jee-main

Papers (191)
2026
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2025
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2024
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2023
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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
2013 23apr

14 maths questions

Q61 Inequalities Solve Polynomial/Rational Inequality for Solution Set View
The least integral value $\alpha$ of $x$ such that $\frac { x - 5 } { x ^ { 2 } + 5 x - 14 } > 0$, satisfies :
(1) $\alpha ^ { 2 } + 3 \alpha - 4 = 0$
(2) $\alpha ^ { 2 } - 5 \alpha + 4 = 0$
(3) $\alpha ^ { 2 } - 7 \alpha + 6 = 0$
(4) $\alpha ^ { 2 } + 5 \alpha - 6 = 0$
Q62 Complex Numbers Arithmetic Algebraic Conditions for Geometric Properties (Real, Imaginary, Collinear) View
Let $a = \operatorname { Im } \left( \frac { 1 + z ^ { 2 } } { 2 i z } \right)$, where $z$ is any non-zero complex number. The set $\mathrm { A } = \{ a : | z | = 1$ and $z \neq \pm 1 \}$ is equal to:
(1) $( - 1,1 )$
(2) $[ - 1,1 ]$
(3) $[ 0,1 )$
(4) $( - 1,0 ]$
Q63 Arithmetic Sequences and Series Evaluation of a Finite or Infinite Sum View
The sum of the series : $( 2 ) ^ { 2 } + 2 ( 4 ) ^ { 2 } + 3 ( 6 ) ^ { 2 } + \ldots$ upto 10 terms is :
(1) 11300
(2) 11200
(3) 12100
(4) 12300
Q64 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
If $a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots , a _ { n } , \ldots$ are in A.P. such that $a _ { 4 } - a _ { 7 } + a _ { 10 } = m$, then the sum of first 13 terms of this A.P., is :
(1) 10 m
(2) 12 m
(3) 13 m
(4) 15 m
Q65 Binomial Theorem (positive integer n) Count Integral or Rational Terms in a Binomial Expansion View
The sum of the rational terms in the binomial expansion of $\left( 2 ^ { \frac { 1 } { 2 } } + 3 ^ { \frac { 1 } { 5 } } \right) ^ { 10 }$ is :
(1) 25
(2) 32
(3) 9
(4) 41
Q66 Standard trigonometric equations Solve trigonometric equation for solutions in an interval View
The number of solutions of the equation $\sin 2 x - 2 \cos x + 4 \sin x = 4$ in the interval $[ 0,5 \pi ]$ is :
(1) 3
(2) 5
(3) 4
(4) 6
Q67 Vectors 3D & Lines MCQ: Relationship Between Two Lines View
If two lines $L _ { 1 }$ and $L _ { 2 }$ in space, are defined by
$$\begin{gathered} L _ { 1 } = \{ x = \sqrt { \lambda } y + ( \sqrt { \lambda } - 1 ) , \\ z = ( \sqrt { \lambda } - 1 ) y + \sqrt { \lambda } \} \text { and } \\ L _ { 2 } = \{ x = \sqrt { \mu } y + ( 1 - \sqrt { \mu } ) , \\ z = ( 1 - \sqrt { \mu } ) y + \sqrt { \mu } \} \end{gathered}$$
then $L _ { 1 }$ is perpendicular to $L _ { 2 }$, for all nonnegative reals $\lambda$ and $\mu$, such that :
(1) $\sqrt { \lambda } + \sqrt { \mu } = 1$
(2) $\lambda \neq \mu$
(3) $\lambda + \mu = 0$
(4) $\lambda = \mu$
Q68 Straight Lines & Coordinate Geometry Slope and Angle Between Lines View
Let $\theta _ { 1 }$ be the angle between two lines $2 x + 3 y + c _ { 1 } = 0$ and $- x + 5 y + c _ { 2 } = 0$ and $\theta _ { 2 }$ be the angle between two lines $2 x + 3 y + c _ { 1 } = 0$ and $- x + 5 y + c _ { 3 } = 0$, where $c _ { 1 } , c _ { 2 } , c _ { 3 }$ are any real numbers: Statement-1: If $c _ { 2 }$ and $c _ { 3 }$ are proportional, then $\theta _ { 1 } = \theta _ { 2 }$. Statement-2: $\theta _ { 1 } = \theta _ { 2 }$ for all $c _ { 2 }$ and $c _ { 3 }$.
(1) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation of Statement-1.
(2) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation of Statement-1.
(3) Statement-1 is false; Statement-2 is true.
(4) Statement-1 is true; Statement-2 is false.
Q69 Circles Circles Tangent to Each Other or to Axes View
If the circle $x ^ { 2 } + y ^ { 2 } - 6 x - 8 y + \left( 25 - a ^ { 2 } \right) = 0$ touches the axis of $x$, then $a$ equals.
(1) 0
(2) $\pm 4$
(3) $\pm 2$
(4) $\pm 3$
Q70 Circles Tangent and Normal Line Problems View
The point of intersection of the normals to the parabola $y ^ { 2 } = 4 x$ at the ends of its latus rectum is :
(1) $( 0,2 )$
(2) $( 3,0 )$
(3) $( 0,3 )$
(4) $( 2,0 )$
Q71 Circles Locus and Trajectory Derivation View
A tangent to the hyperbola $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 2 } = 1$ meets $x$-axis at P and $y$-axis at Q. Lines PR and QR are drawn such that OPRQ is a rectangle (where O is the origin). Then R lies on :
(1) $\frac { 4 } { x ^ { 2 } } + \frac { 2 } { y ^ { 2 } } = 1$
(2) $\frac { 2 } { x ^ { 2 } } - \frac { 4 } { y ^ { 2 } } = 1$
(3) $\frac { 2 } { x ^ { 2 } } + \frac { 4 } { y ^ { 2 } } = 1$
(4) $\frac { 4 } { x ^ { 2 } } - \frac { 2 } { y ^ { 2 } } = 1$
Q72 Number Theory Proof of Equivalence or Logical Relationship Between Conditions View
For integers $m$ and $n$, both greater than 1, consider the following three statements : $P : m$ divides $n$, $Q : m$ divides $n ^ { 2 }$, $R : m$ is prime, then
(1) $Q \wedge R \rightarrow P$
(2) $P \wedge Q \rightarrow R$
(3) $Q \rightarrow R$
(4) $Q \rightarrow P$
Q73 Measures of Location and Spread View
If the median and the range of four numbers $\{ x , y , 2 x + y , x - y \}$, where $0 < y < x < 2 y$, are 10 and 28 respectively, then the mean of the numbers is :
(1) 18
(2) 10
(3) 5
(4) 14
Q74 Straight Lines & Coordinate Geometry Area Computation in Coordinate Geometry View
If the extremities of the base of an isosceles triangle are the points $( 2 a , 0 )$ and $( 0 , a )$ and the equation of one of the sides is $x = 2 a$, then the area of the triangle, in square units, is :
(1) $\frac { 5 } { 4 } a ^ { 2 }$
(2) $\frac { 5 } { 2 } a ^ { 2 }$
(3) $\frac { 25 a ^ { 2 } } { 4 }$
(4) $5 a^2$