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
2019 session1_12jan_shift2

29 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 Argand & Loci 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 Addition & Double Angle Formulae 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
Q75 Projectiles Projectile Involving Rotational or Combined Physics View
If the angle of elevation of a cloud from a point $P$ which is $25 m$ above a lake be $30 ^ { \circ }$ and the angle of depression of reflection of the cloud in the lake from $P$ be $60 ^ { \circ }$, then the height of the cloud (in meters) from the surface of the lake is :
(1) 50
(2) 60
(3) 45
(4) 42
Q76 Permutations & Arrangements Distribution of Objects into Bins/Groups View
Let $Z$ be the set of integers. If $A = \left\{ x \in Z : 2 ^ { ( x + 2 ) \left( x ^ { 2 } - 5 x + 6 \right) } = 1 \right\}$ and $B = \{ x \in Z : - 3 < 2 x - 1 < 9 \}$, then the number of subsets of the set $A \times B$, is :
(1) $2 ^ { 12 }$
(2) $2 ^ { 10 }$
(3) $2 ^ { 18 }$
(4) $2 ^ { 15 }$
Q77 3x3 Matrices Determinant of Parametric or Structured Matrix View
If $A = \left[ \begin{array} { c c c } 1 & \sin \theta & 1 \\ - \sin \theta & 1 & \sin \theta \\ - 1 & - \sin \theta & 1 \end{array} \right]$, then for all $\theta \in \left( \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } \right) , \operatorname { det } ( A )$ lies in the interval :
(1) $\left( 1 , \frac { 5 } { 2 } \right]$
(2) $\left[ \frac { 5 } { 2 } , 4 \right)$
(3) $\left( \frac { 3 } { 2 } , 3 \right]$
(4) $\left( 0 , \frac { 3 } { 2 } \right]$
Q78 3x3 Matrices Linear System with Parameter — Infinite Solutions View
The set of all values of $\lambda$ for which the system of linear equations $$\begin{aligned} & x - 2 y - 2 z = \lambda x \\ & x + 2 y + z = \lambda y \\ & - x - y = \lambda z \end{aligned}$$ has a non-trivial solution :
(1) is an empty set
(2) contains more than two elements
(3) is a singleton
(4) contains exactly two elements
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) $\frac { 3 } { 2 } - \frac { 1 } { e } - \frac { 1 } { 2 e ^ { 2 } }$
Q84 Sequences and series, recurrence and convergence Summation of sequence terms View
$\lim _ { n \rightarrow \infty } \left( \frac { n } { n ^ { 2 } + 1 ^ { 2 } } + \frac { n } { n ^ { 2 } + 2 ^ { 2 } } + \frac { n } { n ^ { 2 } + 3 ^ { 2 } } + \ldots\ldots + \frac { 1 } { 5 n ^ { 2 } } \right)$ is equal to
(1) $\frac { \pi } { 4 }$
(2) $\tan ^ { - 1 } ( 2 )$
(3) $\frac { \pi } { 2 }$
(4) $\tan ^ { - 1 } ( 3 )$
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) $( 3,0 )$
Q86 Vectors 3D & Lines Vector Algebra and Triple Product Computation View
Let $\vec { a } , \vec { b }$ and $\vec { c }$ be three unit vectors, out of which vectors $\vec { b }$ and $\vec { c }$ are non-parallel. If $\alpha$ and $\beta$ are the angles which vector $\vec { a }$ makes with vectors $\vec { b }$ and $\vec { c }$ respectively and $\vec { a } \times ( \vec { b } \times \vec { c } ) = \frac { 1 } { 2 } \vec { b }$, then $| \alpha - \beta |$ is equal to :
(1) $90 ^ { \circ }$
(2) $60 ^ { \circ }$
(3) $45 ^ { \circ }$
(4) $30 ^ { \circ }$
Q87 Vectors: Lines & Planes Dihedral Angle or Angle Between Planes/Lines View
If an angle between the line, $\frac { x + 1 } { 2 } = \frac { y - 2 } { 1 } = \frac { z - 3 } { - 2 }$ and the plane, $x - 2 y - k z = 3$ is $\cos ^ { - 1 } \left( \frac { 2 \sqrt { 2 } } { 3 } \right)$, then a value of $k$ is
(1) $\sqrt { \frac { 5 } { 3 } }$
(2) $\sqrt { \frac { 3 } { 5 } }$
(3) $- \frac { 3 } { 5 }$
(4) $- \frac { 5 } { 3 }$
Q88 Vectors: Lines & Planes Coplanarity and Relative Position of Planes View
Let $S$ be the set of all real values of $\lambda$ such that a plane passing through the points $\left( - \lambda ^ { 2 } , 1,1 \right) , \left( 1 , - \lambda ^ { 2 } , 1 \right)$ and $\left( 1,1 , - \lambda ^ { 2 } \right)$ also passes through the point $( - 1 , - 1,1 )$. Then $S$ is equal to :
(1) $\{ \sqrt { 3 } \}$
(2) $\{ 3 , - 3 \}$
(3) $\{ 1 , - 1 \}$
(4) $\{ \sqrt { 3 } , - \sqrt { 3 } \}$
Q89 Principle of Inclusion/Exclusion 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) $\frac { 2 } { 3 }$
Q90 Discrete Probability Distributions Expectation and Variance from Context-Based Random Variables View
In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :
(1) $\frac { 400 } { 3 }$ gain
(2) $\frac { 400 } { 9 }$ gain
(3) $\frac { 400 } { 3 }$ loss
(4) 0