jee-main

Papers (169)
2025
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2024
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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 session2_18mar_shift1

12 maths questions

Q3 Power and driving force View
A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time $t$ is proportional to:-
(1) $t ^ { \frac { 2 } { 3 } }$
(2) $t ^ { \frac { 3 } { 2 } }$
(3) $t$
(4) $t ^ { \frac { 1 } { 2 } }$
Q4 Circular Motion 1 Ratio / Comparison of Circular Motion Quantities View
A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with an angular speed $\omega$. Two particles having mass $m$ each are now attached at diametrically opposite points. The angular speed of the ring will become:
(1) $\omega \frac { M } { M + m }$
(2) $\omega \frac { M + 2 m } { M }$
(3) $\omega \frac { M } { M + 2 m }$
(4) $\omega \frac { M - 2 m } { M + 2 m }$
Q61 Sequences and series, recurrence and convergence Convergence proof and limit determination View
The value of $3 + \frac { 1 } { 4 + \frac { 1 } { 3 + \frac { 1 } { 4 + \frac { 1 } { 3 + \ldots . \infty } } } }$ is equal to
(1) $1.5 + \sqrt { 3 }$
(2) $2 + \sqrt { 3 }$
(3) $3 + 2 \sqrt { 3 }$
(4) $4 + \sqrt { 3 }$
Q62 Complex Numbers Argand & Loci Circle Equation and Properties via Complex Number Manipulation View
If the equation $a | z | ^ { 2 } + \overline { \bar { \alpha } z + \alpha \bar { z } } + d = 0$ represents a circle where $a , d$ are real constants then which of the following condition is correct?
(1) $| \alpha | ^ { 2 } - a d \neq 0$
(2) $| \alpha | ^ { 2 } - a d > 0$ and $a \in R - \{ 0 \}$
(3) $| \alpha | ^ { 2 } - a d \geq 0$ and $a \in R$
(4) $\alpha = 0 , a , d \in R ^ { + }$
Q63 Permutations & Arrangements Word Permutations with Repeated Letters View
The sum of all the 4-digit distinct numbers that can be formed with the digits $1, 2, 2$ and 3 is:
(1) 26664
(2) 122664
(3) 122234
(4) 22264
Q64 Arithmetic Sequences and Series Summation of Derived Sequence from AP View
If $\alpha , \beta$ are natural numbers such that $100 ^ { \alpha } - 199 \beta = ( 100 ) ( 100 ) + ( 99 ) ( 101 ) + ( 98 ) ( 102 ) + \ldots . + ( 1 ) ( 199 )$, then the slope of the line passing through $( \alpha , \beta )$ and origin is:
(1) 540
(2) 550
(3) 530
(4) 510
Q65 Sequences and Series Evaluation of a Finite or Infinite Sum View
$\frac { 1 } { 3 ^ { 2 } - 1 } + \frac { 1 } { 5 ^ { 2 } - 1 } + \frac { 1 } { 7 ^ { 2 } - 1 } + \ldots + \frac { 1 } { ( 201 ) ^ { 2 } - 1 }$ is equal to
(1) $\frac { 101 } { 404 }$
(2) $\frac { 25 } { 101 }$
(3) $\frac { 101 } { 408 }$
(4) $\frac { 99 } { 400 }$
Q66 Binomial Theorem (positive integer n) Extract Coefficients Using Roots of Unity or Substitution Filter View
Let $\left( 1 + x + 2 x ^ { 2 } \right) ^ { 20 } = a _ { 0 } + a _ { 1 } x + a _ { 2 } x ^ { 2 } + \ldots + a _ { 40 } x ^ { 40 }$, then $a _ { 1 } + a _ { 3 } + a _ { 5 } + \ldots + a _ { 37 }$ is equal to
(1) $2 ^ { 20 } \left( 2 ^ { 20 } - 21 \right)$
(2) $2 ^ { 19 } \left( 2 ^ { 20 } - 21 \right)$
(3) $2 ^ { 19 } \left( 2 ^ { 20 } + 21 \right)$
(4) $2 ^ { 20 } \left( 2 ^ { 20 } + 21 \right)$
Q67 Quadratic trigonometric equations View
The solutions of the equation $\left| \begin{array} { c c c } 1 + \sin ^ { 2 } x & \sin ^ { 2 } x & \sin ^ { 2 } x \\ \cos ^ { 2 } x & 1 + \cos ^ { 2 } x & \cos ^ { 2 } x \\ 4 \sin 2 x & 4 \sin 2 x & 1 + 4 \sin 2 x \end{array} \right| = 0 , ( 0 < x < \pi )$, are
(1) $\frac { \pi } { 12 } , \frac { \pi } { 6 }$
(2) $\frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$
(3) $\frac { 5 \pi } { 12 } , \frac { 7 \pi } { 12 }$
(4) $\frac { 7 \pi } { 12 } , \frac { 11 \pi } { 12 }$
Q68 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View
The number of integral values of $m$ so that the abscissa of point of intersection of lines $3 x + 4 y = 9$ and $y = m x + 1$ is also an integer, is:
(1) 1
(2) 2
(3) 3
(4) 0
Q69 Straight Lines & Coordinate Geometry Slope and Angle Between Lines View
The equation of one of the straight lines which passes through the point $(1, 3)$ and makes an angle $\tan ^ { - 1 } ( \sqrt { 2 } )$ with the straight line, $y + 1 = 3 \sqrt { 2 } x$ is
(1) $4 \sqrt { 2 } x + 5 y - ( 15 + 4 \sqrt { 2 } ) = 0$
(2) $5 \sqrt { 2 } x + 4 y - ( 15 + 4 \sqrt { 2 } ) = 0$
(3) $4 \sqrt { 2 } x + 5 y - 4 \sqrt { 2 } = 0$
(4) $4 \sqrt { 2 } x - 5 y - ( 5 + 4 \sqrt { 2 } ) = 0$
Q70 Circles Circle Identification and Classification View
Choose the correct statement about two circles whose equations are given below: $x ^ { 2 } + y ^ { 2 } - 10 x - 10 y + 41 = 0$ $x ^ { 2 } + y ^ { 2 } - 22 x - 10 y + 137 = 0$
(1) circles have same centre
(2) circles have no meeting point