jee-main

Papers (191)
2026
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2025
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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
2023 session2_13apr_shift2

24 maths questions

Q2 Variable acceleration (1D) Find velocity/speed by differentiating position View
The distance travelled by an object in time $t$ is given by $s = 2.5 t ^ { 2 }$. The instantaneous speed of the object at $t = 5 \mathrm {~s}$ will be :
(1) $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $62.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $12.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
Q3 Constant acceleration (SUVAT) Relative velocity and observed length/time View
A passenger sitting in a train $A$ moving at $90 \mathrm {~km} \mathrm {~h} ^ { - 1 }$ observes another train $B$ moving in the opposite direction for 8 s . If the velocity of the train $B$ is $54 \mathrm {~km} \mathrm {~h} ^ { - 1 }$, then length of train $B$ is:
(1) 120 m
(2) 320 m
(3) 80 m
(4) 200 m
Q4 Circular Motion 1 Centripetal Acceleration / Force Calculation View
A vehicle of mass 200 kg is moving along a levelled curved road of radius 70 m with angular velocity of $0.2 \mathrm { rad } \mathrm { s } ^ { - 1 }$. The centripetal force acting on the vehicle is:
(1) 560 N
(2) 2800 N
(3) 2240 N
(4) 14 N
Q10 Simple Harmonic Motion View
A particle executes SHM of amplitude $A$. The distance from the mean position when its kinetic energy becomes equal to its potential energy is:
(1) $\frac { 1 } { \sqrt { 2 } } A$
(2) $2 A$
(3) $\sqrt { 2 A }$
(4) $\frac { 1 } { 2 } A$
Q21 Work done and energy Work-energy theorem: finding speed or kinetic energy from net work View
A car accelerates from rest to $u \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The energy spent in this process is $E \mathrm {~J}$. The energy required to accelerate the car from $u \mathrm {~m} \mathrm {~s} ^ { - 1 }$ to $2u \mathrm {~m} \mathrm {~s} ^ { - 1 }$ is $nE \mathrm {~J}$. The value of $n$ is $\_\_\_\_$.
Q22 Moments View
A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be $\_\_\_\_$ rad $s ^ { - 2 }$.
Q61 Roots of polynomials Vieta's formulas: compute symmetric functions of roots View
Let $\alpha , \beta$ be the roots of the equation $x ^ { 2 } - \sqrt { 2 } x + 2 = 0$. Then $\alpha ^ { 14 } + \beta ^ { 14 }$ is equal to
(1) $- 64$
(2) $- 64 \sqrt { 2 }$
(3) $- 128$
(4) $- 128 \sqrt { 2 }$
Q62 Complex Numbers Arithmetic Conjugate and Modulus Equation Problems View
Let $S = \{ z \in \mathbb { C } : \bar { z } = i z ^ { 2 } + \operatorname { Re } ( \bar { z } ) \}$. Then $\sum _ { z \in S } | z | ^ { 2 }$ is equal to
(1) $\frac { 5 } { 2 }$
(2) 4
(3) $\frac { 7 } { 2 }$
(4) 3
Q63 Permutations & Arrangements Dictionary Order / Rank of a Permutation View
All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is
(1) 327
(2) 328
(3) 324
(4) 326
Q64 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
Let $a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots$ be a G.P. of increasing positive numbers. Let the sum of its $6 ^ { \text {th} }$ and $8 ^ { \text {th} }$ terms be 2 and the product of its $3 ^ { \text {rd} }$ and $5 ^ { \text {th} }$ terms be $\frac { 1 } { 9 }$. Then $6 ( a _ { 2 } + a _ { 4 } )( a _ { 4 } + a _ { 6 } )$ is equal to
(1) 3
(2) $3 \sqrt { 3 }$
(3) 2
(4) $2 \sqrt { 2 }$
Q65 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
The coefficient of $x ^ { 5 }$ in the expansion of $\left( 2 x ^ { 3 } - \frac { 1 } { 3 x ^ { 2 } } \right) ^ { 5 }$ is
(1) $\frac { 80 } { 9 }$
(2) 9
(3) 8
(4) $\frac { 26 } { 3 }$
Q66 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
Let $( \alpha , \beta )$ be the centroid of the triangle formed by the lines $15 x - y = 82$, $6 x - 5 y = - 4$ and $9 x + 4 y = 17$. Then $\alpha + 2 \beta$ and $2 \alpha - \beta$ are the roots of the equation
(1) $x ^ { 2 } - 7 x + 12 = 0$
(2) $x ^ { 2 } - 14 x + 48 = 0$
(3) $x ^ { 2 } - 13 x + 42 = 0$
(4) $x ^ { 2 } - 10 x + 25 = 0$
Q67 Circles Circle Equation Derivation View
Let the centre of a circle $C$ be $( \alpha , \beta )$ and its radius $r < 8$. Let $3 x + 4 y = 24$ and $3 x - 4 y = 32$ be two tangents and $4 x + 3 y = 1$ be a normal to $C$. Then $( \alpha - \beta + r )$ is equal to
(1) 7
(2) 5
(3) 6
(4) 9
Q68 Chain Rule Limit evaluation using series expansion or exponential asymptotics View
If $\lim _ { x \rightarrow 0 } \frac { e ^ { ax } - \cos ( bx ) - \frac { cx e ^ { cx } } { 2 } } { 1 - \cos ( 2 x ) } = 17$, then $5 a ^ { 2 } + b ^ { 2 }$ is equal to
(1) 64
(2) 72
(3) 68
(4) 76
Q70 3x3 Matrices Determinant and Rank Computation View
Let for $A = \begin{pmatrix} 1 & 2 & 3 \\ \alpha & 3 & 1 \\ 1 & 1 & 2 \end{pmatrix}$, $|A| = 2$. If $| 2 \operatorname { adj } ( 2 \operatorname { adj } ( 2 A ) ) | = 32 ^ { n }$, then $3 n + \alpha$ is equal to
(1) 9
(2) 11
(3) 12
(4) 10
Q71 Simultaneous equations View
If the system of equations $$\begin{aligned} & 2 x + y - z = 5 \\ & 2 x - 5 y + \lambda z = \mu \\ & x + 2 y - 5 z = 7 \end{aligned}$$ has infinitely many solutions, then $( \lambda + \mu ) ^ { 2 } + ( \lambda - \mu ) ^ { 2 }$ is equal to
(1) 904
(2) 916
(3) 912
(4) 920
Q72 Function Transformations Determine Domain or Range of a Composite Function View
The range of $f(x) = 4 \sin ^ { - 1 } \left( \frac { x ^ { 2 } } { x ^ { 2 } + 1 } \right)$ is
(1) $[ 0,2 \pi ]$
(2) $[ 0 , \pi ]$
(3) $[ 0,2 \pi )$
(4) $[ 0 , \pi )$
Q73 Integration by Substitution Reduction Formula or Recurrence via Integration by Parts View
The value of $\dfrac { e ^ { - \frac { \pi } { 4 } } + \int _ { 0 } ^ { \frac { \pi } { 4 } } e ^ { - x } \tan ^ { 50 } x \, d x } { \int _ { 0 } ^ { \frac { \pi } { 4 } } e ^ { - x } \left( \tan ^ { 49 } x + \tan ^ { 51 } x \right) d x }$
(1) 51
(2) 50
(3) 25
(4) 49
Q74 Areas by integration Area Involving Piecewise or Composite Functions View
The area of the region $\{ ( x , y ) : x ^ { 2 } \leq y \leq | x ^ { 2 } - 4 | , y \geq 1 \}$ is
(1) $\frac { 4 } { 3 } ( 4 \sqrt { 2 } - 1 )$
(2) $\frac { 4 } { 3 } ( 4 \sqrt { 2 } + 1 )$
(3) $\frac { 3 } { 4 } ( 4 \sqrt { 2 } + 1 )$
(4) $\frac { 3 } { 4 } ( 4 \sqrt { 2 } - 1 )$
Q75 Vectors: Cross Product & Distances View
Let $| \vec { a } | = 2 , | \vec { b } | = 3$ and the angle between the vectors $\vec { a }$ and $\vec { b }$ be $\frac { \pi } { 4 }$. Then $| ( \vec { a } + 2 \vec { b } ) \times ( 2 \vec { a } - 3 \vec { b } ) | ^ { 2 }$ is equal to
(1) 441
(2) 482
(3) 841
(4) 882
Q76 Vectors: Cross Product & Distances Vector Algebra and Triple Product Computation View
Let for a triangle $ABC$ $$\begin{aligned} & \overrightarrow { AB } = - 2 \hat { i } + \hat { j } + 3 \hat { k } \\ & \overrightarrow { CB } = \alpha \hat { i } + \beta \hat { j } + \gamma \hat { k } \\ & \overrightarrow { CA } = 4 \hat { i } + 3 \hat { j } + \delta \hat { k } \end{aligned}$$ If $\delta > 0$ and the area of the triangle $ABC$ is $5 \sqrt { 6 }$ then $\overrightarrow { CB } \cdot \overrightarrow { CA }$ is equal to
(1) 60
(2) 54
(3) 108
(4) 120
Q77 Vectors: Lines & Planes Find Cartesian Equation of a Plane View
The plane, passing through the points $( 0 , - 1 , 2 )$ and $( - 1 , 2 , 1 )$ and parallel to the line passing through $( 5 , 1 , - 7 )$ and $( 1 , - 1 , - 1 )$, also passes through the point
(1) $( - 2 , 5 , 0 )$
(2) $( 1 , - 2 , 1 )$
(3) $( 2 , 0 , 1 )$
(4) $( 0 , 5 , - 2 )$
Q78 Vectors: Lines & Planes Coplanarity and Relative Position of Planes View
The line, that is coplanar to the line $\frac { x + 3 } { - 3 } = \frac { y - 1 } { 1 } = \frac { z - 5 } { 5 }$, is
(1) $\frac { x + 1 } { - 1 } = \frac { y - 2 } { 2 } = \frac { z - 5 } { 4 }$
(2) $\frac { x + 1 } { - 1 } = \frac { y - 2 } { 2 } = \frac { z - 5 } { 5 }$
(3) $\frac { x - 1 } { - 1 } = \frac { y - 2 } { 2 } = \frac { z - 5 } { 5 }$
(4) $\frac { x + 1 } { 1 } = \frac { y - 2 } { 2 } = \frac { z - 5 } { 5 }$
Q79 Vectors: Lines & Planes Distance Computation (Point-to-Plane or Line-to-Line) View
Let $N$ be the foot of perpendicular from the point $P ( 1 , - 2 , 3 )$ on the line passing through the points $( 4 , 5 , 8 )$ and $( 1 , - 7 , 5 )$. Then the distance of $N$ from the plane $2x - 2y + z + 5 = 0$ is $\_\_\_\_$.