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
2020 session2_02sep_shift2

17 maths questions

Q51 Solving quadratics and applications Determining quadratic function from given conditions View
Let $f ( x )$ be a quadratic polynomial such that $f ( - 1 ) + f ( 2 ) = 0$. If one of the roots of $f ( x ) = 0$ is 3 , then its other root lies in
(1) $( - 1,0 )$
(2) $( 1,3 )$
(3) $( - 3 , - 1 )$
(4) $( 0,1 )$
Q52 Complex Numbers Arithmetic Identifying Real/Imaginary Parts or Components View
The imaginary part of $( 3 + 2 \sqrt { - 54 } ) ^ { \frac { 1 } { 2 } } - ( 3 - 2 \sqrt { - 54 } ) ^ { \frac { 1 } { 2 } }$, can be
(1) $- \sqrt { 6 }$
(2) $- 2 \sqrt { 6 }$
(3) 6
(4) $\sqrt { 6 }$
Q53 Combinations & Selection Geometric Combinatorics View
Let $n > 2$ be an integer. Suppose that there are $n$ Metro stations in a city located around a circular path. Each pair of the nearest stations is connected by a straight track only. Further, each pair of the nearest station is connected by blue line, whereas all remaining pairs of stations are connected by red line. If number of red lines is 99 times the number of blue lines, then the value of $n$ is
(1) 201
(2) 200
(3) 101
(4) 199
Q54 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
If the sum of first 11 terms of an A.P. , $a _ { 1 } , a _ { 2 } , a _ { 3 } \ldots\ldots$ is $0 \left( a _ { 1 } \neq 0 \right)$ then the sum of the A.P $a _ { 1 } , a _ { 3 } , a _ { 5 } , \ldots\ldots a _ { 23 }$ is $k a _ { 1 }$ where $k$ is equal to
(1) $- \frac { 121 } { 10 }$
(2) $\frac { 121 } { 10 }$
(3) $\frac { 72 } { 5 }$
(4) $- \frac { 72 } { 5 }$
Q55 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
Let $S$ be the sum of the first 9 term of the series : $\{ x + k a \} + \left\{ x ^ { 2 } + ( k + 2 ) a \right\} + \left\{ x ^ { 3 } + ( k + 4 ) a \right\} + \left\{ x ^ { 4 } + ( k + 6 ) a \right\} + \ldots$ where $a \neq 0$ and $x \neq 1$. If $S = \frac { x ^ { 10 } - x + 45 a ( x - 1 ) } { x - 1 }$, then $k$ is equal to
(1) - 5
(2) 1
(3) - 3
(4) 3
Q56 Quadratic trigonometric equations View
If the equation $\cos ^ { 4 } \theta + \sin ^ { 4 } \theta + \lambda = 0$ has real solutions for $\theta$ then $\lambda$ lies in interval
(1) $\left( - \frac { 5 } { 4 } , - 1 \right)$
(2) $\left[ - 1 , - \frac { 1 } { 2 } \right]$
(3) $\left( - \frac { 1 } { 2 } , - \frac { 1 } { 4 } \right]$
(4) $\left[ - \frac { 3 } { 2 } , - \frac { 5 } { 4 } \right]$
Q57 Standard trigonometric equations Solve trigonometric inequality View
The set of all possible values of $\theta$ in the interval $( 0 , \pi )$ for which the points $( 1,2 )$ and $( \sin \theta , \cos \theta )$ lie on the same side of the line $x + y = 1$ is?
(1) $\left( 0 , \frac { \pi } { 2 } \right)$
(2) $\left( \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } \right)$
(3) $\left( 0 , \frac { 3 \pi } { 4 } \right)$
(4) $\left( 0 , \frac { \pi } { 4 } \right)$
Q58 Areas by integration View
The area (in sq. units) of an equilateral triangle inscribed in the parabola $y ^ { 2 } = 8 x$, with one of its vertices on the vertex of this parabola is
(1) $64 \sqrt { 3 }$
(2) $256 \sqrt { 3 }$
(3) $192 \sqrt { 3 }$
(4) $128 \sqrt { 3 }$
Q59 Conic sections Eccentricity or Asymptote Computation View
For some $\theta \in \left( 0 , \frac { \pi } { 2 } \right)$, if the eccentricity of the hyperbola, $x ^ { 2 } - y ^ { 2 } \sec ^ { 2 } \theta = 10$ is $\sqrt { 5 }$ times the eccentricity of the ellipse, $x ^ { 2 } \sec ^ { 2 } \theta + y ^ { 2 } = 5$, then the length of the latus rectum of the ellipse, is
(1) $2 \sqrt { 6 }$
(2) $\sqrt { 30 }$
(3) $\frac { 2 \sqrt { 5 } } { 3 }$
(4) $\frac { 4 \sqrt { 5 } } { 3 }$
Q60 Differentiation from First Principles View
$\lim _ { x \rightarrow 0 } \left( \tan \left( \frac { \pi } { 4 } + x \right) \right) ^ { 1 / x }$ is equal to
(1) $e$
(2) 2
(3) 1
(4) $e ^ { 2 }$
Q61 Proof True/False Justification View
Which of the following is a tautology?
(1) $( \sim p ) \wedge ( p \vee q ) \rightarrow q$
(2) $( q \rightarrow p ) \vee \sim ( p \rightarrow q )$
(3) $( \sim q ) \vee ( p \wedge q ) \rightarrow q$
(4) $( p \rightarrow q ) \wedge ( q \rightarrow p )$
Q62 Matrices Linear System and Inverse Existence View
Let $A = \left\{ X = ( x , y , z ) ^ { T } : P X = 0 \text{ and } x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1 \right\}$ where $P = \left[ \begin{array} { c c c } 1 & 2 & 1 \\ - 2 & 3 & - 4 \\ 1 & 9 & - 1 \end{array} \right]$ then the set $A$
(1) Is a singleton.
(2) Is an empty set.
(3) Contains more than two elements
(4) Contains exactly two elements
Q63 3x3 Matrices Matrix Algebraic Properties and Abstract Reasoning View
Let $a , b , c \in R$ be all non-zero and satisfies $a ^ { 3 } + b ^ { 3 } + c ^ { 3 } = 2$. If the matrix $A = \left[ \begin{array} { c c c } a & b & c \\ b & c & a \\ c & a & b \end{array} \right]$ satisfies $A ^ { T } A = I$, then a value of $a b c$ can be
(1) $- \frac { 1 } { 3 }$
(2) $\frac { 1 } { 3 }$
(3) 3
(4) $\frac { 2 } { 3 }$
Q64 Sequences and Series Recurrence Relations and Sequence Properties View
Let $f : R \rightarrow R$ be a function which satisfies $f ( x + y ) = f ( x ) + f ( y ) , \forall x , y \in R$. If $f ( 1 ) = 2$ and $g ( n ) = \sum _ { k = 1 } ^ { ( n - 1 ) } f ( k ) , n \in N$ then the value of $n$, for which $g ( n ) = 20$, is
(1) 5
(2) 20
(3) 4
(4) 9
Q65 Tangents, normals and gradients Normal or perpendicular line problems View
The equation of the normal to the curve $y = ( 1 + x ) ^ { 2 y } + \cos ^ { 2 } \left( \sin ^ { - 1 } x \right)$, at $x = 0$ is
(1) $y + 4 x = 2$
(2) $y = 4 x + 2$
(3) $x + 4 y = 8$
(4) $2 y + x = 4$
Q66 Applied differentiation Full function study (variation table, limits, asymptotes) View
Let $f : ( - 1 , \infty ) \rightarrow R$ be defined by $f ( 0 ) = 1$ and $f ( x ) = \frac { 1 } { x } \log _ { e } ( 1 + x ) , x \neq 0$. Then the function $f$
(1) Decreases in $( - 1,0 )$ and increases in $( 0 , \infty )$
(2) Increases in $( - 1 , \infty )$
(3) Increases in $( - 1,0 )$ and decreases in $( 0 , \infty )$
(4) Decreases in $( - 1 , \infty )$
Q67 Areas Between Curves Find Parameter Given Area Condition View
Consider a region $R = \left\{ ( x , y ) \in R ^ { 2 } : x ^ { 2 } \leq y \leq 2 x \right\}$. If a line $y = \alpha$ divides the area of region $R$ into two equal parts, then which of the following is true?
(1) $\alpha ^ { 3 } - 6 \alpha ^ { 2 } + 16 = 0$
(2) $3 \alpha ^ { 2 } - 8 \alpha ^ { 3 / 2 } + 8 = 0$
(3) $3 \alpha ^ { 2 } - 8 \alpha + 8 = 0$
(4) $\alpha ^ { 3 } - 6 \alpha ^ { 3/2 } + 16 = 0$