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
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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
2026 session1_22jan_shift1

16 maths questions

Q1 Projectiles Velocity or Momentum at a Given Time View
A projectile is projected at angle of projection $60 ^ { \circ }$ with speed $u$. When its velocity makes an angle $45 ^ { \circ }$ with horizontal its speed is $20 \mathrm {~m} / \mathrm { s }$. Find u ?
(A) $\mathbf { 1 0 } \sqrt { \mathbf { 2 } }$
(B) $20 \mathrm {~m} / \mathrm { s }$
(C) $20 \sqrt { 2 } \mathrm {~m} / \mathrm { s }$
(D) $40 \mathrm {~m} / \mathrm { s }$
Q2 Circular Motion 1 Ratio / Comparison of Circular Motion Quantities View
Two disc having same moment of inertia about their axis. Thickness is $t _ { 1 }$ and $t _ { 2 }$ and they have same density. If $R _ { 1 } / R _ { 2 } = 1 / 2$, then find $t _ { 1 } / t _ { 2 }$.
(A) 4
(B) $1 / 4$
(C) $1 / 16$
(D) 16
Q3 Moments View
Two thin circular rings are lying in the same plane and are touching each other at a single point. The first ring has mass 5 kg and radius 10 cm , while the second ring has mass 10 kg and radius 20 cm . Find the moment of inertia of the combined system about a straight line passing through the point of contact and lying in the plane of the rings.
(A) $\frac { 27 } { 50 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$
(B) $\frac { 24 } { 40 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$
(C) $\frac { 27 } { 40 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$
(D) $\frac { 17 } { 12 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$
Q21 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
If sum of first 4 terms of an A.P is 6 and sum of first 6 terms is 4, then sum of first 12 terms of an A.P is
(A) -21
(B) -22
(C) -23
(D) - 24
Q22 Inequalities Absolute Value Inequality View
$x | x + 4 | + 3 | x + 2 | + 10 = 0$ No. of real soln.
Q23 Matrices Determinant and Rank Computation View
If $A = \left[ \begin{array} { l l } 2 & 3 \\ 3 & 5 \end{array} \right]$, then the value of $\left| \vec { A } ^ { 2025 } - 3 A ^ { 2024 } + A ^ { 2023 } \right|$ is
Q24 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
If the domain of the function $\frac { 1 } { \ln ( 10 - x ) } + \sin ^ { - 1 } \left( \frac { x + 2 } { 2 x + 3 } \right)$ is $( - \infty , - a ] \cup ( - 1 , b ) \cup ( b , c )$, then $( b + c - 3 a )$ is equal to
(A) $20 - \frac { 5 } { 3 }$
(B) $21$
(C) 23
(D) 24
Q25 Indefinite & Definite Integrals Piecewise/Periodic Function Integration View
$\int _ { \frac { - \pi } { 2 } } ^ { \frac { \pi } { 2 } } \frac { d x } { [ x ] + 5 }$ is equal to: ([.] denotes greatest integer function)
(A) $\frac { \pi } { 4 } - \frac { 1 } { 10 }$
(B) $\frac { \pi } { 4 } - \frac { 1 } { 20 }$
(C) $\frac { \pi } { 12 } - \frac { 1 } { 10 }$
(D) $\frac { \pi } { 4 } - \frac { 1 } { 5 }$
Q26 Indefinite & Definite Integrals Finding a Function from an Integral Equation View
If $6 \left( \int _ { 1 } ^ { \mathbf { x } } \mathbf { f } ( \mathbf { t } ) \mathbf { d t } \right) = 3 \left( \mathbf { x } \mathbf { f } ( \mathbf { x } ) + \mathbf { x } ^ { 3 } - 4 \right)$, then find the value of $\mathbf { f } ( 2 ) - \mathbf { f } ( 3 )$
Q27 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Product of Binomial/Polynomial Expressions View
The coefficient of $\mathrm { x } ^ { 48 }$ in
$1 \cdot ( 1 + \mathrm { x } ) + 2 \cdot ( 1 + \mathrm { x } ) ^ { 2 } + 3 \cdot ( 1 + \mathrm { x } ) ^ { 3 } + \ldots + 100 \cdot ( 1 + \mathrm { x } ) ^ { 100 }$ is
(A) $\left( { } ^ { { } ^ { 101 } } \mathrm { C } _ { 46 } \right) - 100$
(B) $\mathbf { 1 0 0 } \left( { } ^ { \mathbf { 1 0 1 } } \mathbf { C } _ { \mathbf { 4 6 } } \right) - { } ^ { \mathbf { 1 0 1 } } \mathbf { C } _ { \mathbf { 4 7 } }$
(C) $\mathbf { 1 0 0 } \left( { } ^ { { } ^ { 101 } } C _ { 49 } \right) - { } ^ { 101 } C _ { 50 }$
(D) ${ } ^ { { } ^ { 101 } } \mathrm { C } _ { 47 } - { } ^ { 101 } \mathrm { C } _ { 46 }$
Q28 Independent Events View
Let $\mathrm { M } = \{ 1,2,3 , \ldots , 16 \}$ and R be a relation on M defined by xRy if and only if $4 y = 5 x - 3$. Then, the number of elements required to added in R to make it symmetric is
(A) 3
(B) 2
(C) 5
(D) 4
Q29 Differential equations First-Order Linear DE: General Solution View
The solution of the differential equation $\mathbf { x d y } - \mathbf { y d x } = \sqrt { \mathbf { x } ^ { 2 } + \mathbf { y } ^ { 2 } } \mathbf { d x }$ is (where c is integration constant)
(A) $\sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } } = \mathrm { cx } ^ { 2 } - \mathrm { y }$
(B) $\sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } } = \mathrm { cx } ^ { 2 } + \mathrm { y }$
(C) $\sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } } = \mathrm { cx } - \mathrm { y }$
(D) $\sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } } = \mathrm { cx } + \mathrm { y }$
Q30 Standard trigonometric equations Inverse trigonometric equation View
The number of values of $x$ satisfying $\tan ^ { - 1 } ( 4 x ) + \tan ^ { - 1 } ( 6 x ) = \frac { \pi } { 6 }$ and $\mathrm { x } \in \left[ - \frac { 1 } { 2 \sqrt { 6 } } , \frac { 1 } { 2 \sqrt { 6 } } \right]$ is
(A) 0
(B) 1
(C) 2
(D) 3
Q31 Addition & Double Angle Formulae Simplification of Trigonometric Expressions with Specific Angles View
If $\frac { \cos ^ { 2 } 48 ^ { \circ } - \sin ^ { 2 } 12 ^ { \circ } } { \sin ^ { 2 } 24 ^ { \circ } - \sin ^ { 2 } 6 ^ { \circ } } = \frac { \alpha + \sqrt { 5 } \beta } { 2 }$. Then, the value of $( \alpha + \beta )$ is
(A) 3
(B) 2
(C) 11
(D) 4
Q32 Standard Integrals and Reverse Chain Rule Definite Integral Evaluation via Substitution or Standard Forms View
If $\int ( \cos x ) ^ { - 5 / 2 } ( \sin x ) ^ { - 11 / 2 } d x = \frac { p _ { 1 } } { q _ { 1 } } ( \cot x ) ^ { 9 / 2 } + \frac { p _ { 2 } } { q _ { 2 } } ( \cot x ) ^ { 5 / 2 } + \frac { p _ { 3 } } { q _ { 3 } } ( \cot x ) ^ { 1 / 2 } - \frac { p _ { 4 } } { q _ { 4 } } ( \cot x ) ^ { - 3 / 2 } + c$ (where c is constant of integration), then value of $\frac { 15 p _ { 1 } p _ { 2 } p _ { 3 } p _ { 4 } } { q _ { 1 } q _ { 2 } q _ { 3 } q _ { 4 } }$ is
(A) 16
(B) 14
Q33 Areas by integration View
If the area of the region $\left\{ ( x , y ) : x ^ { 2 } + 1 \leq y \leq 3 - x \right\}$ is divided by the line $x = - 1$ in the ratio $m : n$ (where $m$ and $n$ are coprime natural numbers). Then, the value of $\mathrm { m } + \mathrm { n }$ is