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
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_10apr_shift2

15 maths questions

Q61 Complex Numbers Argand & Loci Algebraic Conditions for Geometric Properties (Real, Imaginary, Collinear) View
Let $S = \left\{ z = x + iy : \frac { 2z - 3i } { 4z + 2i } \text{ is a real number} \right\}$. Then which of the following is NOT correct?
(1) $y + x ^ { 2 } + y ^ { 2 } \neq - \frac { 1 } { 4 }$
(2) $( x , y ) = \left( 0 , - \frac { 1 } { 2 } \right)$
(3) $x = 0$
(4) $y \in \left( - \infty , - \frac { 1 } { 2 } \right) \cup \left( - \frac { 1 } { 2 } , \infty \right)$
Q62 Combinations & Selection Partitioning into Teams or Groups View
Eight persons are to be transported from city $A$ to city $B$ in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is
(1) 1120
(2) 3360
(3) 1680
(4) 560
Q63 Sequences and Series Evaluation of a Finite or Infinite Sum View
If $S _ { n } = 4 + 11 + 21 + 34 + 50 + \ldots$ to $n$ terms, then $\frac { 1 } { 60 } \left( S _ { 29 } - S _ { 9 } \right)$ is equal to
(1) 223
(2) 226
(3) 220
(4) 227
Q64 Number Theory Modular Arithmetic Computation View
Let the number $( 22 ) ^ { 2022 } + ( 2022 ) ^ { 22 }$ leave the remainder $\alpha$ when divided by 3 and $\beta$ when divided by 7 . Then $\left( \alpha ^ { 2 } + \beta ^ { 2 } \right)$ is equal to
(1) 20
(2) 13
(3) 5
(4) 10
Q65 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
If the coefficients of $x$ and $x ^ { 2 }$ in $( 1 + x ) ^ { p } ( 1 - x ) ^ { q }$ are 4 and $-5$ respectively, then $2p + 3q$ is equal to
(1) 60
(2) 69
(3) 66
(4) 63
Q66 Trigonometric equations in context View
Let $S = \left\{ x \in \left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right) : 9 ^ { 1 - \tan ^ { 2 } x } + 9 ^ { \tan ^ { 2 } x } = 10 \right\}$ and $\beta = \sum _ { x \in S } \tan ^ { 2 } \frac { x } { 3 }$, then $\frac { 1 } { 6 } ( \beta - 14 ) ^ { 2 }$ is equal to
(1) 16
(2) 8
(3) 64
(4) 32
Q67 Circles Circle-Related Locus Problems View
Let $A$ be the point $(1, 2)$ and $B$ be any point on the curve $x ^ { 2 } + y ^ { 2 } = 16$. If the centre of the locus of the point $P$, which divides the line segment $AB$ in the ratio $3 : 2$ is the point $C( \alpha , \beta )$, then the length of the line segment $AC$ is
(1) $\frac { 3 \sqrt { 5 } } { 5 }$
(2) $\frac { 4 \sqrt { 5 } } { 5 }$
(3) $\frac { 2 \sqrt { 5 } } { 5 }$
(4) $\frac { 6 \sqrt { 5 } } { 5 }$
Q68 Conic sections Circle-Conic Interaction with Tangency or Intersection View
Let a circle of radius 4 be concentric to the ellipse $15 x ^ { 2 } + 19 y ^ { 2 } = 285$. Then the common tangents are inclined to the minor axis of the ellipse at the angle
(1) $\frac { \pi } { 3 }$
(2) $\frac { \pi } { 4 }$
(3) $\frac { \pi } { 6 }$
(4) $\frac { \pi } { 12 }$
Q69 Proof Proof of Equivalence or Logical Relationship Between Conditions View
The statement $\sim p \vee ( \sim p \wedge q )$ is equivalent to
(1) $\sim p \wedge q$
(2) $p \wedge q \wedge \sim p$
(3) $\sim p \wedge q \wedge q$
(4) $\sim p \vee q$
Q70 Measures of Location and Spread View
Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution
$X _ { i }$012345
$f _ { i }$$k + 2$$2k$$k ^ { 2 } - 1$$k ^ { 2 } - 1$$k ^ { 2 } + 1$$k - 3$

where $\Sigma f _ { i } = 62$. If $\lfloor x \rfloor$ denotes the greatest integer $\leq x$, then $\lfloor \mu ^ { 2 } + \sigma ^ { 2 } \rfloor$ is equal to
(1) 9
(2) 8
(3) 7
(4) 6
Q71 Permutations & Arrangements Counting Functions with Constraints View
Let $A = \{2, 3, 4\}$ and $B = \{8, 9, 12\}$. Then the number of elements in the relation $R = \{ ( ( a _ { 1 } , b _ { 1 } ) , ( a _ { 2 } , b _ { 2 } ) ) \in ( A \times B ) \times ( A \times B ) : a _ { 1 }$ divides $b _ { 2 }$ and $a _ { 2 }$ divides $b _ { 1 } \}$ is
(1) 36
(2) 24
(3) 18
(4) 12
Q72 Matrices Determinant and Rank Computation View
If $A = \frac { 1 } { 5! \cdot 6! \cdot 7! } \begin{vmatrix} 5! & 6! & 7! \\ 6! & 7! & 8! \\ 7! & 8! & 9! \end{vmatrix}$, then $|\text{adj}(\text{adj}(2A))|$ is equal to
(1) $2 ^ { 20 }$
(2) $2 ^ { 8 }$
(3) $2 ^ { 12 }$
(4) $2 ^ { 16 }$
Q73 Applied differentiation Convexity and inflection point analysis View
Let $g(x) = f(x) + f(1 - x)$ and $f ^ { \prime \prime } (x) > 0 , x \in (0,1)$. If $g$ is decreasing in the interval $(0 , \alpha)$ and increasing in the interval $(\alpha , 1)$, then $\tan ^ { - 1 } (2\alpha) + \tan ^ { - 1 } \left( \frac { 1 } { \alpha } \right) + \tan ^ { - 1 } \left( \frac { \alpha + 1 } { \alpha } \right)$ is equal to
(1) $\pi$
(2) $\frac { 5\pi } { 4 }$
(3) $\frac { 3\pi } { 4 }$
(4) $\frac { 3\pi } { 2 }$
Q74 Integration by Parts Indefinite Integration by Parts View
For $\alpha , \beta , \gamma , \delta \in \mathbb { N }$, if $\int \left( \frac { x^2 e^x + e^{2x} } { x } \log _ { e } x \right) dx = \frac { 1 } { \alpha } \frac { x^{\beta} e^x } { 1 } - \frac { 1 } { \gamma } \frac { e ^ { \delta x } } { x } + C$, where $e = \sum _ { n = 0 } ^ { \infty } \frac { 1 } { n ! }$ and $C$ is constant of integration, then $\alpha + 2\beta + 3\gamma - 4\delta$ is equal to
(1) 1
(2) 4
(3) $-4$
(4) $-8$
Q75 Indefinite & Definite Integrals Finding a Function from an Integral Equation View
Let f be a continuous function satisfying $\int _ { 0 } ^ { t ^ { 2 } } \left( f(x) + x^2 \right) dx = \frac { 4 } { 3 } t ^ { 3 } , \forall t > 0$. Then $f\left( \frac { \pi ^ { 2 } } { 4 } \right)$ is equal to
(1) $\pi ^ { 2 } \left( 1 - \frac { \pi ^ { 2 } } { 16 } \right)$
(2) $- \pi \left( 1 + \frac { \pi ^ { 3 } } { 16 } \right)$
(3) $\pi \left( 1 - \frac { \pi ^ { 3 } } { 16 } \right)$
(4) $- \pi ^ { 2 } \left( 1 + \frac { \pi ^ { 2 } } { 16 } \right)$