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
2020 session2_06sep_shift1

13 maths questions

Q51 Solving quadratics and applications Evaluating an algebraic expression given a constraint View
If $\alpha$ and $\beta$ be two roots of the equation $x ^ { 2 } - 64 x + 256 = 0$. Then the value of $\left( \frac { \alpha ^ { 3 } } { \beta ^ { 5 } } \right) ^ { \frac { 1 } { 8 } } + \left( \frac { \beta ^ { 3 } } { \alpha ^ { 5 } } \right) ^ { \frac { 1 } { 8 } }$ is :
(1) 2
(2) 3
(3) 1
(4) 4
Q52 Complex Numbers Argand & Loci Locus Identification from Modulus/Argument Equation View
The region represented by $\{ z = x + i y \in C : | z | - \operatorname { Re } ( z ) \leq 1 \}$ is also given by the inequality
(1) $y ^ { 2 } \geq 2 ( x + 1 )$
(2) $y ^ { 2 } \leq 2 \left( x + \frac { 1 } { 2 } \right)$
(3) $y ^ { 2 } \leq \left( x + \frac { 1 } { 2 } \right)$
(4) $y ^ { 2 } \geq x + 1$
Q53 Permutations & Arrangements Linear Arrangement with Constraints View
Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated ?
(1) $2 ! 3 ! 4$ !
(2) $( 3 ! ) ^ { 3 } \cdot ( 4 ! )$
(3) $( 3 ! ) 2 . ( 4 ! )$
(4) $3 ! ( 4 ! ) ^ { 3 }$
Q54 Geometric Sequences and Series Proof of a Structural Property of Geometric Sequences View
Let $a , b , c , d$ and $p$ be non-zero distinct real numbers such that $\left( a ^ { 2 } + b ^ { 2 } + c ^ { 2 } \right) p ^ { 2 } - 2 ( a b + b c + c d ) p + \left( b ^ { 2 } + c ^ { 2 } + d ^ { 2 } \right) = 0$. Then
(1) $a , b , c$ are in A.P.
(2) $a , c , p$ are in G.P.
(3) $a , b , c , d$ are in G.P.
(4) $a , b , c , d$ are in A.P.
Q55 Binomial Theorem (positive integer n) Integer Part or Limit Involving Conjugate Surd Binomial Expansions View
If $\{ \mathrm { p } \}$ denotes the fractional part of the number p , then $\left\{ \frac { 3 ^ { 200 } } { 8 } \right\}$ is equal to
(1) $\frac { 5 } { 8 }$
(2) $\frac { 7 } { 8 }$
(3) $\frac { 3 } { 8 }$
(4) $\frac { 1 } { 8 }$
Q56 Straight Lines & Coordinate Geometry Reflection and Image in a Line View
A ray of light coming from the point $( 2,2 \sqrt { 3 } )$ is incident at an angle $30 ^ { \circ }$ on the line $x = 1$ at the point $A$. The ray gets reflected on the line $x = 1$ and meets $x$-axis at the point $B$. Then, the line $A B$ passes through the point
(1) $\left( 3 , - \frac { 1 } { \sqrt { 3 } } \right)$
(2) $\left( 4 , - \frac { \sqrt { 3 } } { 2 } \right)$
(3) $( 3 , - \sqrt { 3 } )$
(4) $( 4 , - \sqrt { 3 } )$
Q57 Conic sections Tangent and Normal Line Problems View
Let $L _ { 1 }$ be a tangent to the parabola $y ^ { 2 } = 4 ( x + 1 )$ and $L _ { 2 }$ be a tangent to the parabola $y ^ { 2 } = 8 ( x + 2 )$ such that $L _ { 1 }$ and $L _ { 2 }$ intersect at right angles. Then $L _ { 1 }$ and $L _ { 2 }$ meet on the straight line:
(1) $x + 3 = 0$
(2) $2 x + 1 = 0$
(3) $x + 2 = 0$
(4) $x + 2 y = 0$
Q58 Conic sections Locus and Trajectory Derivation View
Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 2 } = 1$ from any of its foci?
(1) $( - 2 , \sqrt { 3 } )$
(2) $( - 1 , \sqrt { 2 } )$
(3) $( - 1 , \sqrt { 3 } )$
(4) $( 1,2 )$
Q59 Proof Direct Proof of a Stated Identity or Equality View
The negation of the Boolean expression $p \vee ( \sim p \wedge q )$ is equivalent to :
(1) $p \wedge \sim q$
(2) $\sim p \wedge \sim q$
(3) $\sim p \vee \sim \mathrm { q }$
(4) $\sim p \vee q$
Q60 Measures of Location and Spread View
If $\sum _ { i = 1 } ^ { n } \left( x _ { i } - a \right) = n$ and $\sum _ { i = 1 } ^ { n } \left( x _ { i } - a \right) ^ { 2 } = n a , ( n , a > 1 )$, then the standard deviation of $n$ observations $x _ { 1 } , x _ { 2 } , \ldots , x _ { n }$ is
(1) $a - 1$
(2) $n \sqrt { ( a - 1 ) }$
(3) $\sqrt { n ( a - 1 ) }$
(4) $\sqrt { ( a - 1 ) }$
Q61 Matrices Determinant and Rank Computation View
Let $m$ and $M$ be respectively the minimum and maximum values of $\left| \begin{array} { c c c } \cos ^ { 2 } x & 1 + \sin ^ { 2 } x & \sin 2 x \\ 1 + \cos ^ { 2 } x & \sin ^ { 2 } x & \sin 2 x \\ \cos ^ { 2 } x & \sin ^ { 2 } x & 1 + \sin 2 x \end{array} \right|$. Then the ordered pair $( \mathrm { m } , \mathrm { M } )$ is equal to:
(1) $( 3,3 )$
(2) $( - 3 , - 1 )$
(3) $( 4,1 )$
(4) $( 1,3 )$
Q62 Matrices Linear System and Inverse Existence View
The values of $\lambda$ and $\mu$ for which the system of linear equations $x + y + z = 2 , x + 2 y + 3 z = 5$, $x + 3 y + \lambda z = \mu$ has infinitely many solutions, are respectively
(1) 6 and 8
(2) 5 and 7
(3) 5 and 8
(4) 4 and 9
Q63 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
If $f ( x + y ) = f ( x ) f ( y )$ and $\sum_{x=1}^{n} f(x) = 2$, then the value of $\sum_{x=1}^{n} f(x)$ is given. [Content truncated in source]