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
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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
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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
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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
2022 session2_29jul_shift1

18 maths questions

Q2 Constant acceleration (SUVAT) Vertical projection from ground level View
A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height $h$. Find the ratio of the times in which it is at height $\frac { h } { 3 }$ while going up and coming down respectively.
(1) $\frac { \sqrt { 2 } - 1 } { \sqrt { 2 } + 1 }$
(2) $\frac { \sqrt { 3 } - \sqrt { 2 } } { \sqrt { 3 } + \sqrt { 2 } }$
(3) $\frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 }$
(4) $\frac { 1 } { 3 }$
Q3 Chain Rule Chain Rule with Composition of Explicit Functions View
If $t = \sqrt { x } + 4$, then $\left( \frac { \mathrm { d } x } { \mathrm {~d} t } \right) _ { t = 4 }$ is:
(1) 4
(2) Zero
(3) 8
(4) 16
Q4 Projectiles Kinetic Energy at a Point in Flight View
A ball is projected with kinetic energy $E$, at an angle of $60 ^ { \circ }$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :
(1) Zero
(2) $\frac { E } { 2 }$
(3) $\frac { E } { 4 }$
(4) $E$
Q6 Vectors Introduction & 2D Magnitude of Vector Expression View
Two bodies of mass 1 kg and 3 kg have position vectors $\hat { \mathrm { i } } + 2 \hat { \mathrm { j } } + \widehat { \mathrm { k } }$ and $- 3 \hat { \mathrm { i } } - 2 \hat { \mathrm { j } } + \widehat { \mathrm { k } }$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :
(1) $\hat { \mathrm { i } } - 2 \hat { \mathrm { j } } + \widehat { \mathrm { k } }$
(2) $- 3 \hat { \mathrm { i } } - 2 \hat { \mathrm { j } } + \widehat { \mathrm { k } }$
(3) $- 2 \hat { \mathrm { i } } + 2 \widehat { \mathrm { k } }$
(4) $- 2 \hat { \mathrm { i } } - \hat { \mathrm { j } } + 2 \widehat { \mathrm { k } }$
Q21 Projectiles Range and Complementary Angle Relationships View
An object is projected in the air with initial velocity $u$ at an angle $\theta$. The projectile motion is such that the horizontal range $R$, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be $\_\_\_\_$ degree.
Q61 Complex Numbers Arithmetic Powers of i or Complex Number Integer Powers View
If $z = 2 + 3 i$, then $z ^ { 5 } + ( \bar { z } ) ^ { 5 }$ is equal to:
(1) 244
(2) 224
(3) 245
(4) 265
Q62 Arithmetic Sequences and Series Telescoping or Non-Standard Summation Involving an AP View
If $\frac { 1 } { ( 20 - a ) ( 40 - a ) } + \frac { 1 } { ( 40 - a ) ( 60 - a ) } + \ldots\ldots + \frac { 1 } { ( 180 - a ) ( 200 - a ) } = \frac { 1 } { 256 }$, then the maximum value of $a$ is
(1) 198
(2) 202
(3) 212
(4) 218
Q63 Straight Lines & Coordinate Geometry Triangle Properties and Special Points View
Let the circumcentre of a triangle with vertices $A ( a , 3 ) , B ( b , 5 )$ and $C ( a , b ) , a b > 0$ be $P ( 1,1 )$. If the line $A P$ intersects the line $B C$ at the point $Q \left( k _ { 1 } , k _ { 2 } \right)$, then $k _ { 1 } + k _ { 2 }$ is equal to
(1) 2
(2) $\frac { 4 } { 7 }$
(3) $\frac { 2 } { 7 }$
(4) 4
Q64 Conic sections Eccentricity or Asymptote Computation View
Let a line $L$ pass through the point of intersection of the lines $b x + 10 y - 8 = 0$ and $2 x - 3 y = 0$, $b \in R - \left\{ \frac { 4 } { 3 } \right\}$. If the line $L$ also passes through the point $( 1,1 )$ and touches the circle $17 \left( x ^ { 2 } + y ^ { 2 } \right) = 16$, then the eccentricity of the ellipse $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ is
(1) $\frac { 2 } { \sqrt { 5 } }$
(2) $\sqrt { \frac { 3 } { 5 } }$
(3) $\frac { 1 } { \sqrt { 5 } }$
(4) $\sqrt { \frac { 2 } { 5 } }$
Q65 Conic sections Triangle or Quadrilateral Area and Perimeter with Foci View
Let the focal chord of the parabola $P : y ^ { 2 } = 4 x$ along the line $L : y = m x + c , m > 0$ meet the parabola at the points $M$ and $N$. Let the line $L$ be a tangent to the hyperbola $H : x ^ { 2 } - y ^ { 2 } = 4$. If $O$ is the vertex of $P$ and $F$ is the focus of $H$ on the positive $x$-axis, then the area of the quadrilateral $O M F N$ is
(1) $2 \sqrt { 6 }$
(2) $2 \sqrt { 14 }$
(3) $4 \sqrt { 6 }$
(4) $4 \sqrt { 14 }$
Q67 Proof Proof of Equivalence or Logical Relationship Between Conditions View
The statement $( p \wedge q ) \Rightarrow ( p \wedge r )$ is equivalent to
(1) $q \Rightarrow ( p \wedge r )$
(2) $p \Rightarrow ( p \wedge r )$
(3) $( p \wedge r ) \Rightarrow ( p \wedge q )$
(4) $( p \wedge q ) \Rightarrow r$
Q68 Sine and Cosine Rules Heights and distances / angle of elevation problem View
The angle of elevation of the top of a tower from a point $A$ due north of it is $\alpha$ and from a point $B$ at a distance of 9 units due west of $A$ is $\cos ^ { - 1 } \left( \frac { 3 } { \sqrt { 13 } } \right)$. If the distance of the point $B$ from the tower is 15 units, then $\cot \alpha$ is equal to
(1) $\frac { 6 } { 5 }$
(2) $\frac { 9 } { 5 }$
(3) $\frac { 4 } { 3 }$
(4) $\frac { 7 } { 3 }$
Q69 Number Theory Prime Number Properties and Identification View
Let $R$ be a relation from the set $\{ 1,2,3 \ldots\ldots . , 60 \}$ to itself such that $R = \{ ( a , b ) : b = p q$, where $p , q \geq 3$ are prime numbers\}. Then, the number of elements in $R$ is
(1) 600
(2) 660
(3) 540
(4) 720
Q70 Matrices Linear Transformation and Endomorphism Properties View
Let $A$ and $B$ be two $3 \times 3$ non-zero real matrices such that $A B$ is a zero matrix. Then
(1) The system of linear equations $A X = 0$ has a unique solution
(2) The system of linear equations $A X = 0$ has infinitely many solutions
(3) $B$ is an invertible matrix
(4) $\operatorname { adj } ( A )$ is an invertible matrix
Q71 Applied differentiation MCQ on derivative and graph interpretation View
The number of points, where the function $f : R \rightarrow R , f ( x ) = | x - 1 | \cos | x - 2 | \sin | x - 1 | + ( x - 3 ) \left| x ^ { 2 } - 5 x + 4 \right|$, is NOT differentiable, is
(1) 1
(2) 2
(3) 3
(4) 4
Q72 Stationary points and optimisation Find concavity, inflection points, or second derivative properties View
Let $f ( x ) = 3 ^ { \left( x ^ { 2 } - 2 \right) ^ { 3 } + 4 } , \mathrm { x } \in R$. Then which of the following statements are true? $P : x = 0$ is a point of local minima of $f$ $Q : x = \sqrt { 2 }$ is a point of inflection of $f$ $R : f ^ { \prime }$ is increasing for $x > \sqrt { 2 }$
(1) Only $P$ and $Q$
(2) Only $P$ and $R$
(3) Only $Q$ and $R$
(4) All $P , Q$ and $R$
Q73 Integration by Substitution Substitution to Evaluate a Definite Integral (Numerical Answer) View
The integral $\int _ { 0 } ^ { \frac { \pi } { 2 } } \frac { 1 } { 3 + 2 \sin x + \cos x } d x$ is equal to:
(1) $\tan ^ { - 1 } ( 2 )$
(2) $\tan ^ { - 1 } ( 2 ) - \frac { \pi } { 4 }$
(3) $\frac { 1 } { 2 } \tan ^ { - 1 } ( 2 ) - \frac { \pi } { 8 }$
(4) $\frac { 1 } { 2 }$
Q74 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution View
If $f ( \alpha ) = \int _ { 1 } ^ { \alpha } \frac { \log _ { 10 } t } { 1 + t } d t , \alpha > 0$, then $f \left( e ^ { 3 } \right) + f \left( e ^ { - 3 } \right)$ is equal to
(1) 9
(2) $\frac { 9 } { 2 }$