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 session2_12apr_shift2

9 maths questions

Q1 Variable acceleration (1D) Velocity as a function of position View
A particle is moving with speed $v = b \sqrt { x }$ along positive $x$ - axis. Calculate the speed of the particle at time $t = \tau$ (assume that the particle is at origin at $t = 0$ )
(1) $b ^ { 2 } \tau$
(2) $\frac { b ^ { 2 } \tau } { \sqrt { 2 } }$
(3) $\frac { b ^ { 2 } \tau } { 2 }$
(4) $\frac { b ^ { 2 } \tau } { 4 }$
Q2 Projectiles Range and Complementary Angle Relationships View
Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $\mathrm { h } _ { 1 }$ and $\mathrm { h } _ { 2 }$. Which of the following is correct?
(1) $R ^ { 2 } = h _ { 1 } h _ { 2 }$
(2) $R ^ { 2 } = 4 h _ { 1 } h _ { 2 }$
(3) $R ^ { 2 } = 2 h _ { 1 } h _ { 2 }$
(4) $R ^ { 2 } = 16 h _ { 1 } h _ { 2 }$
Q3 Friction Pushing vs Pulling Force Comparison View
A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force $\mathrm { F } = 20 \mathrm {~N}$, making an angle of $30 ^ { \circ }$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$. The difference between the accelerations of the block, in case ( B ) and case ( A ) will be: ( $\mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ )
(1) $3.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$
(2) $0 \mathrm {~m} \mathrm {~s} ^ { - 2 }$
(3) $0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$
(4) $0.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }$
Q5 Centre of Mass 1 View
Three particles of masses $50 \mathrm {~g} , 100 \mathrm {~g}$ and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The $( \mathrm { x } , \mathrm { y } )$ coordinates of the centre of mass will be:
(1) $\left( \frac { 7 } { 12 } \mathrm {~m} , \frac { \sqrt { 3 } } { 4 } \mathrm {~m} \right)$
(2) $\left( \frac { 7 } { 12 } \mathrm {~m} , \frac { \sqrt { 3 } } { 8 } \mathrm {~m} \right)$
(3) $\left( \frac { \sqrt { } 3 } { 4 } \mathrm {~m} , \frac { 5 } { 12 } \mathrm {~m} \right)$
(4) $\left( \frac { \sqrt { 3 } } { 8 } \mathrm {~m} , \frac { 7 } { 12 } \mathrm {~m} \right)$
Q6 Circular Motion 1 Bead/Object on Rotating Curved Surface View
A smooth wire of length $2 \pi r$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $\omega$ about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of $\omega ^ { 2 }$ is equal to:
(1) $2 \mathrm {~g} / \mathrm { r }$
(2) $\frac { \sqrt { 3 } \mathrm {~g} } { 2 \mathrm { r } }$
(3) $2 g / ( r \sqrt { 3 } )$
(4) $( \mathrm { g } \sqrt { 3 } ) / \mathrm { r }$
Q61 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
If $\alpha , \beta$ and $\gamma$ are three consecutive terms of a non-constant G.P. Such that the equations $\alpha x ^ { 2 } + 2 \beta x + \gamma = 0$ and $x ^ { 2 } + x - 1 = 0$ have a common root, then $\alpha ( \beta + \gamma )$ is equal to:
(1) $\beta \gamma$
(2) $\alpha \beta$
(3) $\alpha \gamma$
(4) 0
Q62 Complex Numbers Arithmetic Systems of Equations via Real and Imaginary Part Matching View
Let $z \in C$ with $\operatorname { Im } ( z ) = 10$ and it satisfies $\frac { 2 z - n } { 2 z + n } = 2 i - 1$ for some natural number $n$. Then
(1) $n = 20$ and $\operatorname { Re } ( z ) = 10$
(2) $n = 40$ and $\operatorname { Re } ( z ) = 10$
(3) $n = 20$ and $\operatorname { Re } ( z ) = - 10$
(4) $n = 40$ and $\operatorname { Re } ( z ) = - 10$
Q63 Combinations & Selection Selection with Group/Category Constraints View
A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to
(1) 24
(2) 27
(3) 25
(4) 28
Q64 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
If $a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots$ are in A.P. such that $a _ { 1 } + a _ { 7 } + a _ { 16 } = 40$, then the sum of the first 15 terms of this A.P. is