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
2021 session1_26feb_shift2

15 maths questions

Q3 Constant acceleration (SUVAT) Acceleration then deceleration (two-phase motion) View
A scooter accelerates from rest for time $t _ { 1 }$ at constant rate $a _ { 1 }$ and then retards at constant rate $a _ { 2 }$ for time $t _ { 2 }$ and comes to rest. The correct value of $\frac { t _ { 1 } } { t _ { 2 } }$ will be :
(1) $\frac { a _ { 2 } } { a _ { 1 } }$
(2) $\frac { a _ { 1 } } { a _ { 2 } }$
(3) $\frac { a _ { 1 } + a _ { 2 } } { a _ { 1 } }$
(4) $\frac { a _ { 1 } + a _ { 2 } } { a _ { 2 } }$
Q4 Projectiles Trajectory Equation Analysis View
The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta x ^ { 2 }$, where $\alpha$ and $\beta$ are constants and $x \& y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $H$ are respectively given by
(1) $\tan ^ { - 1 } \alpha , \frac { 4 \alpha ^ { 2 } } { \beta }$
(2) $\tan ^ { - 1 } \left( \frac { \beta } { \alpha } \right) , \frac { \alpha ^ { 2 } } { \beta }$
(3) $\tan ^ { - 1 } \beta , \frac { \alpha ^ { 2 } } { 2 \beta }$
(4) $\tan ^ { - 1 } \alpha , \frac { \alpha ^ { 2 } } { 4 \beta }$
Q7 Advanced work-energy problems Rolling body energy and incline problems View
A cord is wound round the circumference of wheel of radius $r$, The axis of the wheel is horizontal and the moment of inertia about it is $I$. A weight $m g$ is attached to the cord at the end. The weight falls from rest. After falling through a distance h , the square of angular velocity of wheel will be
(1) $\frac { 2 m g h } { I + m r ^ { 2 } }$
(2) $\frac { 2 m g h } { I + 2 m r ^ { 2 } }$
(3) $2 g h$
(4) $\frac { 2 g h } { I + m r ^ { 2 } }$
Q61 Number Theory Divisibility and Divisor Analysis View
A natural number has prime factorization given by $n = 2 ^ { x } 3 ^ { y } 5 ^ { z }$, where $y$ and $z$ are such that $y + z = 5$ and $y ^ { - 1 } + z ^ { - 1 } = \frac { 5 } { 6 } , y > z$. Then the number of odd divisors of $n$, including 1 , is:
(1) 12
(2) 6
(3) 11
(4) $6 x$
Q62 Sequences and series, recurrence and convergence Evaluation of a Finite or Infinite Sum View
The sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 2 } + 6 n + 10 } { ( 2 n + 1 ) ! }$ is equal to
(1) $\frac { 41 } { 8 } e + \frac { 19 } { 8 } e ^ { - 1 } + 10$
(2) $\frac { 41 } { 8 } e + \frac { 19 } { 8 } e ^ { - 1 } - 10$
(3) $- \frac { 41 } { 8 } e + \frac { 19 } { 8 } e ^ { - 1 } - 10$
(4) $\frac { 41 } { 8 } e - \frac { 19 } { 8 } e ^ { - 1 } - 10$
Q63 Sequences and series, recurrence and convergence Identify a closed-form function from its Taylor series View
If $0 < a , b < 1$, and $\tan ^ { - 1 } a + \tan ^ { - 1 } b = \frac { \pi } { 4 }$, then the value of $( a + b ) - \left( \frac { a ^ { 2 } + b ^ { 2 } } { 2 } \right) + \left( \frac { a ^ { 3 } + b ^ { 3 } } { 3 } \right) - \left( \frac { a ^ { 4 } + b ^ { 4 } } { 4 } \right) + \ldots$ is :
(1) $\log _ { \mathrm { e } } \left( \frac { e } { 2 } \right)$
(2) $e$
(3) $e ^ { 2 } - 1$
(4) $\log _ { e } 2$
Q64 Circles Circle-Related Locus Problems View
If the locus of the mid-point of the line segment from the point $( 3,2 )$ to a point on the circle, $x ^ { 2 } + y ^ { 2 } = 1$ is a circle of radius $r$, then $r$ is equal to
(1) $\frac { 1 } { 4 }$
(2) 1
(3) $\frac { 1 } { 3 }$
(4) $\frac { 1 } { 2 }$
Q65 Curve Sketching Optimization on a Circle View
Let $A ( 1,4 )$ and $B ( 1 , - 5 )$ be two points. Let $P$ be a point on the circle $( ( x - 1 ) ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 1$, such that $( P A ) ^ { 2 } + ( P B ) ^ { 2 }$ have maximum value, then the points, $P , A$ and $B$ lie on
(1) a hyperbola
(2) a straight line
(3) an ellipse
(4) a parabola
Q66 Differentiation from First Principles View
Let $f ( x )$ be a differentiable function at $x = a$ with $f ^ { \prime } ( a ) = 2$ and $f ( a ) = 4$. Then $\lim _ { x \rightarrow a } \frac { x f ( a ) - a f ( x ) } { x - a }$ equals:
(1) $a + 4$
(2) $2 a - 4$
(3) $4 - 2 a$
(4) $2 a + 4$
Q68 Simultaneous equations Linear System and Inverse Existence View
Consider the following system of equations: $$\begin{aligned} & x + 2 y - 3 z = a \\ & 2 x + 6 y - 11 z = b \\ & x - 2 y + 7 z = c \end{aligned}$$ where $a , b$ and $c$ are real constants. Then the system of equations :
(1) has a unique solution when $5 a = 2 b + c$
(2) has no solution for all $a , b$ and $c$
(3) has infinite number of solutions when $5 a = 2 b + c$
(4) has a unique solution for all $a , b$ and $c$
Q70 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
Let $f ( x ) = \sin ^ { - 1 } x$ and $g ( x ) = \frac { x ^ { 2 } - x - 2 } { 2 x ^ { 2 } - x - 6 }$. If $g ( 2 ) = \lim _ { x \rightarrow 2 } g ( x )$, then the domain of the function $f o g$ is
(1) $( - \infty , - 1 ] \cup [ 2 , \infty )$
(2) $( - \infty , - 2 ] \cup \left[ - \frac { 3 } { 2 } , \infty \right)$
(3) $( - \infty , - 2 ] \cup \left[ - \frac { 4 } { 3 } , \infty \right)$
(4) $( - \infty , - 2 ] \cup [ - 1 , \infty )$
Q71 Curve Sketching Determine Domain or Range of a Composite Function View
Let $f : R \rightarrow R$ be defined as $f ( x ) = \begin{cases} 2 \sin \left( - \frac { \pi x } { 2 } \right) , & \text { if } x < - 1 \\ \left| a x ^ { 2 } + x + b \right| , & \text { if } - 1 \leq x \leq 1 \\ \sin ( \pi x ) , & \text { if } x > 1 \end{cases}$ If $f ( x )$ is continuous on $R$, then $a + b$ equals :
(1) 1
(2) 3
(3) - 3
(4) - 1
Q72 Stationary points and optimisation Geometric or applied optimisation problem View
The triangle of maximum area that can be inscribed in a given circle of radius ' $r$ ' is :
(1) An equilateral triangle having each of its side of length $\sqrt { 3 } r$.
(2) An isosceles triangle with base equal to $2 r$.
(3) An equilateral triangle of height $\frac { 2 r } { 3 }$.
(4) A right angle triangle having two of its sides of length $2 r$ and $r$.
Q73 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution View
For $x > 0$, if $f ( x ) = \int _ { 1 } ^ { x } \frac { \log _ { e } t } { ( 1 + t ) } d t$, then $f ( e ) + f \left( \frac { 1 } { e } \right)$ is equal to
(1) 0
(2) $\frac { 1 } { 2 }$
(3) - 1
(4) 1
Q74 Differential equations Integral Equations Reducible to DEs View
Let $f ( x ) = \int _ { 0 } ^ { x } e ^ { t } f ( t ) d t + e ^ { x }$ be a differentiable function for all $x \in R$. Then $f ( x )$ equals:
(1) $e ^ { \left( e ^ { x } - 1 \right) }$
(2) $e ^ { e ^ { x } } - 1$
(3) $2 e ^ { e ^ { x } } - 1$