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
2020 session1_08jan_shift1

5 maths questions

Q21 Variable acceleration (1D) Find velocity/speed by differentiating position View
A particle is moving along the $x$-axis with its coordinate with time $t$ given by $x ( t ) = 10 + 8 t - 3 t ^ { 2 }$. Another particle is moving along the $y$-axis with its coordinate as a function of time given by $y ( t ) = 5 - 8 t ^ { 3 }$. At $t = 1 \mathrm {~s}$, the speed of the second particle as measured in the frame of the first particle is given as $\sqrt { v }$. Then $v$ (in $\mathrm { m s } ^ { - 1 }$) is $\_\_\_\_$.
Q22 Momentum and Collisions Elastic Collision – Velocity or Mass Determination View
A body A of mass $m = 0.1 \mathrm {~kg}$ has an initial velocity of $3 \hat { \mathrm { i } } \mathrm { m s } ^ { - 1 }$. It collides elastically with another body B of the same mass which has an initial velocity of $5 \hat { \mathrm { j } } \mathrm { m s } ^ { - 1 }$. After the collision, A moves with a velocity $\vec { v } = 4 ( \hat { \mathrm { i } } + \hat { \mathrm { j } } ) \mathrm { m s } ^ { - 1 }$. The energy of B after the collision is written as $\frac { x } { 10 } \mathrm {~J}$. The value of $x$ is $\_\_\_\_$.
Q51 Complex Numbers Argand & Loci Solving Complex Equations with Geometric Interpretation View
If the equation $x ^ { 2 } + b x + 45 = 0 , b \in R$ has conjugate complex roots and they satisfy $| z + 1 | = 2 \sqrt { 10 }$, then
(1) $b ^ { 2 } - b = 30$
(2) $b ^ { 2 } + b = 72$
(3) $b ^ { 2 } - b = 42$
(4) $b ^ { 2 } + b = 12$
Q52 Arithmetic Sequences and Series Optimization Involving an Arithmetic Sequence View
Let $f : R \rightarrow R$ be such that for all $x \in R$, $\left( 2 ^ { 1 + x } + 2 ^ { 1 - x } \right)$, $f ( x )$ and $\left( 3 ^ { x } + 3 ^ { - x } \right)$ are in A.P., then the minimum value of $f ( x )$ is
(1) 2
(2) 3
(3) 0
(4) 4
Q53 Combinations & Selection Basic Combination Computation View
If $a , b$ and $c$ are the greatest values of ${}^{ 19 } C _ { p } , {}^{ 20 } C _ { q }$ and ${}^{ 21 } C _ { r }$ respectively, then:
(1) $\frac { a } { 11 } = \frac { b } { 22 } = \frac { c } { 21 }$
(2) $\frac { a } { 10 } = \frac { b } { 20 } = \frac { c } { 21 }$
(3) $\frac { a } { 11 } = \frac { b } { 22 } = \frac { c } { 42 }$
(4) $\frac { a } { 10 } = \frac { b } { 11 } = \frac { c } { 42 }$