jee-main

Papers (169)
2025
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2024
session1_01feb_shift1 4 session1_01feb_shift2 22 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 30 session1_29jan_shift2 23 session1_30jan_shift1 17 session1_30jan_shift2 30 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 4 session2_04apr_shift2 30 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 22 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 30 session2_09apr_shift1 5 session2_09apr_shift2 30
2023
session1_01feb_shift1 24 session1_01feb_shift2 3 session1_24jan_shift1 13 session1_24jan_shift2 12 session1_25jan_shift1 28 session1_25jan_shift2 27 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 2 session1_30jan_shift2 29 session1_31jan_shift1 28 session1_31jan_shift2 17 session2_06apr_shift1 5 session2_06apr_shift2 17 session2_08apr_shift1 29 session2_08apr_shift2 14 session2_10apr_shift1 29 session2_10apr_shift2 15 session2_11apr_shift1 5 session2_11apr_shift2 4 session2_12apr_shift1 26 session2_13apr_shift1 25 session2_13apr_shift2 20 session2_15apr_shift1 20
2022
session1_24jun_shift1 20 session1_24jun_shift2 25 session1_25jun_shift1 14 session1_25jun_shift2 17 session1_26jun_shift1 26 session1_26jun_shift2 23 session1_27jun_shift1 4 session1_27jun_shift2 29 session1_28jun_shift1 13 session1_29jun_shift1 20 session1_29jun_shift2 5 session2_25jul_shift1 29 session2_25jul_shift2 22 session2_26jul_shift1 29 session2_26jul_shift2 24 session2_27jul_shift1 26 session2_27jul_shift2 29 session2_28jul_shift1 12 session2_28jul_shift2 29 session2_29jul_shift1 18 session2_29jul_shift2 17
2021
session1_24feb_shift1 10 session1_24feb_shift2 7 session1_25feb_shift1 29 session1_25feb_shift2 29 session1_26feb_shift2 17 session2_16mar_shift1 29 session2_16mar_shift2 15 session2_17mar_shift1 20 session2_17mar_shift2 24 session2_18mar_shift1 12 session2_18mar_shift2 11 session3_20jul_shift1 30 session3_20jul_shift2 29 session3_22jul_shift1 7 session3_25jul_shift1 2 session3_25jul_shift2 15 session3_27jul_shift1 3 session3_27jul_shift2 4 session4_01sep_shift2 11 session4_26aug_shift1 5 session4_26aug_shift2 2 session4_27aug_shift1 3 session4_27aug_shift2 28 session4_31aug_shift1 28 session4_31aug_shift2 4
2020
session1_07jan_shift1 26 session1_07jan_shift2 17 session1_08jan_shift1 5 session1_08jan_shift2 12 session1_09jan_shift1 22 session1_09jan_shift2 18 session2_02sep_shift1 19 session2_02sep_shift2 17 session2_03sep_shift1 21 session2_03sep_shift2 9 session2_04sep_shift1 10 session2_04sep_shift2 24 session2_05sep_shift1 23 session2_05sep_shift2 27 session2_06sep_shift1 13 session2_06sep_shift2 10
2019
session1_09jan_shift1 6 session1_09jan_shift2 29 session1_10jan_shift1 30 session1_10jan_shift2 12 session1_11jan_shift1 6 session1_11jan_shift2 5 session1_12jan_shift1 10 session1_12jan_shift2 20 session2_08apr_shift1 29 session2_08apr_shift2 29 session2_09apr_shift1 29 session2_09apr_shift2 29 session2_10apr_shift1 2 session2_10apr_shift2 3 session2_12apr_shift1 3 session2_12apr_shift2 9
2018
08apr 29 15apr 28 15apr_shift1 28 15apr_shift2 2 16apr 15
2017
02apr 28 08apr 29 09apr 30
2016
03apr 30 09apr 30 10apr 28
2015
04apr 29 10apr 30
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
2013
07apr 29 09apr 14 22apr 5 23apr 14 25apr 13
2012
07may 18 12may 22 19may 13 26may 17 offline 30
2011
jee-main_2011.pdf 13
2010
jee-main_2010.pdf 1
2009
jee-main_2009.pdf 1
2008
jee-main_2008.pdf 1
2007
jee-main_2007.pdf 38
2005
jee-main_2005.pdf 19
2004
jee-main_2004.pdf 11
2003
jee-main_2003.pdf 9
2002
jee-main_2002.pdf 8
2021 session1_24feb_shift2

7 maths questions

Q61 Arithmetic Sequences and Series Find Specific Term from Given Conditions View
Let $a , b , c$ be in arithmetic progression. Let the centroid of the triangle with vertices $( a , c ) , ( 2 , b )$ and $( a , b )$ be $\left( \frac { 10 } { 3 } , \frac { 7 } { 3 } \right)$. If $\alpha , \beta$ are the roots of the equation $a x ^ { 2 } + b x + 1 = 0$, then the value of $\alpha ^ { 2 } + \beta ^ { 2 } - \alpha \beta$ is:
(1) $- \frac { 71 } { 256 }$
(2) $\frac { 69 } { 256 }$
(3) $\frac { 71 } { 256 }$
(4) $- \frac { 69 } { 256 }$
Q62 Sequences and Series Evaluation of a Finite or Infinite Sum View
If $n \geqslant 2$ is a positive integer, then the sum of the series ${ } ^ { n + 1 } C _ { 2 } + 2 \left( { } ^ { 2 } C _ { 2 } + { } ^ { 3 } C _ { 2 } + { } ^ { 4 } C _ { 2 } + \ldots + { } ^ { n } C _ { 2 } \right)$ is
(1) $\frac { n ( n - 1 ) ( 2 n + 1 ) } { 6 }$
(2) $\frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 }$
(3) $\frac { n ( n + 1 ) ^ { 2 } ( n + 2 ) } { 12 }$
(4) $\frac { n ( 2 n + 1 ) ( 3 n + 1 ) } { 6 }$
Q63 Stationary points and optimisation Geometric or applied optimisation problem View
If $P$ is a point on the parabola $y = x ^ { 2 } + 4$ which is closest to the straight line $y = 4 x - 1$, then the coordinates of $P$ are:
(1) $( - 2,8 )$
(2) $( 1,5 )$
(3) $( 2,8 )$
(4) $( 3,13 )$
Q64 Proof True/False Justification View
The negation of the statement $\sim p \wedge ( p \vee q )$ is:
(1) $\sim p \vee q$
(2) $\sim p \wedge q$
(3) $p \vee \sim q$
(4) $p \wedge \sim q$
Q65 Proof True/False Justification View
For the statements $p$ and $q$, consider the following compound statements: $( a ) ( \sim q \wedge ( p \rightarrow q ) ) \rightarrow \sim p$
(b) $( ( p \vee q ) \wedge \sim p ) \rightarrow q$ Then which of the following statements is correct?
(1) (b) is a tautology but not (a).
(2) (a) and (b) both are tautologies.
(3) (a) and (b) both are not tautologies.
(4) (a) is a tautology but not (b).
Q66 Sine and Cosine Rules Heights and distances / angle of elevation problem View
The angle of elevation of a jet plane from a point $A$ on the ground is $60 ^ { \circ }$. After a flight of 20 seconds at the speed of 432 km / hour, the angle of elevation changes to $30 ^ { \circ }$. If the jet plane is flying at a constant height, then its height is:
(1) $1200 \sqrt { 3 } \mathrm {~m}$
(2) $2400 \sqrt { 3 } \mathrm {~m}$
(3) $1800 \sqrt { 3 } \mathrm {~m}$
(4) $3600 \sqrt { 3 } \mathrm {~m}$
Q67 Matrices Linear System and Inverse Existence View
For the system of linear equations: $$x - 2 y = 1 , x - y + k z = - 2 , k y + 4 z = 6 , k \in R$$ Consider the following statements:
(A) The system has unique solution if $k \neq 2 , k \neq - 2$.
(B) The system has unique solution if $k = - 2$.
(C) The system has unique solution if $k = 2$.
(D) The system has no-solution if $k = 2$.
(E) The system has infinitely many solutions if $k = - 2$.