jee-main

Papers (169)
2025
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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_09jan_shift2

18 maths questions

Q51 Inequalities Set Operations Using Inequality-Defined Sets View
If $A = \{ x \in R : | x | < 2 \}$ and $B = \{ x \in R : | x - 2 | \geq 3 \}$; then
(1) $A \cap B = ( - 2 , - 1 )$
(2) $B - A = R - ( - 2,5 )$
(3) $A \cup B = R - ( 2,5 )$
(4) $A - B = [ - 1,2 )$
Q52 Solving quadratics and applications Finding roots or coefficients of a quadratic using Vieta's relations View
Let $a , b \in R , a \neq 0$ be such that the equation, $a x ^ { 2 } - 2 b x + 5 = 0$ has a repeated root $\alpha$, which is also a root of the equation, $x ^ { 2 } - 2 b x - 10 = 0$. If $\beta$ is the other root of this equation, then $\alpha ^ { 2 } + \beta ^ { 2 }$ is equal to:
(1) 25
(2) 26
(3) 28
(4) 24
Q53 Complex Numbers Argand & Loci Distance and Region Optimization on Loci View
If $z$ is a complex number satisfying $| \operatorname { Re } ( z ) | + | \operatorname { Im } ( z ) | = 4$, then $| z |$ cannot be
(1) $\sqrt { \frac { 17 } { 2 } }$
(2) $\sqrt { 10 }$
(3) $\sqrt { 7 }$
(4) $\sqrt { 8 }$
Q54 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
Let $a _ { n }$ be the $n ^ { \text {th } }$ term of a G.P. of positive terms. If $\sum _ { n = 1 } ^ { 100 } a _ { 2 n + 1 } = 200$ and $\sum _ { n = 1 } ^ { 100 } a _ { 2 n } = 100$, then $\sum _ { n = 1 } ^ { 200 } a _ { n }$ is equal to:
(1) 300
(2) 225
(3) 175
(4) 150
Q55 Geometric Sequences and Series Geometric Series with Trigonometric or Functional Terms View
If $x = \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \tan ^ { 2 } \theta$ and $y = \sum _ { n = 0 } ^ { \infty } \cos ^ { 2 n } \theta$, for $0 < \theta < \frac { \pi } { 4 }$, then:
(1) $x ( 1 + y ) = 1$
(2) $y ( 1 - x ) = 1$
(3) $y ( 1 + x ) = 1$
(4) $x ( 1 - y ) = 1$
Q56 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion View
In the expansion of $\left( \frac { x } { \cos \theta } + \frac { 1 } { x \sin \theta } \right) ^ { 16 }$, if $l _ { 1 }$ is the least value of the term independent of $x$ when $\frac { \pi } { 8 } \leq \theta \leq \frac { \pi } { 4 }$ and $l _ { 2 }$ is the least value of the term independent of $x$ when $\frac { \pi } { 16 } \leq \theta \leq \frac { \pi } { 8 }$, then the ratio $l _ { 2 } : l _ { 1 }$ is equal to:
(1) $1 : 8$
(2) $16 : 1$
(3) $8 : 1$
(4) $1 : 16$
Q57 Conic sections Focal Chord and Parabola Segment Relations View
If one end of a focal chord $AB$ of the parabola $y ^ { 2 } = 8 x$ is at $A \left( \frac { 1 } { 2 } , - 2 \right)$, then the equation of the tangent to it at $B$ is:
(1) $2 x + y - 24 = 0$
(2) $x - 2 y + 8 = 0$
(3) $x + 2 y + 8 = 0$
(4) $2 x - y - 24 = 0$
Q58 Conic sections Eccentricity or Asymptote Computation View
The length of the minor axis (along $y$-axis) of an ellipse in the standard form is $\frac { 4 } { \sqrt { 3 } }$. If this ellipse touches the line $x + 6 y = 8$ then its eccentricity is:
(1) $\frac { 1 } { 2 } \sqrt { \frac { 11 } { 3 } }$
(2) $\sqrt { \frac { 5 } { 6 } }$
(3) $\frac { 1 } { 2 } \sqrt { \frac { 5 } { 3 } }$
(4) $\frac { 1 } { 3 } \sqrt { \frac { 11 } { 3 } }$
Q59 Proof True/False Justification View
If $p \rightarrow ( p \wedge \sim q )$ is false, then the truth values of $p$ and $q$ are respectively
(1) $F , F$
(2) $T , F$
(3) $T , T$
(4) $F , T$
Q60 3x3 Matrices Linear System Existence and Uniqueness via Determinant View
The following system of linear equations $7 x + 6 y - 2 z = 0$ $3 x + 4 y + 2 z = 0$ $x - 2 y - 6 z = 0$, has
(1) infinitely many solutions, ( $x , y , z$ ) satisfying $y = 2z$
(2) no solution
(3) infinitely many solutions, $( x , y , z )$ satisfying $x = 2z$
(4) only the trivial solution
Q61 Matrices Determinant and Rank Computation View
Let $a - 2 b + c = 1$. If $f ( x ) = \left| \begin{array} { l l l } x + a & x + 2 & x + 1 \\ x + b & x + 3 & x + 2 \\ x + c & x + 4 & x + 3 \end{array} \right|$, then:
(1) $f ( - 50 ) = 501$
(2) $f ( - 50 ) = - 1$
(3) $f ( 50 ) = - 501$
(4) $f ( 50 ) = 1$
Q62 Curve Sketching Continuity and Discontinuity Analysis of Piecewise Functions View
Let $[ t ]$ denote the greatest integer $\leq t$ and $\lim _ { x \rightarrow 0 } x \left[ \frac { 4 } { x } \right] = A$. Then the function, $f ( x ) = \left[ x ^ { 2 } \right] \sin ( \pi x )$ is discontinuous, when $x$ is equal to:
(1) $\sqrt { A + 1 }$
(2) $\sqrt { A + 5 }$
(3) $\sqrt { A + 21 }$
(4) $\sqrt { A }$
Q63 Parametric differentiation View
If $x = 2 \sin \theta - \sin 2 \theta$ and $y = 2 \cos \theta - \cos 2 \theta , \theta \in [ 0,2 \pi ]$, then $\frac { d ^ { 2 } y } { d x ^ { 2 } }$ at $\theta = \pi$ is:
(1) $\frac { 3 } { 4 }$
(2) $- \frac { 3 } { 8 }$
(3) $\frac { 3 } { 2 }$
(4) $- \frac { 3 } { 4 }$
Q64 Composite & Inverse Functions Derivative of an Inverse Function View
Let $f$ and $g$ be differentiable functions on $R$ such that $f \circ g$ is the identity function. If for some $a , b \in R , g ^ { \prime } ( a ) = 5$ and $g ( a ) = b$, then $f ^ { \prime } ( b )$ is equal to:
(1) $\frac { 1 } { 5 }$
(2) 1
(3) 5
(4) $\frac { 2 } { 5 }$
Q65 Stationary points and optimisation Find critical points and classify extrema of a given function View
Let a function $f : [ 0,5 ] \rightarrow R$ be continuous, $f ( 1 ) = 3$ and $F$ be defined as: $F ( x ) = \int _ { 1 } ^ { x } t ^ { 2 } g ( t ) d t$, where $g ( t ) = \int _ { 1 } ^ { t } f ( u ) d u$. Then for the function $F ( x )$, the point $x = 1$ is:
(1) a point of local minima
(2) not a critical point
(3) a point of local maxima
(4) a point of inflection
Q66 Standard Integrals and Reverse Chain Rule Verify or Prove an Antiderivative/Integral Identity View
If $\int \frac { d \theta } { \cos ^ { 2 } \theta ( \tan 2 \theta + \sec 2 \theta ) } = \lambda \tan \theta + 2 \log _ { e } | f ( \theta ) | + C$ where $C$ is a constant of integration, then the ordered pair $( \lambda , f ( \theta ) )$ is equal to:
(1) $( 1,1 - \tan \theta )$
(2) $( - 1,1 - \tan \theta )$
(3) $( - 1,1 + \tan \theta )$
(4) $( 1,1 + \tan \theta )$
Q67 Areas Between Curves Compute Area Directly (Numerical Answer) View
Let $g ( x ) = \left( x - \frac { 1 } { 2 } \right) ^ { 2 } , x \in R$. Then, the area (in sq. units) of the region bounded by the curves, $y = f ( x )$ and $y = g ( x )$ between the lines $2 x = 1$ and $2 x = \sqrt { 3 }$, is:
(1) $\frac { 1 } { 3 } + \frac { \sqrt { 3 } } { 4 }$
(2) $\frac { \sqrt { 3 } } { 4 } - \frac { 1 } { 3 }$
(3) $\frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 4 }$
(4) $\frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 4 }$
Q68 Differential equations Solving Separable DEs with Initial Conditions View
If $\frac { d y } { d x } = \frac { x y } { x ^ { 2 } + y ^ { 2 } } ; y ( 1 ) = 1$; then a value of $x$ satisfying $y(x) = e$ is: