jee-main

Papers (191)
2026
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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
2021 session2_18mar_shift1

18 maths questions

Q3 Applied differentiation Kinematics via differentiation View
A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time $t$ is proportional to:-
(1) $t ^ { \frac { 2 } { 3 } }$
(2) $t ^ { \frac { 3 } { 2 } }$
(3) $t$
(4) $t ^ { \frac { 1 } { 2 } }$
Q4 Circular Motion 1 Ratio / Comparison of Circular Motion Quantities View
A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with an angular speed $\omega$. Two particles having mass $m$ each are now attached at diametrically opposite points. The angular speed of the ring will become:
(1) $\omega \frac { M } { M + m }$
(2) $\omega \frac { M + 2 m } { M }$
(3) $\omega \frac { M } { M + 2 m }$
(4) $\omega \frac { M - 2 m } { M + 2 m }$
Q5 Circular Motion 1 Centripetal Acceleration / Force Calculation View
The time period of a satellite in a circular orbit of the radius $R$ is $T$. The period of another satellite in a circular orbit of the radius $9R$ is:
(1) $9T$
(2) $27T$
(3) $12T$
(4) $3T$
Q21 SUVAT in 2D & Gravity View
A person is swimming with a speed of $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at an angle of $120 ^ { \circ }$ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is $x \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The value of $x$ to the nearest integer is $\_\_\_\_$.
Q22 Constant acceleration (SUVAT) Penetration and deceleration to rest View
A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of the bullet before hitting the wood is $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and, it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is $x \mathrm {~N}$. The value of $x$ to the nearest integer is
Q23 Work done and energy Potential energy function and energy diagram interpretation View
As shown in the figure, a particle of mass 10 kg is placed at a point $A$. When the particle is slightly displaced to its right, it starts moving and reaches the point $B$. The speed of the particle at $B$ is $x \mathrm {~m} \mathrm {~s} ^ { - 1 }$. (Take $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$) The value of $x$ to the nearest integer is [Figure]
Q24 Momentum and Collisions Explosion or Breakup – Fragment Velocities or Energies View
A ball of mass 10 kg moving with a velocity $10 \sqrt { 3 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$ along the $x$-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along $y$-axis with a speed of $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The second piece starts moving at an angle of $30 ^ { \circ }$ with respect to the $x$-axis. The velocity of the ball moving at $30 ^ { \circ }$ with $x$-axis is $x \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The configuration of pieces after the collision is shown in the figure below. The value of $x$ to the nearest integer is [Figure]
Q26 Simple Harmonic Motion View
A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $\frac { 1 } { a } \mathrm {~s}$. The value of $a$ to the nearest integer is
Q61 Sequences and series, recurrence and convergence Convergence proof and limit determination View
The value of $3 + \frac { 1 } { 4 + \frac { 1 } { 3 + \frac { 1 } { 4 + \frac { 1 } { 3 + \ldots . \infty } } } }$ is equal to
(1) $1.5 + \sqrt { 3 }$
(2) $2 + \sqrt { 3 }$
(3) $3 + 2 \sqrt { 3 }$
(4) $4 + \sqrt { 3 }$
Q62 Complex Numbers Argand & Loci Circle Equation and Properties via Complex Number Manipulation View
If the equation $a | z | ^ { 2 } + \overline { \bar { \alpha } z + \alpha \bar { z } } + d = 0$ represents a circle where $a , d$ are real constants then which of the following condition is correct?
(1) $| \alpha | ^ { 2 } - a d \neq 0$
(2) $| \alpha | ^ { 2 } - a d > 0$ and $a \in R - \{ 0 \}$
(3) $| \alpha | ^ { 2 } - a d \geq 0$ and $a \in R$
(4) $\alpha = 0 , a , d \in R ^ { + }$
Q63 Permutations & Arrangements Word Permutations with Repeated Letters View
The sum of all the 4-digit distinct numbers that can be formed with the digits $1, 2, 2$ and 3 is:
(1) 26664
(2) 122664
(3) 122234
(4) 22264
Q64 Arithmetic Sequences and Series Summation of Derived Sequence from AP View
If $\alpha , \beta$ are natural numbers such that $100 ^ { \alpha } - 199 \beta = ( 100 ) ( 100 ) + ( 99 ) ( 101 ) + ( 98 ) ( 102 ) + \ldots . + ( 1 ) ( 199 )$, then the slope of the line passing through $( \alpha , \beta )$ and origin is:
(1) 540
(2) 550
(3) 530
(4) 510
Q65 Arithmetic Sequences and Series Evaluation of a Finite or Infinite Sum View
$\frac { 1 } { 3 ^ { 2 } - 1 } + \frac { 1 } { 5 ^ { 2 } - 1 } + \frac { 1 } { 7 ^ { 2 } - 1 } + \ldots + \frac { 1 } { ( 201 ) ^ { 2 } - 1 }$ is equal to
(1) $\frac { 101 } { 404 }$
(2) $\frac { 25 } { 101 }$
(3) $\frac { 101 } { 408 }$
(4) $\frac { 99 } { 400 }$
Q66 Binomial Theorem (positive integer n) Extract Coefficients Using Roots of Unity or Substitution Filter View
Let $\left( 1 + x + 2 x ^ { 2 } \right) ^ { 20 } = a _ { 0 } + a _ { 1 } x + a _ { 2 } x ^ { 2 } + \ldots + a _ { 40 } x ^ { 40 }$, then $a _ { 1 } + a _ { 3 } + a _ { 5 } + \ldots + a _ { 37 }$ is equal to
(1) $2 ^ { 20 } \left( 2 ^ { 20 } - 21 \right)$
(2) $2 ^ { 19 } \left( 2 ^ { 20 } - 21 \right)$
(3) $2 ^ { 19 } \left( 2 ^ { 20 } + 21 \right)$
(4) $2 ^ { 20 } \left( 2 ^ { 20 } + 21 \right)$
Q67 Trig Proofs Trigonometric Identity Simplification View
The solutions of the equation $\left| \begin{array} { c c c } 1 + \sin ^ { 2 } x & \sin ^ { 2 } x & \sin ^ { 2 } x \\ \cos ^ { 2 } x & 1 + \cos ^ { 2 } x & \cos ^ { 2 } x \\ 4 \sin 2 x & 4 \sin 2 x & 1 + 4 \sin 2 x \end{array} \right| = 0 , ( 0 < x < \pi )$, are
(1) $\frac { \pi } { 12 } , \frac { \pi } { 6 }$
(2) $\frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$
(3) $\frac { 5 \pi } { 12 } , \frac { 7 \pi } { 12 }$
(4) $\frac { 7 \pi } { 12 } , \frac { 11 \pi } { 12 }$
Q68 Simultaneous equations Line Equation and Parametric Representation View
The number of integral values of $m$ so that the abscissa of point of intersection of lines $3 x + 4 y = 9$ and $y = m x + 1$ is also an integer, is:
(1) 1
(2) 2
(3) 3
(4) 0
Q69 Straight Lines & Coordinate Geometry Slope and Angle Between Lines View
The equation of one of the straight lines which passes through the point $(1, 3)$ and makes an angle $\tan ^ { - 1 } ( \sqrt { 2 } )$ with the straight line, $y + 1 = 3 \sqrt { 2 } x$ is
(1) $4 \sqrt { 2 } x + 5 y - ( 15 + 4 \sqrt { 2 } ) = 0$
(2) $5 \sqrt { 2 } x + 4 y - ( 15 + 4 \sqrt { 2 } ) = 0$
(3) $4 \sqrt { 2 } x + 5 y - 4 \sqrt { 2 } = 0$
(4) $4 \sqrt { 2 } x - 5 y - ( 5 + 4 \sqrt { 2 } ) = 0$
Q70 Circles Circle Identification and Classification View
Choose the correct statement about two circles whose equations are given below: $x ^ { 2 } + y ^ { 2 } - 10 x - 10 y + 41 = 0$ $x ^ { 2 } + y ^ { 2 } - 22 x - 10 y + 137 = 0$
(1) circles have same centre
(2) circles have no meeting point