jee-main

Papers (191)
2026
session1_21jan_shift1 13 session1_21jan_shift2 9 session1_22jan_shift1 16 session1_22jan_shift2 10 session1_23jan_shift1 11 session1_23jan_shift2 7 session1_24jan_shift1 14 session1_24jan_shift2 10 session1_28jan_shift1 10 session1_28jan_shift2 9
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 session2_02apr_shift1 31 session2_02apr_shift2 36 session2_03apr_shift1 35 session2_03apr_shift2 35 session2_04apr_shift1 37 session2_04apr_shift2 33 session2_07apr_shift1 32 session2_07apr_shift2 32 session2_08apr_shift1 36 session2_08apr_shift2 35
2024
session1_01feb_shift1 5 session1_01feb_shift2 21 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 28 session1_29jan_shift2 29 session1_30jan_shift1 20 session1_30jan_shift2 29 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 5 session2_04apr_shift2 28 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 21 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 29 session2_09apr_shift1 8 session2_09apr_shift2 30
2023
session1_01feb_shift1 28 session1_01feb_shift2 3 session1_24jan_shift1 11 session1_24jan_shift2 11 session1_25jan_shift1 29 session1_25jan_shift2 29 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 5 session1_30jan_shift2 27 session1_31jan_shift1 28 session1_31jan_shift2 15 session2_06apr_shift1 5 session2_06apr_shift2 16 session2_08apr_shift1 29 session2_08apr_shift2 13 session2_10apr_shift1 29 session2_10apr_shift2 16 session2_11apr_shift1 6 session2_11apr_shift2 8 session2_12apr_shift1 26 session2_13apr_shift1 24 session2_13apr_shift2 24 session2_15apr_shift1 19
2022
session1_24jun_shift1 19 session1_24jun_shift2 25 session1_25jun_shift1 14 session1_25jun_shift2 14 session1_26jun_shift1 29 session1_26jun_shift2 24 session1_27jun_shift1 4 session1_27jun_shift2 29 session1_28jun_shift1 13 session1_29jun_shift1 20 session1_29jun_shift2 4 session2_25jul_shift1 29 session2_25jul_shift2 20 session2_26jul_shift1 29 session2_26jul_shift2 23 session2_27jul_shift1 28 session2_27jul_shift2 29 session2_28jul_shift1 11 session2_28jul_shift2 29 session2_29jul_shift1 17 session2_29jul_shift2 18
2021
session1_24feb_shift1 9 session1_24feb_shift2 4 session1_25feb_shift1 29 session1_25feb_shift2 29 session1_26feb_shift2 15 session2_16mar_shift1 29 session2_16mar_shift2 18 session2_17mar_shift1 21 session2_17mar_shift2 27 session2_18mar_shift1 18 session2_18mar_shift2 9 session3_20jul_shift1 29 session3_20jul_shift2 29 session3_22jul_shift1 9 session3_25jul_shift1 8 session3_25jul_shift2 14 session3_27jul_shift1 4 session3_27jul_shift2 7 session4_01sep_shift2 14 session4_26aug_shift1 5 session4_26aug_shift2 2 session4_27aug_shift1 3 session4_27aug_shift2 29 session4_31aug_shift1 28 session4_31aug_shift2 4
2020
session1_07jan_shift1 28 session1_07jan_shift2 20 session1_08jan_shift1 5 session1_08jan_shift2 11 session1_09jan_shift1 26 session1_09jan_shift2 16 session2_02sep_shift1 18 session2_02sep_shift2 16 session2_03sep_shift1 23 session2_03sep_shift2 8 session2_04sep_shift1 14 session2_04sep_shift2 27 session2_05sep_shift1 22 session2_05sep_shift2 29 session2_06sep_shift1 11 session2_06sep_shift2 10
2019
session1_09jan_shift1 6 session1_09jan_shift2 29 session1_10jan_shift1 29 session1_10jan_shift2 14 session1_11jan_shift1 6 session1_11jan_shift2 5 session1_12jan_shift1 10 session1_12jan_shift2 29 session2_08apr_shift1 29 session2_08apr_shift2 29 session2_09apr_shift1 29 session2_09apr_shift2 29 session2_10apr_shift1 2 session2_10apr_shift2 5 session2_12apr_shift1 3 session2_12apr_shift2 9
2018
08apr 30 15apr 28 15apr_shift1 28 15apr_shift2 6 16apr 19
2017
02apr 30 08apr 30 09apr 34
2016
03apr 28 09apr 29 10apr 30
2015
04apr 29 10apr 29 11apr 8
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
2013
07apr 29 09apr 12 22apr 5 23apr 14 25apr 13
2012
07may 17 12may 21 19may 14 26may 17 offline 30
2011
jee-main_2011.pdf 18
2010
jee-main_2010.pdf 6
2009
jee-main_2009.pdf 2
2008
jee-main_2008.pdf 4
2007
jee-main_2007.pdf 38
2006
jee-main_2006.pdf 15
2005
jee-main_2005.pdf 25
2004
jee-main_2004.pdf 22
2003
jee-main_2003.pdf 8
2002
jee-main_2002.pdf 12
2020 session2_06sep_shift2

10 maths questions

Q51 Roots of polynomials Finding roots or coefficients of a quadratic using Vieta's relations View
If $\alpha$ and $\beta$ are the roots of the equation $2\mathrm{x}(2\mathrm{x}+1)=1$, then $\beta$ is equal to:
(1) $2\alpha(\alpha+1)$
(2) $-2\alpha(\alpha+1)$
(3) $2\alpha(\alpha-1)$
(4) $2\alpha^{2}$
Q52 Complex Numbers Arithmetic Systems of Equations via Real and Imaginary Part Matching View
Let $\mathrm{z}=\mathrm{x}+\mathrm{iy}$ be a non-zero complex number such that $\mathrm{z}^{2}=\mathrm{i}|\mathrm{z}|^{2}$, where $\mathrm{i}=\sqrt{-1}$, then z lies on the:
(1) line, $y=-x$
(2) imaginary axis
(3) line, $y=x$
(4) real axis
Q53 Arithmetic Sequences and Series Find Common Difference from Given Conditions View
The common difference of the A.P. $b_{1},b_{2},\ldots,b_{m}$ is 2 more than common difference of A.P. $\mathrm{a}_{1},\mathrm{a}_{2},\ldots,\mathrm{a}_{\mathrm{n}}$. If $\mathrm{a}_{40}=-159,\mathrm{a}_{100}=-399$ and $\mathrm{b}_{100}=\mathrm{a}_{70}$, then $\mathrm{b}_{1}$ is equal to:
(1) 81
(2) $-127$
(3) $-81$
(4) 127
Q54 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
If the constant term in the binomial expansion of $\left(\sqrt{\mathrm{x}}-\frac{\mathrm{k}}{\mathrm{x}^{2}}\right)^{10}$ is 405, then $|\mathrm{k}|$ equals:
(1) 9
(2) 1
(3) 3
(4) 2
Q55 Straight Lines & Coordinate Geometry Reflection and Image in a Line View
Let $L$ denote the line in the $xy$-plane with $x$ and $y$ intercepts as 3 and 1 respectively. Then the image of the point $(-1,-4)$ in the line is:
(1) $\left(\frac{11}{5},\frac{28}{5}\right)$
(2) $\left(\frac{29}{5},\frac{8}{5}\right)$
(3) $\left(\frac{8}{5},\frac{29}{5}\right)$
(4) $\left(\frac{29}{5},\frac{11}{5}\right)$
Q56 Circles Circle Equation Derivation View
The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^{2}$ at the point $(2,4)$ is
(1) $\left(\frac{-53}{10},\frac{16}{5}\right)$
(2) $\left(\frac{6}{5},\frac{53}{10}\right)$
(3) $\left(\frac{3}{10},\frac{16}{5}\right)$
(4) $\left(\frac{-16}{5},\frac{53}{10}\right)$
Q57 Conic sections Eccentricity or Asymptote Computation View
If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies:
(1) $\mathrm{e}^{4}+2\mathrm{e}^{2}-1=0$
(2) $\mathrm{e}^{2}+\mathrm{e}-1=0$
(3) $\mathrm{e}^{4}+\mathrm{e}^{2}-1=0$
(4) $\mathrm{e}^{2}+2\mathrm{e}-1=0$
Q58 Proof Direct Proof of a Stated Identity or Equality View
Consider the statement: ``For an integer n, if $\mathrm{n}^{3}-1$ is even, then n is odd''. The contrapositive statement of this statement is:
(1) For an integer n, if n is even, then $\mathrm{n}^{3}-1$ is odd.
(2) For an integer n, if $\mathrm{n}^{3}-1$ is not even, then n is not odd.
(3) For an integer n, if n is even, then $\mathrm{n}^{3}-1$ is even.
(4) For an integer n, if n is odd, then $\mathrm{n}^{3}-1$ is even.
Q59 Sine and Cosine Rules Heights and distances / angle of elevation problem View
The angle of elevation of the summit of a mountain from a point on the ground is $45^{\circ}$. After climbing up one km towards the summit at an inclination of $30^{\circ}$ from the ground, the angle of elevation of the summit is found to be $60^{\circ}$. Then the height (in km) of the summit from the ground is:
(1) $\frac{\sqrt{3}-1}{\sqrt{3}+1}$
(2) $\frac{\sqrt{3}+1}{\sqrt{3}-1}$
(3) $\frac{1}{\sqrt{3}-1}$
(4) $\frac{1}{\sqrt{3}+1}$
Q60 Matrices Determinant and Rank Computation View
Let $\theta=\frac{\pi}{5}$ and $A=\left[\begin{array}{cc}\cos\theta & \sin\theta\\-\sin\theta & \cos\theta\end{array}\right]$. If $B=A+A^{4}$, then $\det(B)$:
(1) is one
(2) lies in $(2,3)$
(3) is zero
(4) lies in $(1,2)$