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_03sep_shift2

8 maths questions

Q51 Discriminant and conditions for roots Parameter range for specific root conditions (location/count) View
The set of all real values of $\lambda$ for which the quadratic equation $\left( \lambda ^ { 2 } + 1 \right) x ^ { 2 } - 4 \lambda x + 2 = 0$ always have exactly one root in the interval $( 0,1 )$ is :
(1) $( - 3 , - 1 )$
(2) $( 0,2 )$
(3) $( 1,3 ]$
(4) $( 2,4 ]$
Q52 Complex Numbers Argand & Loci Locus Identification from Modulus/Argument Equation View
If $z _ { 1 } , z _ { 2 }$ are complex numbers such that $\operatorname { Re } \left( z _ { 1 } \right) = \left| z _ { 1 } - 1 \right|$ and $\operatorname { Re } \left( z _ { 2 } \right) = \left| z _ { 2 } - 1 \right|$ and $\arg \left( z _ { 1 } - z _ { 2 } \right) = \frac { \pi } { 6 }$ , then $\operatorname { Im } \left( z _ { 1 } + z _ { 2 } \right)$ is equal to :
(1) $2 \sqrt { 3 }$
(2) $\frac { \sqrt { 3 } } { 2 }$
(3) $\frac { 1 } { \sqrt { 3 } }$
(4) $\frac { 2 } { \sqrt { 3 } }$
Q53 Arithmetic Sequences and Series Optimization Involving an Arithmetic Sequence View
If the sum of the series $20 + 19 \frac { 3 } { 5 } + 19 \frac { 1 } { 5 } + 18 \frac { 4 } { 5 } + \ldots\ldots\ldots$ up to $n ^ { \text {th} }$ term is 488 and the $n ^ { \text {th} }$ term is negative, then :
(1) $n ^ { \text {th} }$ term is $- 4 \frac { 2 } { 5 }$
(2) $n = 41$
(3) $n ^ { \text {th} }$ term is - 4
(4) $n = 60$
Q54 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
If the term independent of $x$ in the expansion of $\left( \frac { 3 } { 2 } x ^ { 2 } - \frac { 1 } { 3 x } \right) ^ { 9 }$ is $k$, then $18k$ is equal to:
(1) 11
(2) 5
(3) 9
(4) 7
Q55 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
If a $\triangle ABC$ has vertices $A ( - 1,7 ) , B ( - 7,1 )$ and $C ( 5 , - 5 )$, then its orthocentre has coordinates:
(1) $( - 3,3 )$
(2) $( 3 , - 3 )$
(3) $\left( - \frac { 3 } { 5 } , \frac { 3 } { 5 } \right)$
(4) $\left( \frac { 3 } { 5 } , - \frac { 3 } { 5 } \right)$
Q56 Circles Chord Length and Chord Properties View
Let the latus rectum of the parabola $y ^ { 2 } = 4 x$ be the common chord to the circles $C _ { 1 }$ and $C _ { 2 }$ each of them having radius $2 \sqrt { 5 }$. Then, the distance between the centres of the circles $C _ { 1 }$ and $C _ { 2 }$ is :
(1) 12
(2) 8
(3) $8 \sqrt { 5 }$
(4) $4 \sqrt { 5 }$
Q57 Conic sections Focal Distance and Point-on-Conic Metric Computation View
Let $e _ { 1 }$ and $e _ { 2 }$ be the eccentricities of the ellipse $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( b < 5 )$ and the hyperbola $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ respectively satisfying $\mathrm { e } _ { 1 } \mathrm { e } _ { 2 } = 1$. If $\alpha$ and $\beta$ are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair $( \alpha , \beta )$ is equal to:
(1) $( 8,10 )$
(2) $\left( \frac { 20 } { 3 } , 12 \right)$
(3) $( 8,12 )$
(4) $\left( \frac { 24 } { 5 } , 10 \right)$
Q58 Chain Rule Limit Evaluation Involving Composition or Substitution View
$\lim _ { x \rightarrow a } \frac { ( a + 2 x ) ^ { \frac { 1 } { 3 } } - ( 3 x ) ^ { \frac { 1 } { 3 } } } { ( 3 a + x ) ^ { \frac { 1 } { 3 } } - ( 4 x ) ^ { \frac { 1 } { 3 } } } ( a \neq 0 )$ is equal to:
(1) $\left( \frac { 2 } { 9 } \right) \left( \frac { 2 } { 3 } \right) ^ { \frac { 1 } { 3 } }$
(2) $\left( \frac { 2 } { 3 } \right) ^ { \frac { 4 } { 3 } }$
(3) $\left( \frac { 2 } { 9 } \right) ^ { \frac { 4 } { 3 } }$
(4) $\left( \frac { 2 } { 3 } \right) \left( \frac { 2 } { 9 } \right) ^ { \frac { 1 } { 3 } }$