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
2021 session3_25jul_shift2

15 maths questions

Q61 Modulus function Counting solutions satisfying modulus conditions View
The number of real solutions of the equation, $x ^ { 2 } - | x | - 12 = 0$ is:
(1) 2
(2) 3
(3) 1
(4) 4
Q62 Binomial Theorem (positive integer n) Count Integral or Rational Terms in a Binomial Expansion View
The sum of all those terms which are rational numbers in the expansion of $\left( 2 ^ { \frac { 1 } { 3 } } + 3 ^ { \frac { 1 } { 4 } } \right) ^ { 12 }$ is:
(1) 89
(2) 27
(3) 35
(4) 43
Q63 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
If the greatest value of the term independent of $x$ in the expansion of $\left( x \sin \alpha + a \frac { \cos \alpha } { x } \right) ^ { 10 }$ is $\frac { 10 ! } { ( 5 ! ) ^ { 2 } }$, then the value of $a$ is equal to:
(1) - 1
(2) 1
(3) - 2
(4) 2
Q64 Binomial Theorem (positive integer n) Integer Part or Limit Involving Conjugate Surd Binomial Expansions View
The lowest integer which is greater than $\left( 1 + \frac { 1 } { 10 ^ { 100 } } \right) ^ { 10 ^ { 100 } }$ is
(1) 3
(2) 4
(3) 2
(4) 1
Q65 Permutations & Arrangements Factorial and Combinatorial Expression Simplification View
If ${ } ^ { n } P _ { r } = { } ^ { n } P _ { r + 1 }$ and ${ } ^ { n } C _ { r } = { } ^ { n } C _ { r - 1 }$, then the value of $r$ is equal to:
(1) 1
(2) 4
(3) 2
(4) 3
Q66 Addition & Double Angle Formulae Simplification of Trigonometric Expressions with Specific Angles View
The value of $\cot \frac { \pi } { 24 }$ is:
(1) $\sqrt { 2 } + \sqrt { 3 } + 2 - \sqrt { 6 }$
(2) $\sqrt { 2 } + \sqrt { 3 } + 2 + \sqrt { 6 }$
(3) $\sqrt { 2 } - \sqrt { 3 } - 2 + \sqrt { 6 }$
(4) $3 \sqrt { 2 } - \sqrt { 3 } - \sqrt { 6 }$
Q67 Quadratic trigonometric equations View
The number of distinct real roots of $\left| \begin{array} { c c c } \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \end{array} \right| = 0$ in the interval $- \frac { \pi } { 4 } \leq x \leq \frac { \pi } { 4 }$ is:
(1) 4
(2) 1
(3) 2
(4) 3
Q68 Straight Lines & Coordinate Geometry Slope and Angle Between Lines View
Let the equation of the pair of lines, $y = p x$ and $y = q x$, can be written as $( y - p x ) ( y - q x ) = 0$. Then the equation of the pair of the angle bisectors of the lines $x ^ { 2 } - 4 x y - 5 y ^ { 2 } = 0$ is:
(1) $x ^ { 2 } - 3 x y + y ^ { 2 } = 0$
(2) $x ^ { 2 } + 4 x y - y ^ { 2 } = 0$
(3) $x ^ { 2 } + 3 x y - y ^ { 2 } = 0$
(4) $x ^ { 2 } - 3 x y - y ^ { 2 } = 0$
Q69 Conic sections Circle-Conic Interaction with Tangency or Intersection View
If a tangent to the ellipse $x ^ { 2 } + 4 y ^ { 2 } = 4$ meets the tangents at the extremities of its major axis at $B$ and $C$, then the circle with $B C$ as diameter passes through the point.
(1) $( \sqrt { 3 } , 0 )$
(2) $( \sqrt { 2 } , 0 )$
(3) $( 1,1 )$
(4) $( - 1,1 )$
Q70 Proof True/False Justification View
Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following:
(1) The match will not be played and weather is not good and ground is wet.
(2) If the match will not be played, then either weather is not good or ground is wet.
(3) The match will be played and weather is not good or ground is wet.
(4) The match will not be played or weather is good and ground is not wet.
Q71 Measures of Location and Spread View
The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation $\sqrt { 13.44 }$, then the standard deviation of the second sample is:
(1) 8
(2) 6
(3) 4
(4) 5
Q72 Matrices Matrix Power Computation and Application View
If $P = \left[ \begin{array} { c c } 1 & 0 \\ \frac { 1 } { 2 } & 1 \end{array} \right]$, then $P ^ { 50 }$ is:
(1) $\left[ \begin{array} { l l } 1 & 0 \\ 25 & 1 \end{array} \right]$
(2) $\left[ \begin{array} { l l } 1 & 50 \\ 0 & 1 \end{array} \right]$
(3) $\left[ \begin{array} { l l } 1 & 25 \\ 0 & 1 \end{array} \right]$
(4) $\left[ \begin{array} { l l } 1 & 0 \\ 50 & 1 \end{array} \right]$
Q73 Sequences and Series Evaluation of a Finite or Infinite Sum View
If $[ x ]$ be the greatest integer less than or equal to $x$, then $\sum _ { n = 8 } ^ { 100 } \left[ \frac { ( - 1 ) ^ { n } n } { 2 } \right]$ is equal to:
(1) 0
(2) 4
(3) - 2
(4) 2
Q74 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification View
Consider function $f : A \rightarrow B$ and $g : B \rightarrow C ( A , B , C \subseteq R )$ such that $( g o f ) ^ { - 1 }$ exists, then:
(1) $f$ and $g$ both are one-one
(2) $f$ and $g$ both are onto
(3) $f$ is one-one and $g$ is onto
(4) $f$ is onto and $g$ is one-one
Q75 Indefinite & Definite Integrals Properties of Integral-Defined Functions (Continuity, Differentiability) View
If $f ( x ) = \left\{ \begin{array} { l l } \int _ { 0 } ^ { x } ( 5 + | 1 - t | ) d t , & x > 2 \\ 5 x + 1 , & x \leq 2 \end{array} \right.$, then
(1) $f ( x )$ is not continuous at $x = 2$
(2) $f ( x )$ is everywhere differentiable
(3) $f ( x )$ is continuous but not differentiable at $x = 2$
(4) $f ( x )$ is not differentiable at $x = 1$