jee-main

Papers (191)
2026
session1_21jan_shift1 13 session1_21jan_shift2 9 session1_22jan_shift1 16 session1_22jan_shift2 10 session1_23jan_shift1 11 session1_23jan_shift2 7 session1_24jan_shift1 14 session1_24jan_shift2 10 session1_28jan_shift1 10 session1_28jan_shift2 9
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 session2_02apr_shift1 31 session2_02apr_shift2 36 session2_03apr_shift1 35 session2_03apr_shift2 35 session2_04apr_shift1 37 session2_04apr_shift2 33 session2_07apr_shift1 32 session2_07apr_shift2 32 session2_08apr_shift1 36 session2_08apr_shift2 35
2024
session1_01feb_shift1 5 session1_01feb_shift2 21 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 28 session1_29jan_shift2 29 session1_30jan_shift1 20 session1_30jan_shift2 29 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 5 session2_04apr_shift2 28 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 21 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 29 session2_09apr_shift1 8 session2_09apr_shift2 30
2023
session1_01feb_shift1 28 session1_01feb_shift2 3 session1_24jan_shift1 11 session1_24jan_shift2 11 session1_25jan_shift1 29 session1_25jan_shift2 29 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 5 session1_30jan_shift2 27 session1_31jan_shift1 28 session1_31jan_shift2 15 session2_06apr_shift1 5 session2_06apr_shift2 16 session2_08apr_shift1 29 session2_08apr_shift2 13 session2_10apr_shift1 29 session2_10apr_shift2 16 session2_11apr_shift1 6 session2_11apr_shift2 8 session2_12apr_shift1 26 session2_13apr_shift1 24 session2_13apr_shift2 24 session2_15apr_shift1 19
2022
session1_24jun_shift1 19 session1_24jun_shift2 25 session1_25jun_shift1 14 session1_25jun_shift2 14 session1_26jun_shift1 29 session1_26jun_shift2 24 session1_27jun_shift1 4 session1_27jun_shift2 29 session1_28jun_shift1 13 session1_29jun_shift1 20 session1_29jun_shift2 4 session2_25jul_shift1 29 session2_25jul_shift2 20 session2_26jul_shift1 29 session2_26jul_shift2 23 session2_27jul_shift1 28 session2_27jul_shift2 29 session2_28jul_shift1 11 session2_28jul_shift2 29 session2_29jul_shift1 17 session2_29jul_shift2 18
2021
session1_24feb_shift1 9 session1_24feb_shift2 4 session1_25feb_shift1 29 session1_25feb_shift2 29 session1_26feb_shift2 15 session2_16mar_shift1 29 session2_16mar_shift2 18 session2_17mar_shift1 21 session2_17mar_shift2 27 session2_18mar_shift1 18 session2_18mar_shift2 9 session3_20jul_shift1 29 session3_20jul_shift2 29 session3_22jul_shift1 9 session3_25jul_shift1 8 session3_25jul_shift2 14 session3_27jul_shift1 4 session3_27jul_shift2 7 session4_01sep_shift2 14 session4_26aug_shift1 5 session4_26aug_shift2 2 session4_27aug_shift1 3 session4_27aug_shift2 29 session4_31aug_shift1 28 session4_31aug_shift2 4
2020
session1_07jan_shift1 28 session1_07jan_shift2 20 session1_08jan_shift1 5 session1_08jan_shift2 11 session1_09jan_shift1 26 session1_09jan_shift2 16 session2_02sep_shift1 18 session2_02sep_shift2 16 session2_03sep_shift1 23 session2_03sep_shift2 8 session2_04sep_shift1 14 session2_04sep_shift2 27 session2_05sep_shift1 22 session2_05sep_shift2 29 session2_06sep_shift1 11 session2_06sep_shift2 10
2019
session1_09jan_shift1 6 session1_09jan_shift2 29 session1_10jan_shift1 29 session1_10jan_shift2 14 session1_11jan_shift1 6 session1_11jan_shift2 5 session1_12jan_shift1 10 session1_12jan_shift2 29 session2_08apr_shift1 29 session2_08apr_shift2 29 session2_09apr_shift1 29 session2_09apr_shift2 29 session2_10apr_shift1 2 session2_10apr_shift2 5 session2_12apr_shift1 3 session2_12apr_shift2 9
2018
08apr 30 15apr 28 15apr_shift1 28 15apr_shift2 6 16apr 19
2017
02apr 30 08apr 30 09apr 34
2016
03apr 28 09apr 29 10apr 30
2015
04apr 29 10apr 29 11apr 8
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
2013
07apr 29 09apr 12 22apr 5 23apr 14 25apr 13
2012
07may 17 12may 21 19may 14 26may 17 offline 30
2011
jee-main_2011.pdf 18
2010
jee-main_2010.pdf 6
2009
jee-main_2009.pdf 2
2008
jee-main_2008.pdf 4
2007
jee-main_2007.pdf 38
2006
jee-main_2006.pdf 15
2005
jee-main_2005.pdf 25
2004
jee-main_2004.pdf 22
2003
jee-main_2003.pdf 8
2002
jee-main_2002.pdf 12
2023 session1_24jan_shift1

11 maths questions

Q21 Vectors Introduction & 2D Perpendicularity or Parallel Condition View
Vectors $a \hat { i } + b \hat { j } + \hat { k }$ and $2 \hat { i } - 3 \hat { j } + 4 \hat { k }$ are perpendicular to each other when $3 a + 2 b = 7$, the ratio of $a$ to $b$ is $\frac { x } { 2 }$. The value of $x$ is $\_\_\_\_$ .
Q61 Complex Numbers Arithmetic Trigonometric/Polar Form and De Moivre's Theorem View
Let $p , \quad q \in \mathbb { R }$ and $( 1 - \sqrt { 3 } i ) ^ { 200 } = 2 ^ { 199 } ( p + i q ) , i = \sqrt { - 1 }$. Then, $p + q + q ^ { 2 }$ and $p - q + q ^ { 2 }$ are roots of the equation.
(1) $x ^ { 2 } + 4 x - 1 = 0$
(2) $x ^ { 2 } - 4 x + 1 = 0$
(3) $x ^ { 2 } + 4 x + 1 = 0$
(4) $x ^ { 2 } - 4 x - 1 = 0$
Q62 Arithmetic Sequences and Series Solve a Logarithmic Equation View
For three positive integers $p , q , r , x ^ { p q ^ { 2 } } = y ^ { q r } = z ^ { p ^ { 2 } r }$ and $r = p q + 1$ such that 3, $3 \log _ { y } x , 3 \log _ { z } y , 7 \log _ { x } z$ are in A.P. with common difference $\frac { 1 } { 2 }$. The $r - p - q$ is equal to
(1) 2
(2) 6
(3) 12
(4) - 6
Q63 Binomial Theorem (positive integer n) Evaluate a Summation Involving Binomial Coefficients View
The value of $\sum _ { r } ^ { 22 } = 0 { } ^ { 22 } C _ { r } \cdot { } ^ { 23 } C _ { r }$ is
(1) ${ } ^ { 45 } C _ { 23 }$
(2) ${ } ^ { 44 } C _ { 23 }$
(3) ${ } ^ { 45 } C _ { 24 }$
(4) ${ } ^ { 44 } C _ { 22 }$
Q64 Circles Locus and Trajectory Derivation View
Let a tangent to the curve $y ^ { 2 } = 24 x$ meet the curve $x y = 2$ at the points $A$ and $B$. Then the midpoints of such line segments $A B$ lie on a parabola with the
(1) directrix $4 x = 3$
(2) directrix $4 x = - 3$
(3) Length of latus rectum $\frac { 3 } { 2 }$
(4) Length of latus rectum 2
Q65 Chain Rule Convergence proof and limit determination View
$\lim _ { t \rightarrow 0 } 1 ^ { \frac { 1 } { \sin ^ { 2 } t } } + 2 ^ { \frac { 1 } { \sin ^ { 2 } t } } + 3 ^ { \frac { 1 } { \sin ^ { 2 } t } } \ldots \ldots n ^ { \frac { 1 } { \sin ^ { 2 } t } } \sin ^ { 2 } t$ is equal to
(1) $n ^ { 2 } + n$
(2) $n$
(3) $\frac { n n + 1 } { 2 }$
(4) $n ^ { 2 }$
Q68 Matrices Matrix Algebra and Product Properties View
If $A$ and $B$ are two non-zero $n \times n$ matrices such that $A ^ { 2 } + B = A ^ { 2 } B$, then
(1) $A B = I$
(2) $A ^ { 2 } B = I$
(3) $A ^ { 2 } = I$ or $B = I$
(4) $A ^ { 2 } B = B A ^ { 2 }$
Q69 Simultaneous equations Linear System and Inverse Existence View
Let $N$ denote the number that turns up when a fair die is rolled. If the probability that the system of equations $x + y + z = 1$, $2 x + N y + 2 z = 2$, $3 x + 3 y + N z = 3$ has unique solution is $\frac { k } { 6 }$, then the sum of value of $k$ and all possible values of $N$ is
(1) 18
(2) 19
(3) 20
(4) 21
Q70 Proof Vieta's formulas: compute symmetric functions of roots View
Let $\alpha$ be a root of the equation $( a - c ) x ^ { 2 } + ( b - a ) x + ( c - b ) = 0$ where $a , \quad b , \quad c$ are distinct real numbers such that the matrix $\begin{pmatrix} \alpha ^ { 2 } & \alpha & 1 \end{pmatrix}$ is singular. Then the value of $\frac { ( a - c ) ^ { 2 } } { ( b - a )( c - b ) } + \frac { ( b - a ) ^ { 2 } } { ( a - c )( c - b ) } + \frac { ( c - b ) ^ { 2 } } { ( a - c )( b - a ) }$ is
(1) 6
(2) 3
(3) 9
(4) 12
Q71 Reciprocal Trig & Identities View
$\tan ^ { - 1 } \frac { 1 + \sqrt { 3 } } { 3 + \sqrt { 3 } } + \sec ^ { - 1 } \sqrt { \frac { 8 + 4 \sqrt { 3 } } { 6 + 3 \sqrt { 3 } } } =$
(1) $\frac { \pi } { 4 }$
(2) $\frac { \pi } { 2 }$
(3) $\frac { \pi } { 3 }$
(4) $\frac { \pi } { 6 }$
Q72 Sign Change & Interval Methods Counting solutions or configurations satisfying a quadratic system View
The equation $x ^ { 2 } - 4 x + [ x ] + 3 = x [ x ]$, where $[ x ]$ denotes the greatest integer function, has:
(1) exactly two solutions in $( - \infty , \infty )$
(2) no solution
(3) a unique solution in $( - \infty$, 1)
(4) a unique solution in $( - \infty , \infty )$