jee-main

Papers (169)
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
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
2012 19may

13 maths questions

Q2 Constant acceleration (SUVAT) Velocity at an intermediate point of a uniformly accelerating body View
A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity $u$ and the guard's room passes with velocity $v$. The middle wagon of the train passes the pole with a velocity.
(1) $\frac { u + v } { 2 }$
(2) $\frac { 1 } { 2 } \sqrt { u ^ { 2 } + v ^ { 2 } }$
(3) $\sqrt { u v }$
(4) $\sqrt { \left( \frac { u ^ { 2 } + v ^ { 2 } } { 2 } \right) }$
Q4 Friction Minimum Force to Move or Push a Block on a Horizontal Surface View
A block of weight $W$ rests on a horizontal floor with coefficient of static friction $\mu$. It is desired to make the block move by applying minimum amount of force. The angle $\theta$ from the horizontal at which the force should be applied and magnitude of the force $F$ are respectively.
(1) $\theta = \tan ^ { - 1 } ( \mu ) , F = \frac { \mu W } { \sqrt { 1 + \mu ^ { 2 } } }$
(2) $\theta = \tan ^ { - 1 } \left( \frac { 1 } { \mu } \right) , F = \frac { \mu W } { \sqrt { 1 + \mu ^ { 2 } } }$
(3) $\theta = 0 , F = \mu W$
(4) $\theta = \tan ^ { - 1 } \left( \frac { \mu } { 1 + \mu } \right) , F = \frac { \mu W } { 1 + \mu }$
Q6 Momentum and Collisions Elastic Collision – Velocity or Mass Determination View
A moving particle of mass $m$, makes a head on elastic collision with another particle of mass $2m$, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to
(1) $33 \%$
(2) $67 \%$
(3) $90 \%$
(4) $10 \%$
Q61 Discriminant and conditions for roots Proving no real roots exist for a given expression View
Let $p , q , r \in R$ and $r > p > 0$. If the quadratic equation $p x ^ { 2 } + q x + r = 0$ has two complex roots $\alpha$ and $\beta$, then $| \alpha | + | \beta |$ is
(1) equal to 1
(2) less than 2 but not equal to 1
(3) greater than 2
(4) equal to 2
Q62 Applied differentiation Existence and number of solutions via calculus View
Consider a quadratic equation $a x ^ { 2 } + b x + c = 0$, where $2 a + 3 b + 6 c = 0$ and let $g ( x ) = a \frac { x ^ { 3 } } { 3 } + b \frac { x ^ { 2 } } { 2 } + c x$. Statement 1: The quadratic equation has at least one root in the interval $( 0,1 )$. Statement 2: The Rolle's theorem is applicable to function $g ( x )$ on the interval $[ 0,1 ]$.
(1) Statement 1 is false, Statement 2 is true.
(2) Statement 1 is true, Statement 2 is false.
(3) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
(4) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
Q63 Complex Numbers Argand & Loci True/False or Multiple-Statement Verification View
Let $Z$ and $W$ be complex numbers such that $| Z | = | W |$, and $\arg Z$ denotes the principal argument of $Z$. Statement 1: If $\arg Z + \arg W = \pi$, then $Z = - \bar { W }$. Statement 2: $| Z | = | W |$, implies $\arg Z - \arg \bar { W } = \pi$.
(1) Statement 1 is true, Statement 2 is false.
(2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
(3) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
(4) Statement 1 is false, Statement 2 is true.
Q64 Permutations & Arrangements Selection and Task Assignment View
The number of arrangements that can be formed from the letters $a , b , c , d , e , f$ taken 3 at a time without repetition and each arrangement containing at least one vowel, is
(1) 96
(2) 128
(3) 24
(4) 72
Q65 Sequences and Series Evaluation of a Finite or Infinite Sum View
The sum of the series $1 + \frac { 4 } { 3 } + \frac { 10 } { 9 } + \frac { 28 } { 27 } + \ldots$ upto $n$ terms is
(1) $\frac { 7 } { 6 } n + \frac { 1 } { 6 } - \frac { 2 } { 3.2 ^ { n - 1 } }$
(2) $\frac { 5 } { 3 } n - \frac { 7 } { 6 } + \frac { 1 } { 2.3 ^ { n - 1 } }$
(3) $n + \frac { 1 } { 2 } - \frac { 1 } { 2 \cdot 3 ^ { n } }$
(4) $n - \frac { 1 } { 3 } - \frac { 1 } { 3.2 ^ { n - 1 } }$
Q66 Combinations & Selection Combinatorial Identity or Bijection Proof View
If $n = { } ^ { m } C _ { 2 }$, then the value of ${ } ^ { n } C _ { 2 }$ is given by
(1) $3 \left( { } ^ { m + 1 } C _ { 4 } \right)$
(2) ${ } ^ { m - 1 } C _ { 4 }$
(3) ${ } ^ { m + 1 } C _ { 4 }$
(4) $2 \left( { } ^ { m + 2 } C _ { 4 } \right)$
Q67 Addition & Double Angle Formulae Trigonometric Equation Solving via Identities View
Suppose $\theta$ and $\phi ( \neq 0 )$ are such that $\sec ( \theta + \phi )$, $\sec \theta$ and $\sec ( \theta - \phi )$ are in A.P. If $\cos \theta = k \cos \left( \frac { \phi } { 2 } \right)$ for some $k$, then $k$ is equal to
(1) $\pm \sqrt { 2 }$
(2) $\pm 1$
(3) $\pm \frac { 1 } { \sqrt { 2 } }$
(4) $\pm 2$
Q68 Straight Lines & Coordinate Geometry Reflection and Image in a Line View
Let $L$ be the line $y = 2 x$, in the two dimensional plane. Statement 1: The image of the point $( 0,1 )$ in $L$ is the point $\left( \frac { 4 } { 5 } , \frac { 3 } { 5 } \right)$. Statement 2: The points $( 0,1 )$ and $\left( \frac { 4 } { 5 } , \frac { 3 } { 5 } \right)$ lie on opposite sides of the line $L$ and are at equal distance from it.
(1) Statement 1 is true, Statement 2 is false.
(2) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
(3) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
(4) Statement 1 is false, Statement 2 is true.
Q69 Circles Chord Length and Chord Properties View
If the line $y = m x + 1$ meets the circle $x ^ { 2 } + y ^ { 2 } + 3 x = 0$ in two points equidistant from and on opposite sides of $x$-axis, then
(1) $3 m + 2 = 0$
(2) $3 m - 2 = 0$
(3) $2 m + 3 = 0$
(4) $2 m - 3 = 0$
Q70 Conic sections Tangent and Normal Line Problems View
The equation of the normal to the parabola, $x ^ { 2 } = 8 y$ at $x = 4$ is
(1) $x + 2 y = 0$
(2) $x + y = 2$
(3) $x - 2 y = 0$
(4) $x + y = 6$