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
2020 session2_04sep_shift1

14 maths questions

Q3 SUVAT in 2D & Gravity View
Starting from the origin at time $\mathrm { t } = 0$, with initial velocity $5 \widehat { \mathrm { j } } \mathrm { ms } ^ { - 1 }$, a particle moves in the $x - y$ plane with a constant acceleration of $( 10 \widehat { \mathrm { i } } + 4 \widehat { \mathrm { j } } ) \mathrm { ms } ^ { - 2 }$. At time t , its coordinates are $\left( 20 \mathrm {~m} , \mathrm { y } _ { 0 } \mathrm {~m} \right)$. The values of t and $\mathrm { y } _ { 0 }$ are, respectively:
(1) 2 s and 18 m
(2) 4 s and 52 m
(3) 2 s and 24 m
(4) 5 s and 25 m
Q4 Momentum and Collisions Sequential / Multiple Inelastic Collisions View
Blocks of masses $\mathrm { m } , 2 \mathrm {~m} , 4 \mathrm {~m}$ and 8 m are arranged in a line of a frictionless floor. Another block of mass m , moving with speed $v$ along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8 m starts moving the total energy loss is $\mathrm { p } \%$ of the original energy. Value of 'p' is close to:
(1) 77
(2) 94
(3) 37
(4) 87
Q5 Indefinite & Definite Integrals Antiderivative Verification and Construction View
On the $x$-axis and at a distance $x$ from the origin, the gravitational field due to a mass distribution is given by $\frac { A x } { \left( x ^ { 2 } + a ^ { 2 } \right) ^ { 3 / 2 } }$ in the $x$-direction. The magnitude of the gravitational potential on the $x$-axis at a distance $x$, taking its value to be zero at infinity is:
(1) $\frac { A } { \left( x ^ { 2 } + a ^ { 2 } \right) ^ { 1 / 2 } }$
(2) $\frac { A } { \left( x ^ { 2 } + a ^ { 2 } \right) ^ { 3 / 2 } }$
(3) $A \left( x ^ { 2 } + a ^ { 2 } \right) ^ { 1 / 2 }$
(4) $A \left( x ^ { 2 } + a ^ { 2 } \right) ^ { 3 / 2 }$
Q21 Moments View
$ABC$ is a plane lamina of the shape of an equilateral triangle. $D , E$ are mid-points of $AB , AC$ and $G$ is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through $G$ and perpendicular to the plane $ABC$ is $I _ { 0 }$. If part $ADE$ is removed, the moment of inertia of the remaining part about the same axis is $\frac { N I _ { 0 } } { 16 }$ where $N$ is an integer. Value of $N$ is:
Q22 Impulse and momentum (advanced) View
A circular disc of mass M and radius R is rotating about its axis with angular speed $\omega _ { 1 }$. If another stationary disc having radius $\frac { \mathrm { R } } { 2 }$ and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed $\omega _ { 2 }$. The energy lost in the process is $p \%$ of the initial energy. Value of $p$ is $\_\_\_\_$
Q51 Modulus function Counting solutions or configurations satisfying a quadratic system View
Let $[ \mathrm { t } ]$ denote the greatest integer $\leq \mathrm { t }$. Then the equation in $\mathrm { x } , [ \mathrm { x } ] ^ { 2 } + 2 [ \mathrm { x } + 2 ] - 7 = 0$ has :
(1) exactly two solutions
(2) exactly four integral solutions
(3) no integral solution
(4) infinitely many solutions
Q52 Discriminant and conditions for roots Vieta's formulas: compute symmetric functions of roots View
Let $\alpha$ and $\beta$ be the roots of $x ^ { 2 } - 3 x + p = 0$ and $\gamma$ and $\delta$ be the roots of $x ^ { 2 } - 6 x + q = 0$. If $\alpha , \beta , \gamma , \delta$ from a geometric progression. Then ratio $( 2 q + p ) : ( 2 q - p )$ is
(1) $3 : 1$
(2) $9 : 7$
(3) $5 : 3$
(4) $33 : 31$
Q53 Complex Numbers Argand & Loci Circle Equation and Properties via Complex Number Manipulation View
Let $u = \frac { 2 z + i } { z - k i } , z = x + i y$ and $k > 0$. If the curve represented by Re $( u ) + \operatorname { Im } ( u ) = 1$ intersects the $y$-axis at points P and Q where $\mathrm { PQ } = 5$ then the value of k is
(1) $\frac { 3 } { 2 }$
(2) $\frac { 1 } { 2 }$
(3) 4
(4) 2
Q54 Arithmetic Sequences and Series Summation of Derived Sequence from AP View
If $1 + \left( 1 - 2 ^ { 2 } \cdot 1 \right) + \left( 1 - 4 ^ { 2 } \cdot 3 \right) + \left( 1 - 6 ^ { 2 } \cdot 5 \right) + \ldots \ldots + \left( 1 - 20 ^ { 2 } \cdot 19 \right) = \alpha - 220 \beta$, then an ordered pair $( \alpha , \beta )$ is equal to:
(1) $( 10,97 )$
(2) $( 11,103 )$
(3) $( 10,103 )$
(4) $( 11,97 )$
Q55 Combinations & Selection Combinatorial Identity or Bijection Proof View
The value of $\sum _ { r = 0 } ^ { 20 } { } ^ { 50 - r } C _ { 6 }$ is equal to:
(1) ${ } ^ { 51 } C _ { 7 } - { } ^ { 30 } C _ { 7 }$
(2) ${ } ^ { 50 } C _ { 7 } - { } ^ { 30 } C _ { 7 }$
(3) ${ } ^ { 50 } C _ { 6 } - { } ^ { 30 } C _ { 6 }$
(4) ${ } ^ { 51 } C _ { 7 } + { } ^ { 30 } C _ { 7 }$
Q56 Straight Lines & Coordinate Geometry Area Computation in Coordinate Geometry View
A triangle $ABC$ lying in the first quadrant has two vertices as $A ( 1,2 )$ and $B ( 3,1 )$. If $\angle BAC = 90 ^ { \circ }$, and $\operatorname { ar } ( \Delta \mathrm { ABC } ) = 5 \sqrt { 5 }$ sq. units, then the abscissa of the vertex C is :
(1) $1 + \sqrt { 5 }$
(2) $1 + 2 \sqrt { 5 }$
(3) $2 + \sqrt { 5 }$
(4) $2 \sqrt { 5 } - 1$
Q57 Conic sections Equation Determination from Geometric Conditions View
Let $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b )$ be a given ellipse, length of whose latus rectum is 10 . If its eccentricity is the maximum value of the function, $\phi ( t ) = \frac { 5 } { 12 } + t - t ^ { 2 }$, then $a ^ { 2 } + b ^ { 2 }$ is equal to:
(1) 145
(2) 116
(3) 126
(4) 135
Q58 Conic sections Eccentricity or Asymptote Computation View
Let $P ( 3,3 )$ be a point on the hyperbola, $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$. If the normal to it at $P$ intersects the $x$-axis at $( 9,0 )$ and $e$ is its eccentricity, then the ordered pair $\left( a ^ { 2 } , e ^ { 2 } \right)$ is equal to:
(1) $\left( \frac { 9 } { 2 } , 3 \right)$
(2) $\left( \frac { 3 } { 2 } , 2 \right)$
(3) $\left( \frac { 9 } { 2 } , 2 \right)$
(4) $( 9,3 )$
Q60 Measures of Location and Spread View
The mean and variance of 8 observations are 10 and 13.5 respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is:
(1) 7
(2) 3
(3) 5
(4) 9