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_08apr_shift2

14 maths questions

Q61 Solving quadratics and applications Counting solutions or configurations satisfying a quadratic system View
Let $m$ and $n$ be the numbers of real roots of the quadratic equations $x ^ { 2 } - 12 x + [ x ] + 31 = 0$ and $x ^ { 2 } - 5 | x + 2 | - 4 = 0$ respectively, where $[ x ]$ denotes the greatest integer $\leq x$. Then $m ^ { 2 } + m n + n ^ { 2 }$ is equal to
Q62 Complex numbers 2 Complex Function Evaluation and Algebraic Manipulation View
Let $A = \left\{ \theta \in ( 0,2 \pi ) : \frac { 1 + 2 i \sin \theta } { 1 - i \sin \theta } \right.$ is purely imaginary $\}$ Then the sum of the elements in $A$ is
(1) $4 \pi$
(2) $3 \pi$
(3) $\pi$
(4) $2 \pi$
Q63 Permutations & Arrangements Word Permutations with Repeated Letters View
If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which $C$ and $S$ do not come together, is $( 6 ! ) k$ then $k$ is equal to
(1) 2835
(2) 5670
(3) 1890
(4) 945
Q64 Sequences and Series Evaluation of a Finite or Infinite Sum View
Let $a _ { n }$ be $n ^ { \text {th} }$ term of the series $5 + 8 + 14 + 23 + 35 + 50 + \ldots\ldots$. and $S _ { n } = \sum _ { k = 1 } ^ { n } a _ { k }$. Then $S _ { 30 } - a _ { 40 }$ is equal to
(1) 11310
(2) 11260
(3) 11290
(4) 11280
Q65 Geometric Sequences and Series Arithmetic-Geometric Sequence Interplay View
Let $0 < z < y < x$ be three real numbers such that $\frac { 1 } { x } , \frac { 1 } { y } , \frac { 1 } { z }$ are in an arithmetic progression and $x , \sqrt{2} y , z$ are in a geometric progression. If $x y + y z + z x = \frac { 3 } { \sqrt { 2 } } x y z$, then $3 ( x + y + z ) ^ { 2 }$ is equal to
Q66 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
The absolute difference of the coefficients of $x ^ { 10 }$ and $x ^ { 7 }$ in the expansion of $\left( 2 x ^ { 2 } + \frac { 1 } { 2 x } \right) ^ { 11 }$ is equal to
(1) $13 ^ { 3 } - 13$
(2) $11 ^ { 3 } - 11$
(3) $10 ^ { 3 } - 10$
(4) $12 ^ { 3 } - 12$
Q67 Number Theory Congruence Reasoning and Parity Arguments View
$25 ^ { 190 } - 19 ^ { 190 } - 8 ^ { 190 } + 2 ^ { 190 }$ is divisible by
(1) neither 14 nor 34
(2) 14 but not by 34
(3) 34 but not by 14
(4) both 14 and 34
Q68 Addition & Double Angle Formulae Simplification of Trigonometric Expressions with Specific Angles View
The value of $36 \left( 4 \cos ^ { 2 } 9 ^ { \circ } - 1 \right) \left( 4 \cos ^ { 2 } 27 ^ { \circ } - 1 \right) \left( 4 \cos ^ { 2 } 81 ^ { \circ } - 1 \right) \left( 4 \cos ^ { 2 } 243 ^ { \circ } - 1 \right)$ is
(1) 54
(2) 18
(3) 27
(4) 36
Q69 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
Let $A ( 0,1 ) , B ( 1,1 )$ and $C ( 1,0 )$ be the mid-points of the sides of a triangle with incentre at the point $D$. If the focus of the parabola $y ^ { 2 } = 4 a x$ passing through $D$ is $( \alpha + \beta \sqrt { 2 } , 0 )$, where $\alpha$ and $\beta$ are rational numbers, then $\frac { \alpha } { \beta ^ { 2 } }$ is equal to
(1) 8
(2) 12
(3) 6
(4) $\frac { 9 } { 2 }$
Q70 Circles Inscribed/Circumscribed Circle Computations View
Let $O$ be the origin and $O P$ and $O Q$ be the tangents to the circle $x ^ { 2 } + y ^ { 2 } - 6 x + 4 y + 8 = 0$ at the points $P$ and $Q$ on it. If the circumcircle of the triangle $O P Q$ passes through the point $\left( \alpha , \frac { 1 } { 2 } \right)$, then a value of $\alpha$ is
(1) $\frac { 3 } { 2 }$
(2) $- \frac { 1 } { 2 }$
(3) $\frac { 5 } { 2 }$
(4) 1
Q71 Parametric curves and Cartesian conversion View
The ordinates of the points $P$ and $Q$ on the parabola with focus $( 3,0 )$ and directrix $x = - 3$ are in the ratio 3:1. If $R ( \alpha , \beta )$ is the point of intersection of the tangents to the parabola at $P$ and $Q$, then $\frac { \beta ^ { 2 } } { \alpha }$ is equal to
Q72 Applied differentiation Limit evaluation involving derivatives or asymptotic analysis View
If $\alpha > \beta > 0$ are the roots of the equation $a x ^ { 2 } + b x + 1 = 0$, and $\lim _ { x \rightarrow \frac { 1 } { \alpha } } \left( \frac { 1 - \cos \left( x ^ { 2 } + b x + a \right) } { 2 ( 1 - \alpha x ) ^ { 2 } } \right) ^ { \frac { 1 } { 2 } } = \frac { 1 } { k } \left( \frac { 1 } { \beta } - \frac { 1 } { \alpha } \right)$, then $k$ is equal to
(1) $2 \beta$
(2) $\alpha$
(3) $2 \alpha$
(4) $\beta$
Q73 Proof Proof of Equivalence or Logical Relationship Between Conditions View
The negation of $( p \wedge ( - q ) ) \vee ( - p )$ is equivalent to
(1) $p \wedge ( - q )$
(2) $p \wedge q$
(3) $p \vee ( q \vee ( - p ) )$
(4) $p \wedge ( q \wedge ( - p ) )$
Q74 Measures of Location and Spread View
Let the mean and variance of 12 observations be $\frac { 9 } { 2 }$ and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. Find the correct mean and variance.