jee-main

Papers (169)
2025
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2024
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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
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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
2024 session2_06apr_shift1

22 maths questions

Q21 Vector Product and Surfaces View
For three vectors $\vec { A } = ( - x \hat { i } - 6 \hat { j } - 2 \hat { k } ) , \vec { B } = ( - \hat { i } + 4 \hat { j } + 3 \hat { k } )$ and $\vec { C } = ( - 8 \hat { i } - \hat { j } + 3 \hat { k } )$, if $\vec { A } \cdot ( \vec { B } \times \vec { C } ) = 0$, then value of $x$ is $\_\_\_\_$
Q24 Simple Harmonic Motion View
A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s . The maximum velocity of the particle is $\_\_\_\_$ $\mathrm { cm } / \mathrm { s }$.
Q61 Sequences and series, recurrence and convergence Multiple-choice on sequence properties View
Let $\alpha , \beta$ be the distinct roots of the equation $x ^ { 2 } - \left( t ^ { 2 } - 5 t + 6 \right) x + 1 = 0 , t \in \mathbb { R }$ and $a _ { n } = \alpha ^ { n } + \beta ^ { n }$. Then the minimum value of $\frac { a _ { 2023 } + a _ { 2025 } } { a _ { 2024 } }$ is
(1) $- 1 / 4$
(2) $- 1 / 4$
(3) $- 1 / 2$
(4) $1 / 4$
Q62 Combinations & Selection Geometric Combinatorics View
The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is
(1) 48
(2) 56
(3) 24
(4) 16
Q63 Number Theory Combinatorial Number Theory and Counting View
Let $A = \{ n \in [ 100,700 ] \cap \mathbb { N } : n$ is neither a multiple of 3 nor a multiple of $4 \}$. Then the number of elements in $A$ is
(1) 290
(2) 280
(3) 300
(4) 310
Q64 Straight Lines & Coordinate Geometry Area Computation in Coordinate Geometry View
Let a variable line of slope $m > 0$ passing through the point $( 4 , - 9 )$ intersect the coordinate axes at the points $A$ and $B$. The minimum value of the sum of the distances of $A$ and $B$ from the origin is
(1) 30
(2) 25
(3) 15
(4) 10
Q65 Vectors: Cross Product & Distances View
If $A ( 3,1 , -1 ) , B \left( \frac { 5 } { 3 } , \frac { 7 } { 3 } , \frac { 1 } { 3 } \right) , C ( 2,2,1 )$ and $D \left( \frac { 10 } { 3 } , \frac { 2 } { 3 } , \frac { -1 } { 3 } \right)$ are the vertices of a quadrilateral $ABCD$, then its area is
(1) $\frac { 2 \sqrt { 2 } } { 3 }$
(2) $\frac { 5 \sqrt { 2 } } { 3 }$
(3) $2 \sqrt { 2 }$
(4) $\frac { 4 \sqrt { 2 } } { 3 }$
Q66 Circles Inscribed/Circumscribed Circle Computations View
A circle is inscribed in an equilateral triangle of side of length 12 . If the area and perimeter of any square inscribed in this circle are $m$ and $n$, respectively, then $m + n ^ { 2 }$ is equal to
(1) 408
(2) 414
(3) 396
(4) 312
Q67 Circles Circle Equation Derivation View
Let $C$ be the circle of minimum area touching the parabola $y = 6 - x ^ { 2 }$ and the lines $y = \sqrt { 3 } | x |$. Then, which one of the following points lies on the circle $C$ ?
(1) $( 1,2 )$
(2) $( 1,1 )$
(3) $( 2,2 )$
(4) $( 2,4 )$
Q68 Chain Rule Limit Involving Derivative Definition of Composed Functions View
Let $f : ( - \infty , \infty ) - \{ 0 \} \rightarrow \mathbb { R }$ be a differentiable function such that $f ^ { \prime } ( 1 ) = \lim _ { a \rightarrow \infty } a ^ { 2 } f \left( \frac { 1 } { a } \right)$. Then $\lim _ { a \rightarrow \infty } \frac { a ( a + 1 ) } { 2 } \tan ^ { - 1 } \left( \frac { 1 } { a } \right) + a ^ { 2 } - 2 \log _ { e } a$ is equal to
(1) $\frac { 3 } { 2 } + \frac { \pi } { 4 }$
(2) $\frac { 3 } { 4 } + \frac { \pi } { 8 }$
(3) $\frac { 3 } { 8 } + \frac { \pi } { 4 }$
(4) $\frac { 5 } { 2 } + \frac { \pi } { 8 }$
Q69 Measures of Location and Spread View
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation by mistake was taken 8 instead of 12 . The correct standard deviation is
(1) 1.8
(2) 1.94
(3) $\sqrt { 3.96 }$
(4) $\sqrt { 3.86 }$
Q70 Proof Computation of a Limit, Value, or Explicit Formula View
Let the relations $R _ { 1 }$ and $R _ { 2 }$ on the set $X = \{ 1,2,3 , \ldots , 20 \}$ be given by $R _ { 1 } = \{ ( x , y ) : 2 x - 3 y = 2 \}$ and $R _ { 2 } = \{ ( x , y ) : - 5 x + 4 y = 0 \}$. If $M$ and $N$ be the minimum number of elements required to be added in $R _ { 1 }$ and $R _ { 2 }$, respectively, in order to make the relations symmetric, then $M + N$ equals
(1) 12
(2) 16
(3) 8
(4) 10
Q71 3x3 Matrices Direct Determinant Computation View
For $\alpha , \beta \in \mathbb { R }$ and a natural number $n$, let $A _ { r } = \left| \begin{array} { c c c } r & 1 & \frac { n ^ { 2 } } { 2 } + \alpha \\ 2 r & 2 & n ^ { 2 } - \beta \\ 3 r - 2 & 3 & \frac { n ( 3 n - 1 ) } { 2 } \end{array} \right|$. Then $\sum_{r=1}^{n} A_r$ is
(1) 0
(2) $4 \alpha + 2 \beta$
(3) $2 \alpha + 4 \beta$
(4) $2 n$
Q72 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification View
The function $f : \mathbb{R} \to \mathbb{R}$, $f ( x ) = \frac { x ^ { 2 } + 2 x - 15 } { x ^ { 2 } - 4 x + 9 } , x \in \mathbb { R }$ is
(1) one-one but not onto.
(2) both one-one and onto.
(3) onto but not one-one.
(4) neither one-one nor onto.
Q73 Differentiating Transcendental Functions Higher-order or nth derivative computation View
If $f ( x ) = \left\{ \begin{array} { l } x ^ { 3 } \sin \left( \frac { 1 } { x } \right) , x \neq 0 \\ 0 \quad , x = 0 \end{array} \right.$ then
(1) $f ^ { \prime \prime } \left( \frac { 2 } { \pi } \right) = \frac { 24 - \pi ^ { 2 } } { 2 \pi }$
(2) $f ^ { \prime \prime } \left( \frac { 2 } { \pi } \right) = \frac { 12 - \pi ^ { 2 } } { 2 \pi }$
(3) $f ^ { \prime \prime } ( 0 ) = 1$
(4) $f ^ { \prime \prime } ( 0 ) = 0$
Q74 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions View
The interval in which the function $f ( x ) = x ^ { x } , x > 0$, is strictly increasing is
(1) $\left( 0 , \frac { 1 } { e } \right]$
(2) $( 0 , \infty )$
(3) $\left[ \frac { 1 } { e } , \infty \right)$
(4) $\left[ \frac { 1 } { e ^ { 2 } } , 1 \right)$
Q75 Indefinite & Definite Integrals Definite Integral Evaluation (Computational) View
$\int _ { 0 } ^ { \pi / 4 } \frac { \cos ^ { 2 } x \sin ^ { 2 } x } { \left( \cos ^ { 3 } x + \sin ^ { 3 } x \right) ^ { 2 } } d x$ is equal to
(1) $1 / 6$
(2) $1 / 3$
(3) $1 / 12$
(4) $1 / 9$
Q76 Areas Between Curves Compute Area Directly (Numerical Answer) View
Let the area of the region enclosed by the curves $y = 3 x , 2 y = 27 - 3 x$ and $y = 3 x - x \sqrt { x }$ be $A$. Then $10 A$ is equal to
(1) 172
(2) 162
(3) 154
(4) 184
Q77 First order differential equations (integrating factor) View
Let $y = y ( x )$ be the solution of the differential equation $\left( 1 + x ^ { 2 } \right) \frac { d y } { d x } + y = e ^ { \tan ^ { - 1 } x } , y ( 1 ) = 0$. Then $y ( 0 )$ is
(1) $\frac { 1 } { 2 } \left( e ^ { \pi / 2 } - 1 \right)$
(2) $\frac { 1 } { 2 } \left( 1 - e ^ { \pi / 2 } \right)$
(3) $\frac { 1 } { 4 } \left( 1 - e ^ { \pi / 2 } \right)$
(4) $\frac { 1 } { 4 } \left( e ^ { \pi / 2 } - 1 \right)$
Q78 First order differential equations (integrating factor) View
Let $y = y ( x )$ be the solution of the differential equation $\left( 2 x \log _ { e } x \right) \frac { d y } { d x } + 2 y = \frac { 3 } { x } \log _ { e } x , x > 0$ and $y \left( e ^ { - 1 } \right) = 0$. Then, $y ( e )$ is equal to
(1) $- \frac { 3 } { \mathrm { e } }$
(2) $- \frac { 3 } { 2 e }$
(3) $- \frac { 2 } { 3 e }$
(4) $- \frac { 2 } { \mathrm { e } }$
Q79 Vectors: Lines & Planes Distance Computation (Point-to-Plane or Line-to-Line) View
The shortest distance between the lines $\frac { x - 3 } { 2 } = \frac { y + 15 } { - 7 } = \frac { z - 9 } { 5 }$ and $\frac { x + 1 } { 2 } = \frac { y - 1 } { 1 } = \frac { z - 9 } { - 3 }$ is
(1) $8 \sqrt { 3 }$
(2) $4 \sqrt { 3 }$
(3) $5 \sqrt { 3 }$
(4) $6 \sqrt { 3 }$
Q80 Conditional Probability Bayes' Theorem with Production/Source Identification View
A company has two plants $A$ and $B$ to manufacture motorcycles. $60\%$ motorcycles are manufactured at plant $A$ and the remaining are manufactured at plant $B$. $80\%$ of the motorcycles manufactured at plant $A$ are rated of the standard quality, while $90\%$ of the motorcycles manufactured at plant $B$ are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. Find the probability that it was manufactured at plant $B$.