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
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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
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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
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2016
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2015
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2014
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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
2020 session2_05sep_shift1

22 maths questions

Q22 Moments View
A force $\vec { F } = ( \hat { i } + 2 \hat { j } + 3 \hat { k } ) \mathrm { N }$ acts at a point $( 4 \hat { i } + 3 \hat { j } - \widehat { k } ) \mathrm { m }$. Then the magnitude of torque about the point $( \hat { i } + 2 \hat { j } + \widehat { k } ) \mathrm { m }$ will be $\sqrt { x } \mathrm {~N} - \mathrm { m }$. The value of $x$ is.
Q51 Solving quadratics and applications Finding roots or coefficients of a quadratic using Vieta's relations View
The product of the roots of the equation $9 x ^ { 2 } - 18 | x | + 5 = 0$ is :
(1) $\frac { 5 } { 9 }$
(2) $\frac { 25 } { 81 }$
(3) $\frac { 5 } { 27 }$
(4) $\frac { 25 } { 9 }$
Q52 Complex Numbers Argand & Loci Geometric Properties of Triangles/Polygons from Affixes View
If the four complex numbers $z , \bar { z } , \bar { z } - 2 \operatorname { Re } ( \bar { z } )$ and $z - 2 \operatorname { Re } ( z )$ represent the vertices of a square of side 4 units in the Argand plane, then $| z |$ is equal to :
(1) $4 \sqrt { 2 }$
(2) 4
(3) $2 \sqrt { 2 }$
(4) 2
Q53 Arithmetic Sequences and Series Finite Geometric Sum and Term Relationships View
If $2 ^ { 10 } + 2 ^ { 9 } \cdot 3 ^ { 1 } + 2 ^ { 8 } \cdot 3 ^ { 2 } + \ldots\ldots + 2 \cdot 3 ^ { 9 } + 3 ^ { 10 } = S - 2 ^ { 11 }$, then $S$ is equal to
(1) $3 ^ { 11 } - 2 ^ { 12 }$
(2) $3 ^ { 11 }$
(3) $\frac { 3 ^ { 11 } } { 2 } + 2 ^ { 10 }$
(4) $2.3 ^ { 11 }$
Q54 Arithmetic Sequences and Series Find Specific Term from Given Conditions View
If $3 ^ { 2 \sin 2 \alpha - 1 } , 14$ and $3 ^ { 4 - 2 \sin 2 \alpha }$ are the first three terms of an A.P. for some $\alpha$, then the sixth term of this A.P. is
(1) 66
(2) 81
(3) 65
(4) 78
Q55 Circles Tangent Lines and Tangent Lengths View
If the common tangent to the parabolas, $y ^ { 2 } = 4 x$ and $x ^ { 2 } = 4 y$ also touches the circle, $x ^ { 2 } + y ^ { 2 } = c ^ { 2 }$, then $c$ is equal to :
(1) $\frac { 1 } { 2 \sqrt { 2 } }$
(2) $\frac { 1 } { \sqrt { 2 } }$
(3) $\frac { 1 } { 4 }$
(4) $\frac { 1 } { 2 }$
Q56 Circles Focal Distance and Point-on-Conic Metric Computation View
If the co-ordinates of two points $A$ and $B$ are $( \sqrt { 7 } , 0 )$ and $( - \sqrt { 7 } , 0 )$ respectively and $P$ is any point on the conic, $9 x ^ { 2 } + 16 y ^ { 2 } = 144$, then $PA + PB$ is equal to :
(1) 16
(2) 8
(3) 6
(4) 9
Q57 Circles Optimization on Conics View
If the point $P$ on the curve, $4 x ^ { 2 } + 5 y ^ { 2 } = 20$ is farthest from the point $Q ( 0 , - 4 )$, then $PQ ^ { 2 }$ is equal to
(1) 36
(2) 48
(3) 21
(4) 29
Q58 Chain Rule Limit Evaluation Involving Composition or Substitution View
If $\alpha$ is the positive root of the equation, $p ( x ) = x ^ { 2 } - x - 2 = 0$, then $\lim _ { x \rightarrow \alpha ^ { + } } \frac { \sqrt { 1 - \cos p ( x ) } } { x + \alpha - 4 }$ is equal to
(1) $\frac { 3 } { 2 }$
(2) $\frac { 3 } { \sqrt { 2 } }$
(3) $\frac { 1 } { \sqrt { 2 } }$
(4) $\frac { 1 } { 2 }$
Q60 Measures of Location and Spread View
The mean and variance of 7 observations are 8 and 16, respectively. If five observations are $2, 4, 10, 12, 14$ then the absolute difference of the remaining two observations is :
(1) 1
(2) 4
(3) 2
(4) 3
Q61 Principle of Inclusion/Exclusion View
A survey shows that $73 \%$ of the persons working in an office like coffee, whereas $65 \%$ like tea. If $x$ denotes the percentage of them, who like both coffee and tea, then $x$ cannot be:
(1) 63
(2) 36
(3) 54
(4) 38
Q62 3x3 Matrices Determinant and Rank Computation View
If the minimum and the maximum values of the function $f : \left[ \frac { \pi } { 4 } , \frac { \pi } { 2 } \right] \rightarrow R$, defined by $f ( \theta ) = \left| \begin{array} { c c c } - \sin ^ { 2 } \theta & - 1 - \sin ^ { 2 } \theta & 1 \\ - \cos ^ { 2 } \theta & - 1 - \cos ^ { 2 } \theta & 1 \\ 12 & 10 & - 2 \end{array} \right|$ are $m$ and $M$ respectively, then the ordered pair $( \mathrm { m } , \mathrm { M } )$ is equal to :
(1) $( 0,2 \sqrt { 2 } )$
(2) $( - 4,0 )$
(3) $( - 4,4 )$
(4) $( 0,4 )$
Q63 3x3 Matrices Linear System Existence and Uniqueness via Determinant View
Let $\lambda \in \mathrm { R }$. The system of linear equations $2 x _ { 1 } - 4 x _ { 2 } + \lambda x _ { 3 } = 1$ $x _ { 1 } - 6 x _ { 2 } + x _ { 3 } = 2$ $\lambda x _ { 1 } - 10 x _ { 2 } + 4 x _ { 3 } = 3$ is inconsistent for :
(1) exactly one positive value of $\lambda$
(2) exactly one negative value of $\lambda$
(3) every value of $\lambda$
(4) exactly two values of $\lambda$
Q64 Reciprocal Trig & Identities Addition/Subtraction Formula Evaluation View
If $S$ is the sum of the first 10 terms of the series, $\tan ^ { - 1 } \left( \frac { 1 } { 3 } \right) + \tan ^ { - 1 } \left( \frac { 1 } { 7 } \right) + \tan ^ { - 1 } \left( \frac { 1 } { 13 } \right) + \tan ^ { - 1 } \left( \frac { 1 } { 21 } \right) + \ldots\ldots$. then $\tan ( S )$ is equal to :
(1) $\frac { 5 } { 6 }$
(2) $\frac { 5 } { 11 }$
(3) $- \frac { 5 } { 6 }$
(4) $\frac { 10 } { 11 }$
Q65 Differentiation from First Principles Determine parameters from function or curve conditions View
If the function $f ( x ) = \left\{ \begin{array} { c c } k _ { 1 } ( x - \pi ) ^ { 2 } - 1 , & x \leq \pi \\ k _ { 2 } \cos x , & x > \pi \end{array} \right.$ is twice differentiable, then the ordered pair $\left( k _ { 1 } , k _ { 2 } \right)$ is equal to:
(1) $\left( \frac { 1 } { 2 } , 1 \right)$
(2) $( 1,0 )$
(3) $\left( \frac { 1 } { 2 } , - 1 \right)$
(4) $( 1,1 )$
Q66 Standard Integrals and Reverse Chain Rule Substitution to Compute an Indefinite Integral with Initial Condition View
If $\int \left( e ^ { 2 x } + 2 e ^ { x } - e ^ { - x } - 1 \right) e ^ { \left( e ^ { x } + e ^ { - x } \right) } d x = g ( x ) e ^ { \left( e ^ { x } + e ^ { - x } \right) } + c$, where $c$ is a constant of integration, then $g ( 0 )$ is
(1) $e$
(2) $e ^ { 2 }$
(3) 1
(4) 2
Q67 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution View
The value of $\int _ { - \frac { \pi } { 2 } } ^ { \frac { \pi } { 2 } } \frac { 1 } { 1 + e ^ { \sin x } } d x$ is :
(1) $\frac { \pi } { 4 }$
(2) $\pi$
(3) $\frac { \pi } { 2 }$
(4) $\frac { 3 \pi } { 2 }$
Q68 Differential equations Solving Separable DEs with Initial Conditions View
If $y = y ( x )$ is the solution of the differential equation $\frac { 5 + e ^ { x } } { 2 + y } \cdot \frac { d y } { d x } + e ^ { x } = 0$ satisfying $y ( 0 ) = 1$ then value of $y \left( \log _ { e } 13 \right)$ is
(1) 1
(2) - 1
(3) 0
(4) 2
Q69 Vectors: Cross Product & Distances View
If the volume of a parallelopiped, whose coterminous edges are given by the vectors $\overrightarrow { \mathrm { a } } = \hat { i } + \hat { j } + n \widehat { k }$, $\overrightarrow { \mathrm { b } } = 2 \hat { \mathrm { i } } + 4 \hat { \mathrm { j } } - n \hat { k }$ and, $\overrightarrow { \mathrm { c } } = \hat { \mathrm { i } } + n \hat { j } + 3 \hat { k } ( \mathrm { n } \geq 0 )$ is 158 cubic units, then :
(1) $\overrightarrow { \mathrm { a } } \cdot \overrightarrow { \mathrm { c } } = 17$
(2) $\overrightarrow { \mathrm { b } } \cdot \overrightarrow { \mathrm { c } } = 10$
(3) $n = 7$
(4) $n = 9$
Q70 Vectors 3D & Lines Perpendicular/Orthogonal Projection onto a Plane View
If $( a , b , c )$ is the image of the point $( 1,2 , - 3 )$ in the line, $\frac { x + 1 } { 2 } = \frac { y - 3 } { - 2 } = \frac { z } { - 1 }$, then $a + b + c$ is equal to:
(1) 2
(2) - 1
(3) 3
(4) 1
Q71 Combinations & Selection Selection with Group/Category Constraints View
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is
Q72 Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms View
The natural number $m$, for which the coefficient of $x$ in the binomial expansion of $\left( x ^ { m } + \frac { 1 } { x ^ { 2 } } \right) ^ { 22 }$ is 1540, is