jee-main

Papers (169)
2025
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2024
session1_01feb_shift1 4 session1_01feb_shift2 22 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 30 session1_29jan_shift2 23 session1_30jan_shift1 17 session1_30jan_shift2 30 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 4 session2_04apr_shift2 30 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 22 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 30 session2_09apr_shift1 5 session2_09apr_shift2 30
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
2023 session2_15apr_shift1

20 maths questions

Q21 Work done and energy Work done by constant or variable force via integration View
A block of mass 10 kg is moving along $x$-axis under the action of force $F = 5 x \mathrm {~N}$. The work done by the force in moving the block from $x = 2 \mathrm {~m}$ to 4 m will be $\_\_\_\_$ J.
Q61 Modulus function Counting solutions satisfying modulus conditions View
The number of real roots of the equation $x | x | - 5 | x + 2 | + 6 = 0$, is
(1) 5
(2) 4
(3) 6
(4) 3
Q62 Complex Numbers Argand & Loci Distance and Region Optimization on Loci View
If the set $\left\{ \operatorname { Re } \left( \frac { z - \bar { z } + z \bar { z } } { 2 - 3 z + 5 \bar { z } } \right) : z \in \mathbb { C } , \operatorname { Re } z = 3 \right\}$ is equal to the interval $( \alpha , \beta ]$, then $24 ( \beta - \alpha )$ is equal to
(1) 36
(2) 27
(3) 30
(4) 42
Q63 Permutations & Arrangements Forming Numbers with Digit Constraints View
The total number of three-digit numbers, divisible by 3, which can be formed using the digits $1,3,5,8$, if repetition of digits is allowed, is
(1) 21
(2) 20
(3) 22
(4) 18
Q64 Geometric Sequences and Series Arithmetic-Geometric Sequence Interplay View
Let $A _ { 1 }$ and $A _ { 2 }$ be two arithmetic means and $G _ { 1 } , G _ { 2 }$ and $G _ { 3 }$ be three geometric means of two distinct positive numbers. Then $G _ { 1 } ^ { 4 } + G _ { 2 } ^ { 4 } + G _ { 3 } ^ { 4 } + G _ { 1 } ^ { 2 } G _ { 3 } ^ { 2 }$ is equal to
(1) $\left( A _ { 1 } + A _ { 2 } \right) ^ { 2 } G _ { 1 } G _ { 3 }$
(2) $2 \left( A _ { 1 } + A _ { 2 } \right) G _ { 1 } G _ { 3 }$
(3) $\left( A _ { 1 } + A _ { 2 } \right) G _ { 1 } ^ { 2 } G _ { 3 } ^ { 2 }$
(4) $2 \left( A _ { 1 } + A _ { 2 } \right) G _ { 1 } ^ { 2 } G _ { 3 } ^ { 2 }$
Q65 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
Let $\left( a + b x + c x ^ { 2 } \right) ^ { 10 } = \sum _ { i = 10 } ^ { 20 } p _ { i } x ^ { i } , a , b , c \in \mathbb { N }$. If $p _ { 1 } = 20$ and $p _ { 2 } = 210$, then $2 ( a + b + c )$ is equal to
(1) 6
(2) 15
(3) 12
(4) 8
Q66 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
If $( \alpha , \beta )$ is the orthocenter of the triangle $ABC$ with vertices $A ( 3 , - 7 ) , B ( - 1,2 )$ and $C ( 4,5 )$, then $9 \alpha - 6 \beta + 60$ is equal to
(1) 25
(2) 35
(3) 30
(4) 40
Q67 Circles Tangent Lines and Tangent Lengths View
The number of common tangents, to the circles $x ^ { 2 } + y ^ { 2 } - 18 x - 15 y + 131 = 0$ and $x ^ { 2 } + y ^ { 2 } - 6 x - 6 y - 7 = 0$, is
(1) 3
(2) 1
(3) 4
(4) 2
Q68 Proof True/False Justification View
Negation of $p \wedge ( q \wedge \sim ( p \wedge q ) )$ is
(1) $( \sim ( p \wedge q ) ) \vee p$
(2) $p \vee q$
(3) $\sim ( p \vee q )$
(4) $( \sim ( p \wedge q ) ) \wedge q$
Q69 Measures of Location and Spread View
The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is
(1) 11
(2) 13
(3) 12
(4) 14
Q70 Matrices Determinant and Rank Computation View
Let the determinant of a square matrix $A$ of order $m$ be $m - n$, where m and $n$ satisfy $4 m + n = 22$ and $17 m + 4 n = 93$. If $\operatorname { det } ( n \operatorname { adj } ( \operatorname { adj } ( m A ) ) ) = 3 ^ { a } 5 ^ { b } 6 ^ { c }$, then $a + b + c$ is equal to
(1) 84
(2) 96
(3) 101
(4) 109
Q71 Simultaneous equations View
Let the system of linear equations $- x + 2 y - 9 z = 7$ $- x + 3 y + 7 z = 9$ $- 2 x + y + 5 z = 8$ $- 3 x + y + 13 z = \lambda$ has a unique solution $x = \alpha , y = \beta , z = \gamma$. Then the distance of the point $( \alpha , \beta , \gamma )$ from the plane $2 x - 2 y + z = \lambda$ is
(1) 11
(2) 7
(3) 9
(4) 13
Q72 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
If the domain of the function $f ( x ) = \log _ { e } \left( 4 x ^ { 2 } + 11 x + 6 \right) + \sin ^ { - 1 } ( 4 x + 3 ) + \cos ^ { - 1 } \left( \frac { 10 x + 6 } { 3 } \right)$ is $( \alpha , \beta ]$, then $36 | \alpha + \beta |$ is equal to
(1) 54
(2) 72
(3) 63
(4) 45
Q73 Integration by Substitution Substitution to Evaluate a Definite Integral (Numerical Answer) View
Let $[ x ]$ denote the greatest integer function and $f ( x ) = \max \{ 1 + x + [ x ] , 2 + x , x + 2 [ x ] \} , 0 \leq x \leq 2$, where $m$ is the number of points in $( 0,2 )$ where $f$ is not continuous and $n$ be the number of points in $( 0,2 )$, where $f$ is not differentiable. Then $( m + n ) ^ { 2 } + 2$ is equal to
(1) 2
(2) 11
(3) 6
(4) 3
Q74 Integration by Substitution Substitution Combined with Symmetry or Companion Integral View
If $\int _ { 0 } ^ { 1 } \frac { 1 } { \left( 5 + 2 x - 2 x ^ { 2 } \right) \left( 1 + e ^ { ( 2 - 4 x ) } \right) } d x = \frac { 1 } { \alpha } \log _ { e } \left( \frac { \alpha + 1 } { \beta } \right) , \alpha , \beta > 0$, then $\alpha ^ { 4 } - \beta ^ { 4 }$ is equal to
(1) 19
(2) $- 21$
(3) 0
(4) 21
Q75 First order differential equations (integrating factor) View
Let $x = x ( y )$ be the solution of the differential equation $2 ( y + 2 ) \log _ { e } ( y + 2 ) d x + \left( x + 4 - 2 \log _ { e } ( y + 2 ) \right) d y = 0 , y > - 1$ with $x \left( e ^ { 4 } - 2 \right) = 1$. Then $x \left( e ^ { 9 } - 2 \right)$ is equal to
(1) 3
(2) $\frac { 4 } { 9 }$
(3) $\frac { 32 } { 9 }$
(4) $\frac { 10 } { 3 }$
Q76 Vectors 3D & Lines Vector Algebra and Triple Product Computation View
Let $S$ be the set of all $( \lambda , \mu )$ for which the vectors $\lambda \hat { i } - \hat { j } + \widehat { k } , \hat { i } + 2 \hat { j } + \mu \widehat { k }$ and $3 \hat { i } - 4 \hat { j } + 5 \widehat { k }$, where $\lambda - \mu = 5$, are coplanar, then $\sum _ { ( \lambda , \mu ) \in S } 80 \left( \lambda ^ { 2 } + \mu ^ { 2 } \right)$ is equal to
(1) 2210
(2) 2130
(3) 2290
(4) 2370
Q77 Vectors Introduction & 2D Expressing a Vector as a Linear Combination View
Let $ABCD$ be a quadrilateral. If $E$ and $F$ are the mid points of the diagonals $AC$ and $BD$ respectively and $( \overrightarrow { AB } - \overrightarrow { BC } ) + ( \overrightarrow { AD } - \overrightarrow { DC } ) = k \overrightarrow { FE }$, then $k$ is equal to
(1) 4
(2) $- 2$
(3) 2
(4) $- 4$
Q78 Vectors: Lines & Planes Perpendicular/Orthogonal Projection onto a Plane View
Let the foot of perpendicular of the point $P ( 3 , - 2 , - 9 )$ on the plane passing through the points $( - 1 , - 2 , - 3 ) , ( 9,3,4 ) , ( 9 , - 2,1 )$ be $Q ( \alpha , \beta , \gamma )$. Then the distance of $Q$ from the origin is
(1) $\sqrt { 42 }$
(2) $\sqrt { 38 }$
(3) $\sqrt { 35 }$
(4) $\sqrt { 29 }$
Q79 Vectors: Lines & Planes Distance Computation (Point-to-Plane or Line-to-Line) View
Let $S$ be the set of all values of $\lambda$, for which the shortest distance between the lines $\frac { x - \lambda } { 0 } = \frac { y - 3 } { 4 } = \frac { z + 6 } { 1 }$ and $\frac { x + \lambda } { 3 } = \frac { y } { - 4 } = \frac { z - 6 } { 0 }$ is 13. Then $8 \left| \sum _ { \lambda \in S } \lambda \right|$ is equal to
(1) 306
(2) 304
(3) 308
(4) 302