jee-main

Papers (169)
2025
session1_22jan_shift1 25 session1_22jan_shift2 25 session1_23jan_shift1 25 session1_23jan_shift2 25 session1_24jan_shift1 25 session1_24jan_shift2 25 session1_28jan_shift1 25 session1_28jan_shift2 25 session1_29jan_shift1 29 session1_29jan_shift2 25
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
2020 session1_08jan_shift2

12 maths questions

Q21 Constant acceleration (SUVAT) Free-fall and vertical drop View
A ball is dropped from the top of a 100 m high tower on a planet. In the last $\frac{1}{2}\,\mathrm{s}$ before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in $\mathrm{m\,s^{-2}}$) near the surface on that planet is $\underline{\hspace{1cm}}$
Q51 Inequalities Absolute Value Inequality View
Let $S$ be the set of all real roots of the equation, $3^{x}\left(3^{x} - 1\right) + 2 = \left|3^{x} - 1\right| + \left|3^{x} - 2\right|$, then
(1) contains exactly two elements.
(2) is a singleton.
(3) is an empty set.
(4) contains at least four elements.
Q52 Complex Numbers Arithmetic Roots of Unity and Cyclotomic Expressions View
Let $\alpha = \frac{-1 + i\sqrt{3}}{2}$. If $a = (1 + \alpha)\sum_{k=0}^{100}\alpha^{2k}$ and $b = \sum_{k=0}^{100}\alpha^{3k}$, then $a$ and $b$ are the roots of the quadratic equation.
(1) $x^{2} + 101x + 100 = 0$
(2) $x^{2} - 102x + 101 = 0$
(3) $x^{2} - 101x + 100 = 0$
(4) $x^{2} + 102x + 101 = 0$
Q53 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
If the $10^{\text{th}}$ term of an A.P. is $\frac{1}{20}$, and its $20^{\text{th}}$ term is $\frac{1}{10}$, then the sum of its first 200 terms is.
(1) 50
(2) $50\frac{1}{4}$
(3) 100
(4) $100\frac{1}{2}$
Q54 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
If $\alpha$ and $\beta$ be the coefficients of $x^{4}$ and $x^{2}$, respectively in the expansion of $\left(x + \sqrt{x^{2} - 1}\right)^{6} + \left(x - \sqrt{x^{2} - 1}\right)^{6}$, then
(1) $\alpha + \beta = 60$
(2) $\alpha + \beta = -30$
(3) $\alpha - \beta = 60$
(4) $\alpha - \beta = -132$
Q55 Circles Tangent Lines and Tangent Lengths View
If a line $y = mx + c$ is a tangent to the circle $(x - 3)^{2} + y^{2} = 1$, and it is perpendicular to a line $L_{1}$, where $L_{1}$ is the tangent to the circle $x^{2} + y^{2} = 1$ at the point $\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$, then
(1) $c^{2} - 7c + 6 = 0$
(2) $c^{2} + 7c + 6 = 0$
(3) $c^{2} + 6c + 7 = 0$
(4) $c^{2} - 6c + 7 = 0$
Q56 Conic sections Tangent and Normal Line Problems View
If a hyperbola passes through the point $P(10, 16)$, and it has vertices at $(\pm 6, 0)$, then the equation of the normal to it at $P$ is.
(1) $3x + 4y = 94$
(2) $2x + 5y = 100$
(3) $x + 2y = 42$
(4) $x + 3y = 58$
Q57 Proof True/False Justification View
Which of the following statement is a tautology?
(1) $p \vee (\sim q) \rightarrow p \wedge q$
(2) $\sim(p \wedge \sim q) \rightarrow p \vee q$
(3) $\sim(p \vee \sim q) \rightarrow p \wedge q$
(4) $\sim(p \vee \sim q) \rightarrow p \vee q$
Q58 Measures of Location and Spread View
The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11, then the correct variance is
(1) 3.99
(2) 4.01
(3) 4.02
(4) 3.98
Q59 Matrices Linear System and Inverse Existence View
If $A = \begin{pmatrix} 2 & 2 \\ 9 & 4 \end{pmatrix}$ and $I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$, then $10A^{-1}$ is equal to.
(1) $A - 4I$
(2) $6I - A$
(3) $A - 6I$
(4) $4I - A$
Q60 3x3 Matrices Linear System Existence and Uniqueness via Determinant View
The system of linear equations $\lambda x + 2y + 2z = 5$ $2\lambda x + 3y + 5z = 8$ $4x + \lambda y + 6z = 10$ has
(1) no solution when $\lambda = 8$
(2) a unique solution when $\lambda = -8$
(3) no solution when $\lambda = 2$
(4) infinitely many solutions when $\lambda = 2$
Q61 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
Let $f:(1,3) \rightarrow R$ be a function defined by $f(x) = \frac{x[x]}{1 + x^{2}}$, where $[x]$ denotes the greatest integer $\leq x$. Then the range of $f$ is
(1) $\left(\frac{2}{5}, \frac{3}{5}\right] \cup \left(\frac{3}{4}, \frac{4}{5}\right)$
(2) $\left(\frac{2}{5}, \frac{1}{2}\right) \cup \left(\frac{3}{5}, \frac{4}{5}\right]$
(3) $\left(\frac{2}{5}, \frac{4}{5}\right]$
(4) $\left(\frac{3}{5}, \frac{4}{5}\right)$