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
2021 session1_24feb_shift1

10 maths questions

Q61 Solving quadratics and applications Finding roots or coefficients of a quadratic using Vieta's relations View
Let $p$ and $q$ be two positive numbers such that $p + q = 2$ and $p ^ { 4 } + q ^ { 4 } = 272$. Then $p$ and $q$ are roots of the equation:
(1) $x ^ { 2 } - 2 x + 2 = 0$
(2) $x ^ { 2 } - 2 x + 8 = 0$
(3) $x ^ { 2 } - 2 x + 136 = 0$
(4) $x ^ { 2 } - 2 x + 16 = 0$
Q62 Combinations & Selection Selection with Group/Category Constraints View
A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, is:
(1) 1050
(2) 1625
(3) 575
(4) 560
Q63 Addition & Double Angle Formulae Trigonometric Equation Solving via Identities View
If $e ^ { \cos ^ { 2 } x + \cos ^ { 4 } x + \cos ^ { 6 } x + \ldots \infty \log _ { e } 2 }$ satisfies the equation $t ^ { 2 } - 9 t + 8 = 0$, then the value of $\frac { 2 \sin x } { \sin x + \sqrt { 3 } \cos x }$, where $0 < x < \frac { \pi } { 2 }$, is equal to
(1) $\frac { 3 } { 2 }$
(2) $\frac { 1 } { 2 }$
(3) $\sqrt { 3 }$
(4) $2 \sqrt { 3 }$
Q64 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View
A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $\frac { 1 } { 4 }$. Three stones $A , B$ and $C$ are placed at the points $1,1,2,2$ and $4,4$ respectively. Then which of these stones is / are on the path of the man?
(1) $C$ only
(2) All the three
(3) $B$ only
(4) $A$ only
Q65 Binomial Theorem (positive integer n) Evaluate a Summation Involving Binomial Coefficients View
The value of $-{ } ^ { 15 } C _ { 1 } + 2 \cdot { } ^ { 15 } C _ { 2 } - 3 \cdot { } ^ { 15 } C _ { 3 } + \ldots - 15 \cdot { } ^ { 15 } C _ { 15 } + { } ^ { 14 } C _ { 1 } + { } ^ { 14 } C _ { 3 } + { } ^ { 14 } C _ { 5 } + \ldots + { } ^ { 14 } C _ { 11 }$ is equal to
(1) $2 ^ { 14 }$
(2) $2 ^ { 13 } - 13$
(3) $2 ^ { 16 } - 1$
(4) $2 ^ { 13 } - 14$
Q66 Conic sections Locus and Trajectory Derivation View
The locus of the mid-point of the line segment joining the focus of the parabola $y ^ { 2 } = 4 a x$ to a moving point of the parabola, is another parabola whose directrix is:
(1) $x = a$
(2) $x = 0$
(3) $x = - \frac { a } { 2 }$
(4) $x = \frac { a } { 2 }$
Q67 Proof True/False Justification View
The statement among the following that is a tautology is:
(1) $A \vee A \wedge B$
(2) $A \wedge A \vee B$
(3) $B \rightarrow A \wedge A \rightarrow B$
(4) $A \wedge A \rightarrow B \rightarrow B$
Q68 Sine and Cosine Rules Heights and distances / angle of elevation problem View
Two vertical poles are 150 m apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is:
(1) 25
(2) 30
(3) $20 \sqrt { 3 }$
(4) $25 \sqrt { 3 }$
Q69 Matrices Linear System and Inverse Existence View
The system of linear equations $3 x - 2 y - k z = 10$ $2 x - 4 y - 2 z = 6$ $x + 2 y - z = 5 m$ is inconsistent if:
(1) $k = 3 , \quad m \neq \frac { 4 } { 5 }$
(2) $k = 3 , \quad m = \frac { 4 } { 5 }$
(3) $k \neq 3 , \quad m \in R$
(4) $k \neq 3 , \quad m \neq \frac { 4 } { 5 }$
Q70 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification View
Let $f : R \rightarrow R$ be defined as $f(x) = 2x - 1$ and $g : R - \{1\} \rightarrow R$ be defined as $g(x) = \frac { x - \frac { 1 } { 2 } } { x - 1 }$. Then the composition function $f(g(x))$ is:
(1) neither one-one nor onto
(2) onto but not one-one
(3) both one-one and onto
(4) one-one but not onto