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
2024 session1_30jan_shift1

17 maths questions

Q4 Work done and energy Conservation of energy on frictionless tracks and pendulums View
A particle is placed at the point A of a frictionless track ABC as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point $B$ is: (Take $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ ).
(1) $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $\sqrt { 10 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $2 \sqrt { 10 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
Q5 Impulse and momentum (advanced) View
A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m . The impulse of force imparted by the ground to the body is given by: (given $g = 9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ )
(1) $4.32 \mathrm {~kg} \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $43.2 \mathrm {~kg} \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $23.9 \mathrm {~kg} \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $2.39 \mathrm {~kg} \mathrm {~m} \mathrm {~s} ^ { - 1 }$
Q21 Constant acceleration (SUVAT) Distance in successive equal time intervals View
The displacement and the increase in the velocity of a moving particle in the time interval of $t$ to $( t + 1 )$ s are 125 m and $50 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, respectively. The distance travelled by the particle in $( t + 2 ) ^ { \text {th} } \mathrm { s }$ is $\_\_\_\_$ m.
Q61 Complex Numbers Argand & Loci Solving Complex Equations with Geometric Interpretation View
If $z = x + i y , x y \neq 0$, satisfies the equation $z ^ { 2 } + i \bar { z } = 0$, then $\left| z ^ { 2 } \right|$ is equal to:
(1) 9
(2) 1
(3) 4
(4) $\frac { 1 } { 4 }$
Q62 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
Let $S _ { a }$ denote the sum of first $n$ terms an arithmetic progression. If $S _ { 20 } = 790$ and $S _ { 10 } = 145$, then $S _ { 15 } - S _ { 5 }$ is
(1) 395
(2) 390
(3) 405
(4) 410
Q63 Trigonometric equations in context View
If $2 \sin ^ { 3 } x + \sin 2 x \cos x + 4 \sin x - 4 = 0$ has exactly 3 solutions in the interval $\left[ 0 , \frac { \mathrm { n } \pi } { 2 } \right] , \mathrm { n } \in \mathrm { N }$, then the roots of the equation $x ^ { 2 } + n x + ( n - 3 ) = 0$ belong to :
(1) $( 0 , \infty )$
(2) $( - \infty , 0 )$
(3) $\left( - \frac { \sqrt { 17 } } { 2 } , \frac { \sqrt { 17 } } { 2 } \right)$
(4) $Z$
Q64 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View
A line passing through the point $A ( 9,0 )$ makes an angle of $30 ^ { \circ }$ with the positive direction of $x$-axis. If this line is rotated about $A$ through an angle of $15 ^ { \circ }$ in the clockwise direction, then its equation in the new position is
(1) $\frac { y } { \sqrt { 3 } - 2 } + x = 9$
(2) $\frac { x } { \sqrt { 3 } - 2 } + y = 9$
(3) $\frac { x } { \sqrt { 3 } + 2 } + y = 9$
(4) $\frac { y } { \sqrt { 3 } + 2 } + x = 9$
Q65 Circles Intersection of Circles or Circle with Conic View
If the circles $( x + 1 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = r ^ { 2 }$ and $x ^ { 2 } + y ^ { 2 } - 4 x - 4 y + 4 = 0$ intersect at exactly two distinct points, then
(1) $5 < \mathrm { r } < 9$
(2) $0 < \mathrm { r } < 7$
(3) $3 < r < 7$
(4) $\frac { 1 } { 2 } < \mathrm { r } < 7$
Q66 Stationary points and optimisation Geometric or applied optimisation problem View
The maximum area of a triangle whose one vertex is at $( 0,0 )$ and the other two vertices lie on the curve $y = - 2 x ^ { 2 } + 54$ at points $( x , y )$ and $( - x , y )$ where $\mathrm { y } > 0$ is :
(1) 88
(2) 122
(3) 92
(4) 108
Q67 Conic sections Eccentricity or Asymptote Computation View
If the length of the minor axis of ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :
(1) $\frac { \sqrt { 5 } } { 3 }$
(2) $\frac { \sqrt { 3 } } { 2 }$
(3) $\frac { 1 } { \sqrt { 3 } }$
(4) $\frac { 2 } { \sqrt { 5 } }$
Q68 Indefinite & Definite Integrals Finding a Function from an Integral Equation View
Let $f : \left[ - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right] \rightarrow R$ be a differentiable function such that $f ( 0 ) = \frac { 1 } { 2 }$, If $\lim _ { x \rightarrow 0 } \frac { x \int _ { 0 } ^ { x } f ( t ) d t } { e ^ { x ^ { 2 } } - 1 } = \alpha$, then $8 \alpha ^ { 2 }$ is equal to :
(1) 16
(2) 2
(3) 1
(4) 4
Q69 Measures of Location and Spread View
Let $M$ denote the median of the following frequency distribution.
Class$0 - 4$$4 - 8$$8 - 12$$12 - 16$$16 - 20$
Frequency391086

Then 20 M is equal to :
(1) 416
(2) 104
(3) 52
(4) 208
Q70 3x3 Matrices Direct Determinant Computation View
$f ( x ) = \left| \begin{array} { c c c } 2 \cos ^ { 4 } x & 2 \sin ^ { 4 } x & 3 + \sin ^ { 2 } 2 x \\ 3 + 2 \cos ^ { 4 } x & 2 \sin ^ { 4 } x & \sin ^ { 2 } 2 x \\ 2 \cos ^ { 4 } x & 3 + 2 \sin ^ { 4 } x & \sin ^ { 2 } 2 x \end{array} \right|$ then $\frac { 1 } { 5 } f ^ { \prime } ( 0 )$ is equal to:
(1) 0
(2) 1
(3) 2
(4) 6
Q71 3x3 Matrices Linear System with Parameter — Infinite Solutions View
Consider the system of linear equation $x + y + z = 4 \mu , x + 2 y + 2 \lambda z = 10 \mu , x + 3 y + 4 \lambda ^ { 2 } z = \mu ^ { 2 } + 15$, where $\lambda , \mu \in \mathrm { R }$. Which one of the following statements is NOT correct?
(1) The system has unique solution if $\lambda \neq \frac { 1 } { 2 }$ and $\mu \neq 1$
(2) The system is inconsistent if $\lambda = \frac { 1 } { 2 }$ and $\mu \neq 1, 15$
(3) The system has infinite number of solutions if $\lambda = \frac { 1 } { 2 }$ and $\mu = 15$
(4) The system is consistent if $\lambda \neq \frac { 1 } { 2 }$
Q72 Composite & Inverse Functions Determine Domain or Range of a Composite Function View
If the domain of the function $f ( x ) = \cos ^ { - 1 } \left( \frac { 2 - | x | } { 4 } \right) + \left( \log _ { e } ( 3 - x ) \right) ^ { - 1 }$ is $[ - \alpha , \beta ) - \{ \gamma \}$, then $\alpha + \beta + \gamma$ is equal to :
(1) 12
(2) 9
(3) 11
(4) 8
Q73 Applied differentiation Convexity and inflection point analysis View
Let $g : R \rightarrow R$ be a non constant twice differentiable such that $g ^ { \prime } \left( \frac { 1 } { 2 } \right) = g ^ { \prime } \left( \frac { 3 } { 2 } \right)$. If a real valued function $f$ is defined as $f ( x ) = \frac { 1 } { 2 } [ g ( x ) + g ( 2 - x ) ]$, then
(1) $f ^ { \prime \prime } ( x ) = 0$ for atleast two $x$ in $( 0,2 )$
(2) $f ^ { \prime \prime } ( x ) = 0$ for exactly one $x$ in $( 0,1 )$
(3) $f ^ { \prime \prime } ( x ) = 0$ for no $x$ in $( 0,1 )$
(4) $f ^ { \prime } \left( \frac { 3 } { 2 } \right) + f ^ { \prime } \left( \frac { 1 } { 2 } \right) = 1$
Q74 Indefinite & Definite Integrals Definite Integral as a Limit of Riemann Sums View
The value of $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \frac { n ^ { 3 } } { \left( n ^ { 2 } + k ^ { 2 } \right) \left( n ^ { 2 } + 3 k ^ { 2 } \right) }$ is :
(1) $\frac { ( 2 \sqrt { 3 } + 3 ) \pi } { 24 }$
(2) $\frac { 13 \pi } { 8 ( 4 \sqrt { 3 } + 3 ) }$
(3) $\frac { 13 ( 2 \sqrt { 3 } - 3 ) \pi } { 8 }$
(4) $\frac { ( 2 \sqrt { 3 } - 3 ) \pi } { 24 }$