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
2019 session1_12jan_shift2

20 maths questions

Q61 Discriminant and conditions for roots Parameter range for no real roots (positive definite) View
The number of integral values of $m$ for which the quadratic expression $( 1 + 2 m ) x ^ { 2 } - 2 ( 1 + 3 m ) x + 4 ( 1 + m ) , x \in R$ is always positive, is
(1) 7
(2) 3
(3) 6
(4) 8
Q62 Complex Numbers Arithmetic Modulus Computation View
Let $z _ { 1 }$ and $z _ { 2 }$ be two complex numbers satisfying $\left| z _ { 1 } \right| = 9$ and $\left| z _ { 2 } - 3 - 4 i \right| = 4$. Then the minimum value of $\left| z _ { 1 } - z _ { 2 } \right|$ is :
(1) 2
(2) $\sqrt { 2 }$
(3) 0
(4) 1
Q63 Permutations & Arrangements Handshake / Product Counting View
There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84 , then the value of $m$ is :
(1) 11
(2) 12
(3) 7
(4) 9
Q64 Arithmetic Sequences and Series Summation of Derived Sequence from AP View
If the sum of the first 15 terms of the series $\left( \frac { 3 } { 4 } \right) ^ { 3 } + \left( 1 \frac { 1 } { 2 } \right) ^ { 3 } + \left( 2 \frac { 1 } { 4 } \right) ^ { 3 } + 3 ^ { 3 } + \left( 3 \frac { 3 } { 4 } \right) ^ { 3 } + \ldots$ is equal to 225 K , then $K$ is equal to :
(1) 9
(2) 27
(3) 54
(4) 108
Q65 Trig Proofs Trigonometric Equation Constraint Deduction View
If $\sin ^ { 4 } \alpha + 4 \cos ^ { 4 } \beta + 2 = 4 \sqrt { 2 } \sin \alpha \cos \beta , \alpha , \beta \in [ 0 , \pi ]$, then $\cos ( \alpha + \beta ) - \cos ( \alpha - \beta )$ is equal to
(1) - 1
(2) $- \sqrt { 2 }$
(3) $\sqrt { 2 }$
(4) 0
Q66 Arithmetic Sequences and Series Properties of AP Terms under Transformation View
If ${ } ^ { n } C _ { 4 } , { } ^ { n } C _ { 5 }$ and ${ } ^ { n } C _ { 6 }$ are in A.P., then $n$ can be
(1) 9
(2) 14
(3) 12
(4) 11
Q67 Binomial Theorem (positive integer n) Count Integral or Rational Terms in a Binomial Expansion View
The total number of irrational terms in the binomial expansion of $\left( 7 ^ { \frac { 1 } { 5 } } - 3 ^ { \frac { 1 } { 10 } } \right) ^ { 60 }$ is
(1) 48
(2) 55
(3) 54
(4) 49
Q68 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View
If a straight line passing through the point $P ( - 3,4 )$ is such that its intercepted portion between the coordinate axes is bisected at $P$, then its equation is :
(1) $4 x + 3 y = 0$
(2) $4 x - 3 y + 24 = 0$
(3) $3 x - 4 y + 25 = 0$
(4) $x - y + 7 = 0$
Q69 Circles Circle-Related Locus Problems View
If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B$, then the locus of the foot of perpendicular from $O$ on $AB$ is :
(1) $\left( x ^ { 2 } + y ^ { 2 } \right) ( x + y ) = R ^ { 2 } x y$
(2) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 4 R ^ { 2 } x ^ { 2 } y ^ { 2 }$
(3) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 4 R ^ { 2 } x ^ { 2 } y ^ { 2 }$
(4) $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 4 R x ^ { 2 } y ^ { 2 }$
Q70 Circles Tangent Lines and Tangent Lengths View
The equation of a tangent to the parabola, $x ^ { 2 } = 8 y$, which makes an angle $\theta$ with the positive direction of $x$-axis, is
(1) $y = x \tan \theta + 2 \cot \theta$
(2) $y = x \tan \theta - 2 \cot \theta$
(3) $x = y \cot \theta + 2 \tan \theta$
(4) $x = y \cot \theta - 2 \tan \theta$
Q71 Circles Area and Geometric Measurement Involving Circles View
Let $S$ and $S ^ { \prime }$ be the foci of an ellipse and $B$ be any one of the extremities of its minor axis. If $\Delta S ^ { \prime } B S$ is a right angled triangle with right angle at $B$ and area $\left( \Delta S ^ { \prime } B S \right) = 8$ sq. units, then the length of a latus rectum of the ellipse is :
(1) $2 \sqrt { 2 }$
(2) 2
(3) 4
(4) $4 \sqrt { 2 }$
Q72 Chain Rule Limit Evaluation Involving Composition or Substitution View
$\lim _ { x \rightarrow 1 ^ { - } } \frac { \sqrt { \pi } - \sqrt { 2 \sin ^ { - 1 } x } } { \sqrt { 1 - x } }$ is equal to
(1) $\sqrt { \pi }$
(2) $\sqrt { \frac { 2 } { \pi } }$
(3) $\frac { 1 } { \sqrt { 2 \pi } }$
(4) $\sqrt { \frac { \pi } { 2 } }$
Q74 Measures of Location and Spread View
The mean and the variance of five observations are 4 and 5.20 , respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :
(1) 3
(2) 5
(3) 7
(4) 1
Q79 Chain Rule Chain Rule with Composition of Explicit Functions View
Let $f$ be a differentiable function such that $f ( 1 ) = 2$ and $f ^ { \prime } ( x ) = f ( x )$ for all $x \in R$. If $h ( x ) = f ( f ( x ) )$, then $h ^ { \prime } ( 1 )$ is equal to :
(1) $4 e ^ { 2 }$
(2) $2 e$
(3) $4 e$
(4) $2 e ^ { 2 }$
Q80 Tangents, normals and gradients Find tangent line with a specified slope or from an external point View
The tangent to the curve $y = x ^ { 2 } - 5 x + 5$, parallel to the line $2 y = 4 x + 1$, also passes through the point :
(1) $\left( \frac { 1 } { 4 } , \frac { 7 } { 2 } \right)$
(2) $\left( \frac { 7 } { 2 } , \frac { 1 } { 4 } \right)$
(3) $\left( - \frac { 1 } { 8 } , 7 \right)$
(4) $\left( \frac { 1 } { 8 } , - 7 \right)$
Q81 Stationary points and optimisation Determine parameters from given extremum conditions View
If the function $f$ given by $f ( x ) = x ^ { 3 } - 3 ( a - 2 ) x ^ { 2 } + 3 a x + 7$, for some $a \in R$ is increasing in $( 0,1 ]$ and decreasing in $[ 1,5 )$, then a root of the equation, $\frac { f ( x ) - 14 } { ( x - 1 ) ^ { 2 } } = 0 , ( x \neq 1 )$ is :
(1) 7
(2) - 7
(3) 6
(4) 5
Q82 Integration by Substitution Substitution to Transform Integral Form (Show Transformed Expression) View
The integral $\int \frac { 3 x ^ { 13 } + 2 x ^ { 11 } } { \left( 2 x ^ { 4 } + 3 x ^ { 2 } + 1 \right) ^ { 4 } } d x$, is equal to
(1) $\frac { x ^ { 4 } } { 6 \left( 2 x ^ { 4 } + 3 x ^ { 2 } + 1 \right) ^ { 3 } } + C$
(2) $\frac { x ^ { 4 } } { \left( 2 x ^ { 4 } + 3 x ^ { 2 } + 1 \right) ^ { 3 } } + C$
(3) $\frac { x ^ { 12 } } { \left( 2 x ^ { 4 } + 3 x ^ { 2 } + 1 \right) ^ { 3 } } + C$
(4) $\frac { x ^ { 12 } } { 6 \left( 2 x ^ { 4 } + 3 x ^ { 2 } + 1 \right) ^ { 3 } } + C$
Q83 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
The integral $\int _ { 1 } ^ { e } \left\{ \left( \frac { x } { e } \right) ^ { 2 x } - \left( \frac { e } { x } \right) ^ { x } \right\} \log _ { e } x \, d x$ is equal to
(1) $\frac { 3 } { 2 } - e - \frac { 1 } { 2 e ^ { 2 } }$
(2) $\frac { 1 } { 2 } - e - \frac { 1 } { e ^ { 2 } }$
(3) $- \frac { 1 } { 2 } + \frac { 1 } { e } - \frac { 1 } { 2 e ^ { 2 } }$
(4) $\frac { 3 } { 2 } - \frac { 1 } { e } - \frac { 1 } { 2 e ^ { 2 } }$
Q85 Differential equations Solving Separable DEs with Initial Conditions View
If a curve passes through the point $( 1 , - 2 )$ and has slope of the tangent at any point $( x , y )$ on it as $\frac { x ^ { 2 } - 2 y } { x }$, then the curve also passes through the point
(1) $( \sqrt { 3 } , 0 )$
(2) $( - 1,2 )$
(3) $( - \sqrt { 2 } , 1 )$
(4) $( 3,0 )$
Q89 Probability Definitions Probability Using Set/Event Algebra View
In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :
(1) $\frac { 1 } { 6 }$
(2) $\frac { 5 } { 6 }$
(3) $\frac { 1 } { 3 }$
(4) $\frac { 2 } { 3 }$