jee-main

Papers (191)
2026
session1_21jan_shift1 13 session1_21jan_shift2 9 session1_22jan_shift1 16 session1_22jan_shift2 10 session1_23jan_shift1 11 session1_23jan_shift2 7 session1_24jan_shift1 14 session1_24jan_shift2 10 session1_28jan_shift1 10 session1_28jan_shift2 9
2025
session1_22jan_shift1 25 session1_22jan_shift2 25 session1_23jan_shift1 25 session1_23jan_shift2 25 session1_24jan_shift1 25 session1_24jan_shift2 25 session1_28jan_shift1 25 session1_28jan_shift2 25 session1_29jan_shift1 29 session1_29jan_shift2 25 session2_02apr_shift1 31 session2_02apr_shift2 36 session2_03apr_shift1 35 session2_03apr_shift2 35 session2_04apr_shift1 37 session2_04apr_shift2 33 session2_07apr_shift1 32 session2_07apr_shift2 32 session2_08apr_shift1 36 session2_08apr_shift2 35
2024
session1_01feb_shift1 5 session1_01feb_shift2 21 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 28 session1_29jan_shift2 29 session1_30jan_shift1 20 session1_30jan_shift2 29 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 5 session2_04apr_shift2 28 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 21 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 29 session2_09apr_shift1 8 session2_09apr_shift2 30
2023
session1_01feb_shift1 28 session1_01feb_shift2 3 session1_24jan_shift1 11 session1_24jan_shift2 11 session1_25jan_shift1 29 session1_25jan_shift2 29 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 5 session1_30jan_shift2 27 session1_31jan_shift1 28 session1_31jan_shift2 15 session2_06apr_shift1 5 session2_06apr_shift2 16 session2_08apr_shift1 29 session2_08apr_shift2 13 session2_10apr_shift1 29 session2_10apr_shift2 16 session2_11apr_shift1 6 session2_11apr_shift2 8 session2_12apr_shift1 26 session2_13apr_shift1 24 session2_13apr_shift2 24 session2_15apr_shift1 19
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
2021 session1_25feb_shift2

29 maths questions

Q61 Sequences and series, recurrence and convergence Direct term computation from recurrence View
Let $\alpha$ and $\beta$ be the roots of $x ^ { 2 } - 6 x - 2 = 0$. If $a _ { n } = \alpha ^ { n } - \beta ^ { n }$ for $n \geqslant 1$, then the value of $\frac { a _ { 10 } - 2 a _ { 8 } } { 3 a _ { 9 } }$ is:
(1) 1
(2) 3
(3) 2
(4) 4
Q62 Complex Numbers Arithmetic Systems of Equations via Real and Imaginary Part Matching View
If $\alpha , \beta \in R$ are such that $1 - 2 i$ (here $i ^ { 2 } = - 1$ ) is a root of $z ^ { 2 } + \alpha z + \beta = 0$, then ( $\alpha - \beta$ ) is equal to:
(1) - 7
(2) 7
(3) - 3
(4) 3
Q63 Exponential Functions Exponential Equation Solving View
The minimum value of $f ( x ) = a ^ { a ^ { x } } + a ^ { 1 - a ^ { x } }$, where $a , x \in R$ and $a > 0$, is equal to:
(1) $a + 1$
(2) $2 a$
(3) $a + \frac { 1 } { a }$
(4) $2 \sqrt { a }$
Q64 Addition & Double Angle Formulae Trigonometric Equation Solving via Identities View
If $0 < x , y < \pi$ and $\cos x + \cos y - \cos ( x + y ) = \frac { 3 } { 2 }$, then $\sin x + \cos y$ is equal to:
(1) $\frac { 1 } { 2 }$
(2) $\frac { \sqrt { 3 } } { 2 }$
(3) $\frac { 1 - \sqrt { 3 } } { 2 }$
(4) $\frac { 1 + \sqrt { 3 } } { 2 }$
Q65 Circles Area and Geometric Measurement Involving Circles View
If the curve $x ^ { 2 } + 2 y ^ { 2 } = 2$ intersects the line $x + y = 1$ at two points $P$ and $Q$, then the angle subtended by the line segment $PQ$ at the origin is
(1) $\frac { \pi } { 2 } - \tan ^ { - 1 } \left( \frac { 1 } { 3 } \right)$
(2) $\frac { \pi } { 2 } + \tan ^ { - 1 } \left( \frac { 1 } { 3 } \right)$
(3) $\frac { \pi } { 2 } + \tan ^ { - 1 } \left( \frac { 1 } { 4 } \right)$
(4) $\frac { \pi } { 2 } - \tan ^ { - 1 } \left( \frac { 1 } { 4 } \right)$
Q66 Conic sections Equation Determination from Geometric Conditions View
A hyperbola passes through the foci of the ellipse $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:
(1) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$
(2) $x ^ { 2 } - y ^ { 2 } = 9$
(3) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$
(4) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 4 } = 1$
Q68 Matrices Matrix Algebra and Product Properties View
If for the matrix, $A = \left[ \begin{array} { c c } 1 & - \alpha \\ \alpha & \beta \end{array} \right] , A A ^ { T } = I _ { 2 }$, then the value of $\alpha ^ { 4 } + \beta ^ { 4 }$ is:
(1) 3
(2) 1
(3) 2
(4) 4
Q69 Matrices Direct Determinant Computation View
Let $A$ be a $3 \times 3$ matrix with $\operatorname { det } ( A ) = 4$. Let $R _ { i }$ denote the $i ^ { \text {th} }$ row of $A$. If a matrix $B$ is obtained by performing the operation $R _ { 2 } \rightarrow 2 R _ { 2 } + 5 R _ { 3 }$ on $2 A$, then $\operatorname { det } ( B )$ is equal to:
(1) 64
(2) 16
(3) 128
(4) 80
Q70 Simultaneous equations View
The following system of linear equations $2 x + 3 y + 2 z = 9$ $3 x + 2 y + 2 z = 9$ $x - y + 4 z = 8$
(1) has infinitely many solutions
(2) has a unique solution
(3) has a solution ( $\alpha , \beta , \gamma$ ) satisfying $\alpha + \beta ^ { 2 } + \gamma ^ { 3 } = 12$
(4) does not have any solution
Q71 Reciprocal Trig & Identities Inverse trigonometric equation View
$\operatorname { cosec } \left[ 2 \cot ^ { - 1 } ( 5 ) + \cos ^ { - 1 } \left( \frac { 4 } { 5 } \right) \right]$ is equal to:
(1) $\frac { 65 } { 56 }$
(2) $\frac { 75 } { 56 }$
(3) $\frac { 65 } { 33 }$
(4) $\frac { 56 } { 33 }$
Q72 Arithmetic Sequences and Series Properties of AP Terms under Transformation View
A function $f ( x )$ is given by $f ( x ) = \frac { 5 ^ { x } } { 5 ^ { x } + 5 }$, then the sum of the series $f \left( \frac { 1 } { 20 } \right) + f \left( \frac { 2 } { 20 } \right) + f \left( \frac { 3 } { 20 } \right) + \ldots + f \left( \frac { 39 } { 20 } \right)$ is equal to:
(1) $\frac { 19 } { 2 }$
(2) $\frac { 49 } { 2 }$
(3) $\frac { 39 } { 2 }$
(4) $\frac { 29 } { 2 }$
Q73 Permutations & Arrangements Counting Functions with Constraints View
Let $x$ denote the total number of one-one functions from a set $A$ with 3 elements to a set $B$ with 5 elements and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then:
(1) $y = 273 x$
(2) $2 y = 273 x$
(3) $2 y = 91 x$
(4) $y = 91 x$
Q74 Applied differentiation Applied modeling with differentiation View
The shortest distance between the line $x - y = 1$ and the curve $x ^ { 2 } = 2 y$ is:
(1) $\frac { 1 } { 2 }$
(2) $\frac { 1 } { \sqrt { 2 } }$
(3) $\frac { 1 } { 2 \sqrt { 2 } }$
(4) 0
Q75 Integration by Substitution Substitution to Transform Integral Form (Show Transformed Expression) View
The integral $\int \frac { e ^ { 3 \log _ { e } 2 x } + 5 e ^ { 2 \log _ { e } 2 x } } { e ^ { 4 \log _ { e } x } + 5 e ^ { 3 \log _ { e } x } - 7 e ^ { 2 \log _ { e } x } } d x , x > 0$, is equal to (where $c$ is a constant of integration)
(1) $\log _ { \mathrm { e } } \left| x ^ { 2 } + 5 x - 7 \right| + \mathrm { c }$
(2) $4 \log _ { \mathrm { e } } \left| x ^ { 2 } + 5 x - 7 \right| + \mathrm { c }$
(3) $\frac { 1 } { 4 } \log _ { \mathrm { e } } \left| x ^ { 2 } + 5 x - 7 \right| + \mathrm { c }$
(4) $\log _ { e } \sqrt { x ^ { 2 } + 5 x - 7 } + c$
Q76 Reduction Formulae True/False or Multiple-Statement Verification View
If $I _ { n } = \int _ { \frac { \pi } { 4 } } ^ { \frac { \pi } { 2 } } \cot ^ { n } x \, d x$, then
(1) $I _ { 2 } + I _ { 4 } , \left( I _ { 3 } + I _ { 5 } \right) ^ { 2 } , I _ { 4 } + I _ { 6 }$ are in G.P.
(2) $I _ { 2 } + I _ { 4 } , I _ { 3 } + I _ { 5 } , I _ { 4 } + I _ { 6 }$ are in A.P.
(3) $\frac { 1 } { I _ { 2 } + I _ { 4 } } , \frac { 1 } { I _ { 3 } + I _ { 5 } } , \frac { 1 } { I _ { 4 } + I _ { 6 } }$ are in A.P.
(4) $\frac { 1 } { I _ { 2 } + I _ { 4 } } , \frac { 1 } { I _ { 3 } + I _ { 5 } } , \frac { 1 } { I _ { 4 } + I _ { 6 } }$ are in G.P.
Q77 Indefinite & Definite Integrals Definite Integral as a Limit of Riemann Sums View
$\lim _ { n \rightarrow \infty } \left[ \frac { 1 } { n } + \frac { n } { ( n + 1 ) ^ { 2 } } + \frac { n } { ( n + 2 ) ^ { 2 } } + \ldots + \frac { n } { ( 2 n - 1 ) ^ { 2 } } \right]$ is equal to
(1) $\frac { 1 } { 2 }$
(2) $\frac { 1 } { 4 }$
(3) $\frac { 1 } { 3 }$
(4) 1
Q78 Vectors: Lines & Planes Normal Vector and Plane Equation View
A plane passes through the points $A ( 1,2,3 ) , B ( 2,3,1 )$ and $C ( 2,4,2 )$. If $O$ is the origin and $P$ is $( 2 , - 1,1 )$, then the projection of $\overrightarrow { O P }$ on this plane is of length:
(1) $\sqrt { \frac { 2 } { 5 } }$
(2) $\sqrt { \frac { 2 } { 7 } }$
(3) $\sqrt { \frac { 2 } { 3 } }$
(4) $\sqrt { \frac { 2 } { 11 } }$
Q79 Conditional Probability Bayes' Theorem with Diagnostic/Screening Test View
In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are $35 \% , 20 \%$ and $10 \%$ respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is:
(1) $\frac { 14 } { 45 }$
(2) $\frac { 7 } { 45 }$
(3) $\frac { 8 } { 45 }$
(4) $\frac { 28 } { 45 }$
Q80 Probability Definitions Probability Involving Algebraic or Number-Theoretic Conditions View
Let $A$ be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of $A$ leaves remainder 2 when divided by 5 is:
(1) $\frac { 1 } { 5 }$
(2) $\frac { 122 } { 297 }$
(3) $\frac { 97 } { 297 }$
(4) $\frac { 2 } { 9 }$
Q81 Number Theory Modular Arithmetic Computation View
The total number of two digit numbers $n$, such that $3 ^ { n } + 7 ^ { n }$ is a multiple of 10, is $\underline{\hspace{1cm}}$.
Q82 Number Theory Modular Arithmetic Computation View
If the remainder when $x$ is divided by 4 is 3, then the remainder when $( 2020 + x ) ^ { 2022 }$ is divided by 8 is $\underline{\hspace{1cm}}$.
Q83 Circles Tangent Lines and Tangent Lengths View
A line is a common tangent to the circle $( x - 3 ) ^ { 2 } + y ^ { 2 } = 9$ and the parabola $y ^ { 2 } = 4 x$. If the two points of contact $( a , b )$ and $( c , d )$ are distinct and lie in the first quadrant, then $2 ( a + c )$ is equal to $\underline{\hspace{1cm}}$.
Q84 Chain Rule Limit Evaluation Involving Composition or Substitution View
If $\lim _ { x \rightarrow 0 } \frac { a x - \left( e ^ { 4 x } - 1 \right) } { a x \left( e ^ { 4 x } - 1 \right) }$ exists and is equal to $b$, then the value of $a - 2 b$ is $\underline{\hspace{1cm}}$.
Q85 Curve Sketching Continuity and Discontinuity Analysis of Piecewise Functions View
A function $f$ is defined on $[ - 3,3 ]$ as $$f ( x ) = \left\{ \begin{array} { c } \min \left\{ | x | , 2 - x ^ { 2 } \right\} , - 2 \leq x \leq 2 \\ { [ | x | ] , 2 < | x | \leq 3 } \end{array} \right.$$ where $[ x ]$ denotes the greatest integer $\leq x$. The number of points, where $f$ is not differentiable in $( - 3,3 )$ is $\underline{\hspace{1cm}}$.
Q86 Tangents, normals and gradients Normal or perpendicular line problems View
If the curves $x = y ^ { 4 }$ and $x y = k$ cut at right angles, then $( 4 k ) ^ { 6 }$ is equal to $\underline{\hspace{1cm}}$.
Q87 Indefinite & Definite Integrals Piecewise/Periodic Function Integration View
The value of $\int _ { - 2 } ^ { 2 } \left| 3 x ^ { 2 } - 3 x - 6 \right| d x$ is $\underline{\hspace{1cm}}$.
Q88 Differential equations Solving Separable DEs with Initial Conditions View
If the curve $y = y ( x )$ represented by the solution of the differential equation $\left( 2 x y ^ { 2 } - y \right) d x + x \, d y = 0$, passes through the intersection of the lines $2 x - 3 y = 1$ and $3 x + 2 y = 8$, then $| y ( 1 ) |$ is equal to $\underline{\hspace{1cm}}$.
Q89 Vectors 3D & Lines Dot Product Computation View
Let $\overrightarrow { \mathrm { a } } = \hat { \mathrm { i } } + \alpha \hat { \mathrm { j } } + 3 \hat { \mathrm { k } }$ and $\overrightarrow { \mathrm { b } } = 3 \hat { \mathrm { i } } - \alpha \hat { \mathrm { j } } + \hat { \mathrm { k } }$. If the area of the parallelogram whose adjacent sides are represented by the vectors $\vec { a }$ and $\vec { b }$ is $8 \sqrt { 3 }$ square units, then $\vec { a } \cdot \vec { b }$ is equal to $\underline{\hspace{1cm}}$.
Q90 Vectors 3D & Lines Shortest Distance Between Two Lines View
A line $l$ passing through origin is perpendicular to the lines $l _ { 1 } : \vec { r } = ( 3 + t ) \hat { \mathrm { i } } + ( - 1 + 2 t ) \hat { \mathrm { j } } + ( 4 + 2 t ) \hat { \mathrm { k } }$ $l _ { 2 } : \vec { r } = ( 3 + 2 s ) \hat { \mathrm { i } } + ( 3 + 2 s ) \hat { \mathrm { j } } + ( 2 + s ) \hat { \mathrm { k } }$ If the co-ordinates of the point in the first octant on $l _ { 2 }$ at a distance of $\sqrt { 17 }$ from the point of intersection of $l$ and $l _ { 1 }$ are $( a , b , c )$, then $18 ( a + b + c )$ is equal to $\underline{\hspace{1cm}}$.