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
2021 session2_18mar_shift2

11 maths questions

Q61 Complex Numbers Argand & Loci Geometric Properties of Triangles/Polygons from Affixes View
Let a complex number be $w = 1 - \sqrt { 3 } i$. Let another complex number $z$ be such that $| z w | = 1$ and $\arg ( z ) - \arg ( w ) = \frac { \pi } { 2 }$. Then the area of the triangle (in sq. units) with vertices origin, $z$ and $w$ is equal to
(1) 4
(2) $\frac { 1 } { 2 }$
(3) $\frac { 1 } { 4 }$
(4) 2
Q62 Arithmetic Sequences and Series Compute Partial Sum of an Arithmetic Sequence View
Let $S _ { 1 }$ be the sum of first $2 n$ terms of an arithmetic progression. Let $S _ { 2 }$ be the sum of first $4 n$ terms of the same arithmetic progression. If ( $S _ { 2 } - S _ { 1 }$ ) is 1000 , then the sum of the first $6 n$ terms of the arithmetic progression is equal to:
(1) 1000
(2) 7000
(3) 5000
(4) 3000
Q63 Trig Proofs Power-Sum Evaluation via Trigonometric Constraint View
If $15 \sin ^ { 4 } \alpha + 10 \cos ^ { 4 } \alpha = 6$, for some $\alpha \in R$, then the value of $27 \sec ^ { 6 } \alpha + 8 \operatorname { cosec } ^ { 6 } \alpha$ is equal to:
(1) 350
(2) 500
(3) 400
(4) 250
Q64 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
Let the centroid of an equilateral triangle $ABC$ be at the origin. Let one of the sides of the equilateral triangle be along the straight line $x + y = 3$. If $R$ and $r$ be the radius of circumcircle and incircle respectively of $\triangle ABC$, then $( R + r )$ is equal to:
(1) $\frac { 9 } { \sqrt { 2 } }$
(2) $7 \sqrt { 2 }$
(3) $2 \sqrt { 2 }$
(4) $3 \sqrt { 2 }$
Q65 Circles Circle-Related Locus Problems View
Let $S _ { 1 } : x ^ { 2 } + y ^ { 2 } = 9$ and $S _ { 2 } : ( x - 2 ) ^ { 2 } + y ^ { 2 } = 1$.
Then the locus of center of a variable circle $S$ which touches $S _ { 1 }$ internally and $S _ { 2 }$ externally always passes through the points:
(1) $( 0 , \pm \sqrt { 3 } )$
(2) $\left( \frac { 1 } { 2 } , \pm \frac { \sqrt { 5 } } { 2 } \right)$
(3) $\left( 2 , \pm \frac { 3 } { 2 } \right)$
(4) $( 1 , \pm 2 )$
Q66 Conic sections Optimization on Conics View
Let a tangent be drawn to the ellipse $\frac { x ^ { 2 } } { 27 } + y ^ { 2 } = 1$ at $( 3 \sqrt { 3 } \cos \theta , \sin \theta )$ where $\theta \in \left( 0 , \frac { \pi } { 2 } \right)$. Then the value of $\theta$ such that the sum of intercepts on axes made by this tangent is minimum is equal to:
(1) $\frac { \pi } { 8 }$
(2) $\frac { \pi } { 4 }$
(3) $\frac { \pi } { 6 }$
(4) $\frac { \pi } { 3 }$
Q67 Conic sections Triangle or Quadrilateral Area and Perimeter with Foci View
Consider a hyperbola $H : x ^ { 2 } - 2 y ^ { 2 } = 4$. Let the tangent at a point $P ( 4 , \sqrt { 6 } )$ meet the $x$-axis at $Q$ and latus rectum at $R \left( x _ { 1 } , y _ { 1 } \right) , x _ { 1 } > 0$. If $F$ is a focus of $H$ which is nearer to the point $P$, then the area of $\triangle QFR$ (in sq. units) is equal to
(1) $4 \sqrt { 6 }$
(2) $\sqrt { 6 } - 1$
(3) $\frac { 7 } { \sqrt { 6 } } - 2$
(4) $4 \sqrt { 6 } - 1$
Q68 Proof True/False Justification View
If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?
(1) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow Q$
(2) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow \sim P$
(3) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow P$
(4) $( ( P \Rightarrow Q ) \wedge \sim Q ) \Rightarrow ( P \wedge Q )$
Q69 Measures of Location and Spread View
Let in a series of $2 n$ observations, half of them are equal to $a$ and remaining half are equal to $- a$. Also by adding a constant $b$ in each of these observations, the mean and standard deviation of new set become 5 and 20 , respectively. Then the value of $a ^ { 2 } + b ^ { 2 }$ is equal to:
(1) 425
(2) 650
(3) 250
(4) 925
Q70 Sine and Cosine Rules Heights and distances / angle of elevation problem View
A pole stands vertically inside a triangular park $ABC$. Let the angle of elevation of the top of the pole from each corner of the park be $\frac { \pi } { 3 }$. If the radius of the circumcircle of $\triangle ABC$ is 2 , then the height of the pole is equal to:
(1) $\frac { 2 \sqrt { 3 } } { 3 }$
(2) $2 \sqrt { 3 }$
(3) $\sqrt { 3 }$
(4) $\frac { 1 } { \sqrt { 3 } }$
Q71 Matrices Diagonalizability and Similarity View
Define a relation $R$ over a class of $n \times n$ real matrices $A$ and $B$ as ``$ARB$ iff there exists a non-singular matrix $P$ such that $PAP^{-1} = B$''. Then which of the following is true?