances $x_{1}$ and $x_{2}$ respectively before coming to rest. The ratio $\left(\frac{x_{1}}{x_{2}}\right)$ is
(1) $\frac{m_{2}}{m_{1}}$
(2) $\frac{m_{1}}{m_{2}}$
(3) $\sqrt{\frac{m_{2}}{m_{1}}}$
(4) $\sqrt{\frac{m_{1}}{m_{2}}}$
Q7 Simple Harmonic Motion Rolling body energy and incline problems View
A solid sphere is rolling on a surface as shown in figure, with a translational velocity $v \mathrm{~ms}^{-1}$. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is
(1) $\sqrt{2gh}$
(2) $\sqrt{\frac{7}{5}gh}$
(3) $\sqrt{\frac{7}{2}gh}$
(4) $\sqrt{\frac{10}{7}gh}$
Q61 Arithmetic Sequences and Series Properties of AP Terms under Transformation View
If $a, b, c, d$ and $p$ are distinct real numbers such that $\left(a^{2}+b^{2}+c^{2}\right)p^{2} - 2p(ab+bc+cd) + \left(b^{2}+c^{2}+d^{2}\right) \leq 0$, then
(1) $a, b, c, d$ are in A.P.
(2) $ab = cd$
(3) $ac = bd$
(4) $a, b, c, d$ are in G.P.
Q62 Solving quadratics and applications Optimization or extremal value of an expression via completing the square View
If the sum of the square of the roots of the equation $x^{2} - (\sin\alpha - 2)x - (1+\sin\alpha) = 0$ is least, then $\alpha$ is equal to
(1) $\frac{\pi}{6}$
(2) $\frac{\pi}{4}$
(3) $\frac{\pi}{3}$
(4) $\frac{\pi}{2}$
Q63 Complex Numbers Argand & Loci Geometric Properties of Triangles/Polygons from Affixes View
The area of the triangle whose vertices are complex numbers $z, iz, z+iz$ in the Argand diagram is
(1) $2|z|^{2}$
(2) $\frac{1}{2}|z|^{2}$
(3) $4|z|^{2}$
(4) $|z|^{2}$
Q64 Arithmetic Sequences and Series Evaluation of a Finite or Infinite Sum View
The sum of the series $$\frac{1}{1+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{3}} + \frac{1}{\sqrt{3}+\sqrt{4}} + \ldots$$ upto 15 terms is
(1) 1
(2) 2
(3) 3
(4) 4
Q65 Binomial Theorem (positive integer n) Count Integral or Rational Terms in a Binomial Expansion View
The number of terms in the expansion of $\left(y^{1/5} + x^{1/10}\right)^{55}$, in which powers of $x$ and $y$ are free from radical signs are
(1) six
(2) twelve
(3) seven
(4) five
Q66 Straight Lines & Coordinate Geometry Point-to-Line Distance Computation View
If the point $(1, a)$ lies between the straight lines $x + y = 1$ and $2(x+y) = 3$ then $a$ lies in interval
(1) $\left(\frac{3}{2}, \infty\right)$
(2) $\left(1, \frac{3}{2}\right)$
(3) $(-\infty, 0)$
(4) $\left(0, \frac{1}{2}\right)$
Q67 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
If two vertices of a triangle are $(5, -1)$ and $(-2, 3)$ and its orthocentre is at $(0, 0)$, then the third vertex is
(1) $(4, -7)$
(2) $(-4, -7)$
(3) $(-4, 7)$
(4) $(4, 7)$
Q68 Circles Triangle or Quadrilateral Area and Perimeter with Foci View
The area of triangle formed by the lines joining the vertex of the parabola, $x^{2} = 8y$, to the extremities of its latus rectum is
(1) 2
(2) 8
(3) 1
(4) 4
Q69 Circles Chord Properties and Midpoint Problems View
If $P_{1}$ and $P_{2}$ are two points on the ellipse $\frac{x^{2}}{4} + y^{2} = 1$ at which the tangents are parallel to the chord joining the points $(0, 1)$ and $(2, 0)$, then the distance between $P_{1}$ and $P_{2}$ is
(1) $2\sqrt{2}$
(2) $\sqrt{5}$
(3) $2\sqrt{3}$
(4) $\sqrt{10}$
Q71 Measures of Location and Spread View
If the mean of $4, 7, 2, 8, 6$ and $a$ is 7, then the mean deviation from the median of these observations is
(1) 8
(2) 5
(3) 1
(4) 3
Q72 Sine and Cosine Rules Find an angle using the cosine rule View
If in a triangle $ABC$, $\frac{b+c}{11} = \frac{c+a}{12} = \frac{a+b}{13}$, then $\cos A$ is equal to
(1) $5/7$
(2) $1/5$
(3) $35/19$
(4) $19/35$
Q74 Matrices True/False or Multiple-Select Conceptual Reasoning View
Let $A$ and $B$ be real matrices of the form $\left[\begin{array}{ll}\alpha & 0 \\ 0 & \beta\end{array}\right]$ and $\left[\begin{array}{ll}0 & \gamma \\ \delta & 0\end{array}\right]$, respectively. Statement 1: $AB - BA$ is always an invertible matrix. Statement 2: $AB - BA$ is never an identity matrix.
(1) Statement 1 is true, Statement 2 is false.
(2) Statement 1 is false, Statement 2 is true.
(3) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
(4) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
Q75 3x3 Matrices Determinant and Rank Computation View
$$\left|\begin{array}{ccc} -2a & a+b & a+c \\ b+a & -2b & b+c \\ c+a & b+c & -2c \end{array}\right| = \alpha(a+b)(b+c)(c+a) \neq 0$$
then $\alpha$ is equal to
(1) $a+b+c$
(2) $abc$
(3) 4
(4) 1
Q76 Permutations & Arrangements Counting Functions or Mappings with Constraints View
Statement 1: If $A$ and $B$ be two sets having $p$ and $q$ elements respectively, where $q > p$. Then the total number of functions from set $A$ to set $B$ is $q^{p}$. Statement 2: The total number of selections of $p$ different objects out of $q$ objects is ${}^{q}C_{p}$.
(1) Statement 1 is true, Statement 2 is false.
(2) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
(3) Statement 1 is false, Statement 2 is true.
(4) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
Q78 Chain Rule Chain Rule with Composition of Explicit Functions View
If $f^{\prime}(x) = \sin(\log x)$ and $y = f\left(\frac{2x+3}{3-2x}\right)$, then $\frac{dy}{dx}$ at $x = 1$ is equal to (the question continues with answer options as given in the paper).