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_04sep_shift1

10 maths questions

Q51 Solving quadratics and applications Counting solutions or configurations satisfying a quadratic system View
Let $[ \mathrm { t } ]$ denote the greatest integer $\leq \mathrm { t }$. Then the equation in $\mathrm { x } , [ \mathrm { x } ] ^ { 2 } + 2 [ \mathrm { x } + 2 ] - 7 = 0$ has :
(1) exactly two solutions
(2) exactly four integral solutions
(3) no integral solution
(4) infinitely many solutions
Q52 Roots of polynomials Vieta's formulas: compute symmetric functions of roots View
Let $\alpha$ and $\beta$ be the roots of $x ^ { 2 } - 3 x + p = 0$ and $\gamma$ and $\delta$ be the roots of $x ^ { 2 } - 6 x + q = 0$. If $\alpha , \beta , \gamma , \delta$ from a geometric progression. Then ratio $( 2 q + p ) : ( 2 q - p )$ is
(1) $3 : 1$
(2) $9 : 7$
(3) $5 : 3$
(4) $33 : 31$
Q53 Complex Numbers Argand & Loci Circle Equation and Properties via Complex Number Manipulation View
Let $u = \frac { 2 z + i } { z - k i } , z = x + i y$ and $k > 0$. If the curve represented by Re $( u ) + \operatorname { Im } ( u ) = 1$ intersects the $y$-axis at points P and Q where $\mathrm { PQ } = 5$ then the value of k is
(1) $\frac { 3 } { 2 }$
(2) $\frac { 1 } { 2 }$
(3) 4
(4) 2
Q54 Arithmetic Sequences and Series Summation of Derived Sequence from AP View
If $1 + \left( 1 - 2 ^ { 2 } \cdot 1 \right) + \left( 1 - 4 ^ { 2 } \cdot 3 \right) + \left( 1 - 6 ^ { 2 } \cdot 5 \right) + \ldots \ldots + \left( 1 - 20 ^ { 2 } \cdot 19 \right) = \alpha - 220 \beta$, then an ordered pair $( \alpha , \beta )$ is equal to:
(1) $( 10,97 )$
(2) $( 11,103 )$
(3) $( 10,103 )$
(4) $( 11,97 )$
Q55 Combinations & Selection Combinatorial Identity or Bijection Proof View
The value of $\sum _ { r = 0 } ^ { 20 } { } ^ { 50 - r } C _ { 6 }$ is equal to:
(1) ${ } ^ { 51 } C _ { 7 } - { } ^ { 30 } C _ { 7 }$
(2) ${ } ^ { 50 } C _ { 7 } - { } ^ { 30 } C _ { 7 }$
(3) ${ } ^ { 50 } C _ { 6 } - { } ^ { 30 } C _ { 6 }$
(4) ${ } ^ { 51 } C _ { 7 } + { } ^ { 30 } C _ { 7 }$
Q56 Straight Lines & Coordinate Geometry Area Computation in Coordinate Geometry View
A triangle $ABC$ lying in the first quadrant has two vertices as $A ( 1,2 )$ and $B ( 3,1 )$. If $\angle BAC = 90 ^ { \circ }$, and $\operatorname { ar } ( \Delta \mathrm { ABC } ) = 5 \sqrt { 5 }$ sq. units, then the abscissa of the vertex C is :
(1) $1 + \sqrt { 5 }$
(2) $1 + 2 \sqrt { 5 }$
(3) $2 + \sqrt { 5 }$
(4) $2 \sqrt { 5 } - 1$
Q57 Conic sections Equation Determination from Geometric Conditions View
Let $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b )$ be a given ellipse, length of whose latus rectum is 10 . If its eccentricity is the maximum value of the function, $\phi ( t ) = \frac { 5 } { 12 } + t - t ^ { 2 }$, then $a ^ { 2 } + b ^ { 2 }$ is equal to:
(1) 145
(2) 116
(3) 126
(4) 135
Q58 Conic sections Eccentricity or Asymptote Computation View
Let $P ( 3,3 )$ be a point on the hyperbola, $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$. If the normal to it at $P$ intersects the $x$-axis at $( 9,0 )$ and $e$ is its eccentricity, then the ordered pair $\left( a ^ { 2 } , e ^ { 2 } \right)$ is equal to:
(1) $\left( \frac { 9 } { 2 } , 3 \right)$
(2) $\left( \frac { 3 } { 2 } , 2 \right)$
(3) $\left( \frac { 9 } { 2 } , 2 \right)$
(4) $( 9,3 )$
Q59 Proof True/False Justification View
Given the following two statements: $\left( \mathrm { S } _ { 1 } \right) : ( \mathrm { q } \vee \mathrm { p } ) \rightarrow ( \mathrm { p } \leftrightarrow \sim \mathrm { q } )$ is a tautology $\left( \mathrm { S } _ { 2 } \right) : \sim \mathrm { q } \wedge ( \sim \mathrm { p } \leftrightarrow \mathrm { q } )$ is a fallacy. Then :
(1) both ( $S _ { 1 }$ ) and ( $S _ { 2 }$ ) are not correct.
(2) only ( $S _ { 1 }$ ) is correct.
(3) only ( $S _ { 2 }$ ) is correct.
(4) both $\left( S _ { 1 } \right)$ and $\left( S _ { 2 } \right)$ are correct.
Q60 Measures of Location and Spread View
The mean and variance of 8 observations are 10 and 13.5 respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is:
(1) 7
(2) 3
(3) 5
(4) 9