jee-main

Papers (191)
2026
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2025
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2024
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2023
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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
2012 26may

17 maths questions

Q61 Discriminant and conditions for roots Determining quadratic function from given conditions View
If $a , b , c \in \mathrm { R }$ and 1 is a root of equation $a x ^ { 2 } + b x + c = 0$, then the curve $y = 4 a x ^ { 2 } + 3 b x + 2 c , a \neq 0$ intersect $x$-axis at
(1) two distinct points whose coordinates are always rational numbers
(2) no point
(3) exactly two distinct points
(4) exactly one point
Q62 Complex Numbers Arithmetic Modulus Computation View
$\left| z _ { 1 } + z _ { 2 } \right| ^ { 2 } + \left| z _ { 1 } - z _ { 2 } \right| ^ { 2 }$ is equal to
(1) $2 \left( \left| z _ { 1 } \right| + \left| z _ { 2 } \right| \right)$
(2) $2 \left( \left| z _ { 1 } \right| ^ { 2 } + \left| z _ { 2 } \right| ^ { 2 } \right)$
(3) $\left| z _ { 1 } \right| \left| z _ { 2 } \right|$
(4) $\left| z _ { 1 } \right| ^ { 2 } + \left| z _ { 2 } \right| ^ { 2 }$
Q63 Permutations & Arrangements Circular Arrangement View
If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is
(1) $6 ! 7 !$
(2) $( 6 ! ) ^ { 2 }$
(3) $( 7 ! ) ^ { 2 }$
(4) $7 !$
Q64 Arithmetic Sequences and Series Properties of AP Terms under Transformation View
If the A.M. between $p ^ { \text {th} }$ and $q ^ { \text {th} }$ terms of an A.P. is equal to the A.M. between $r ^ { \text {th} }$ and $s ^ { \text {th} }$ terms of the same A.P., then $p + q$ is equal to
(1) $r + s - 1$
(2) $r + s - 2$
(3) $r + s + 1$
(4) $r + s$
Q65 Arithmetic Sequences and Series Evaluation of a Finite or Infinite Sum View
If the sum of the series $1 ^ { 2 } + 2 \cdot 2 ^ { 2 } + 3 ^ { 2 } + 2 \cdot 4 ^ { 2 } + 5 ^ { 2 } + \ldots 2.6 ^ { 2 } + \ldots$ upto n terms, when n is even, is $\frac { n ( n + 1 ) ^ { 2 } } { 2 }$, then the sum of the series, when n is odd, is
(1) $n ^ { 2 } ( n + 1 )$
(2) $\frac { n ^ { 2 } ( n - 1 ) } { 2 }$
(3) $\frac { n ^ { 2 } ( n + 1 ) } { 2 }$
(4) $n ^ { 2 } ( n - 1 )$
Q66 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Product of Binomial/Polynomial Expressions View
The middle term in the expansion of $\left( 1 - \frac { 1 } { x } \right) ^ { n } \left( 1 - x ^ { n } \right)$ in powers of $x$ is
(1) ${ } ^ { 2 n } \mathrm { C } _ { n - 1 }$
(2) ${ } ^ { - 2 n } \mathrm { C } _ { n }$
(3) ${ } ^ { 2 n } \mathrm { C } _ { n - 1 }$
(4) ${ } ^ { 2 n } \mathrm { C } _ { n }$
Q67 Addition & Double Angle Formulae Simplification of Trigonometric Expressions with Specific Angles View
The value of $\cos 255 ^ { \circ } + \sin 195 ^ { \circ }$ is
(1) $\frac { \sqrt { 3 } - 1 } { 2 \sqrt { 2 } }$
(2) $\frac { \sqrt { 3 } - 1 } { \sqrt { 2 } }$
(3) $- \frac { \sqrt { 3 } - 1 } { \sqrt { 2 } }$
(4) $\frac { \sqrt { 3 } + 1 } { \sqrt { 2 } }$
Q68 Straight Lines & Coordinate Geometry Collinearity and Concurrency View
The line parallel to $x$-axis and passing through the point of intersection of lines $a x + 2 b y + 3 b = 0$ and $b x - 2 a y - 3 a = 0$, where $( a , b ) \neq ( 0,0 )$ is
(1) above $x$-axis at a distance $2/3$ from it
(2) above $x$-axis at a distance $3/2$ from it
(3) below $x$-axis at a distance $3/2$ from it
(4) below $x$-axis at a distance $2/3$ from it
Q69 Straight Lines & Coordinate Geometry Slope and Angle Between Lines View
Consider the straight lines $$\begin{aligned} & L _ { 1 } : x - y = 1 \\ & L _ { 2 } : x + y = 1 \\ & L _ { 3 } : 2 x + 2 y = 5 \\ & L _ { 4 } : 2 x - 2 y = 7 \end{aligned}$$ The correct statement is
(1) $L _ { 1 } \left\| L _ { 4 } , L _ { 2 } \right\| L _ { 3 } , L _ { 1 }$ intersect $L _ { 4 }$.
(2) $L _ { 1 } \perp L _ { 2 } , L _ { 1 } \| L _ { 3 } , L _ { 1 }$ intersect $L _ { 2 }$.
(3) $L _ { 1 } \perp L _ { 2 } , L _ { 2 } \| L _ { 3 } , L _ { 1 }$ intersect $L _ { 4 }$.
(4) $L _ { 1 } \perp L _ { 2 } , L _ { 1 } \perp L _ { 3 } , L _ { 2 }$ intersect $L _ { 4 }$.
Q70 Circles Tangent Lines and Tangent Lengths View
The number of common tangents of the circles given by $x ^ { 2 } + y ^ { 2 } - 8 x - 2 y + 1 = 0$ and $x ^ { 2 } + y ^ { 2 } + 6 x + 8 y = 0$ is
(1) one
(2) four
(3) two
(4) three
Q71 Trig Graphs & Exact Values Chord Properties and Midpoint Problems View
The chord $PQ$ of the parabola $y ^ { 2 } = x$, where one end $P$ of the chord is at point $( 4 , - 2 )$, is perpendicular to the axis of the parabola. Then the slope of the normal at $Q$ is
(1) $-4$
(2) $- \frac { 1 } { 4 }$
(3) $4$
(4) $\frac { 1 } { 4 }$
Q72 Circles Circle-Conic Interaction with Tangency or Intersection View
The normal at $\left( 2 , \frac { 3 } { 2 } \right)$ to the ellipse, $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 3 } = 1$ touches a parabola, whose equation is
(1) $y ^ { 2 } = - 104 x$
(2) $y ^ { 2 } = 14 x$
(3) $y ^ { 2 } = 26 x$
(4) $y ^ { 2 } = - 14 x$
Q73 Chain Rule Limit Evaluation Involving Composition or Substitution View
$\lim _ { x \rightarrow 0 } \frac { \sin \left( \pi \cos ^ { 2 } x \right) } { x ^ { 2 } }$ equals
(1) $- \pi$
(2) $1$
(3) $-1$
(4) $\pi$
Q75 Measures of Location and Spread View
Statement 1: The variance of first $n$ odd natural numbers is $\frac { n ^ { 2 } - 1 } { 3 }$ Statement 2: The sum of first $n$ odd natural numbers is $n ^ { 2 }$ and the sum of squares of first $n$ odd natural numbers is $\frac { n \left( 4 n ^ { 2 } + 1 \right) } { 3 }$.
(1) Statement 1 is true, Statement 2 is false.
(2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
(3) Statement 1 is false, Statement 2 is true.
(4) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
Q76 Matrices Matrix Algebra and Product Properties View
If $A = \left[ \begin{array} { c c c } 1 & 0 & 0 \\ 2 & 1 & 0 \\ -3 & 2 & 1 \end{array} \right]$ and $B = \left[ \begin{array} { c c c } 1 & 0 & 0 \\ -2 & 1 & 0 \\ 7 & -2 & 1 \end{array} \right]$ then $AB$ equals
(1) $I$
(2) $A$
(3) $B$
(4) $0$
Q77 Matrices Linear System and Inverse Existence View
Statement 1: If the system of equations $x + k y + 3 z = 0, 3 x + k y - 2 z = 0, 2 x + 3 y - 4 z = 0$ has a nontrivial solution, then the value of $k$ is $\frac { 31 } { 2 }$. Statement 2: A system of three homogeneous equations in three variables has a non trivial solution if the determinant of the coefficient matrix is zero.
(1) Statement 1 is false, Statement 2 is true.
(2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
(3) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
(4) Statement 1 is true, Statement 2 is false.
Q78 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification View
Let $A$ and $B$ be non empty sets in $\mathbb{R}$ and $f : A \rightarrow B$ is a bijective function. Statement 1: $f$ is an onto function. Statement 2: There exists a function $g : B \rightarrow A$ such that $f \circ g = I _ { B }$.
(1) Statement 1 is true, Statement 2 is false.
(2) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
(3) Statement 1 is false, Statement 2 is true.
(4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.