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
2019 session1_09jan_shift1

6 maths questions

Q1 Differential equations Solving Separable DEs with Initial Conditions View
A particle is moving with a velocity $\vec { v } = K y \hat { i } + x \hat { j }$, where $K$ is a constant. The general equation for its path is:
(1) $y ^ { 2 } = x +$ constant
(2) $x y =$ constant
(3) $y = x ^ { 2 } +$ constant
(4) $y ^ { 2 } = x ^ { 2 } +$ constant
Q3 Motion on a slope View
A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of $3 N$ is applied on the block. The coefficient of static friction between the plane and the block is 0.6 . What should be the minimum value of force $P$, such that the block does not move downward? (take $g = 10 \mathrm {~ms} ^ { - 2 }$)
(1) 23 N
(2) 25 N
(3) 18 N
(4) 32 N
Q4 Simple Harmonic Motion View
A block of mass $m$, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant $k$. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force $F$, the maximum speed of the block is:
(1) $\frac { F } { \sqrt { m k } }$
(2) $\frac { 2 F } { \sqrt { m k } }$
(3) $\frac { \pi F } { \sqrt { m k } }$
(4) $\frac { F } { \pi \sqrt { m k } }$
Q5 Momentum and Collisions Sequential / Multiple Inelastic Collisions View
Three blocks $\mathrm { A } , \mathrm { B }$ and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, $m$ while C has mass $M$. Block A is given an initial speed $v$ towards B due to which it collides with B perfectly inelastically. The combined mass collides with $C$, also perfectly inelastically . $\frac { 5 } { 6 }$ th of the initial kinetic energy is lost in the whole process. What is the value of $M / m$ ?
(1) 3
(2) 4
(3) 5
(4) 2
Q6 Simple Harmonic Motion View
Two masses $m$ and $\frac { m } { 2 }$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system (see figure). Because of torsional constant $k$, the restoring torque is $\tau = k \theta$ for angular displacement $\theta$. If the rod is rotated by $\theta _ { 0 }$ and released, the tension in it when it passes through its mean position will be:
(1) $k \theta _ { 0 } ^ { 2 }$
(2) $\frac { 3 k \theta _ { 0 } { } ^ { 2 } } { l _ { 0 } }$
(3) $\frac { 2 k \theta _ { 0 } { } ^ { 2 } } { l }$
(4) $\frac { k \theta _ { 0 } { } ^ { 2 } } { l }$
Q7 Moments View
An $L$-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If $A B = B C$, and the angle made by $A B$ with downward vertical is $\theta$, then:
(1) $\tan \theta = \frac { 2 } { \sqrt { 3 } }$
(2) $\tan \theta = \frac { 1 } { 3 }$
(3) $\tan \theta = \frac { 1 } { 2 }$
(4) $\tan \theta = \frac { 1 } { 2 \sqrt { 3 } }$