jee-main

Papers (169)
2025
session1_22jan_shift1 25 session1_22jan_shift2 25 session1_23jan_shift1 25 session1_23jan_shift2 25 session1_24jan_shift1 25 session1_24jan_shift2 25 session1_28jan_shift1 25 session1_28jan_shift2 25 session1_29jan_shift1 29 session1_29jan_shift2 25
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
2021 session4_01sep_shift2

11 maths questions

Q3 Projectiles Range and Complementary Angle Relationships View
The ranges and heights for two projectiles projected with the same initial velocity at angles $42 ^ { \circ }$ and $48 ^ { \circ }$ with the horizontal are $R _ { 1 } , \quad R _ { 2 }$ and $H _ { 1 } , \quad H _ { 2 }$ respectively. Choose the correct option:
(1) $R _ { 1 } = R _ { 2 }$ and $H _ { 1 } = H _ { 2 }$
(2) $R _ { 1 } = R _ { 2 }$ and $H _ { 1 } < H _ { 2 }$
(3) $R _ { 1 } > R _ { 2 }$ and $H _ { 1 } = H _ { 2 }$
(4) $R _ { 1 } < R _ { 2 }$ and $H _ { 1 } < H _ { 2 }$
Q4 Newton's laws and connected particles Block on wedge (constraint-based Newton's laws) View
A block of mass $m$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given $m = 8 \mathrm {~kg} , \quad M = 16 \mathrm {~kg}$ Assume all the surfaces shown in the figure to be frictionless.
(1) $\frac { 3 } { 5 } \mathrm {~g}$
(2) $\frac { 4 } { 3 } \mathrm {~g}$
(3) $\frac { 6 } { 5 } \mathrm {~g}$
(4) $\frac { 2 } { 3 } \mathrm {~g}$
Q5 Work done and energy Energy conservation with friction or dissipative forces View
A body of mass $m$ dropped from a height $h$ reaches the ground with a speed of $0.8 \sqrt { g h }$. The value of work done by the air-friction is:
(1) $- 0.68 m g h$
(2) $m g h$
(3) 0.64 mgh
(4) 1.64 mgh
Q7 Circular Motion 1 Two-Body Mutual Circular Orbit View
Four particles each of mass $M$, move along a circle of radius $R$ under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is:
(1) $\frac { 1 } { 2 } \sqrt { \frac { G M } { R } (2 \sqrt { 2 } + 1)}$
(2) $\frac { 1 } { 2 } \sqrt { \frac { G M } { R ( 2 \sqrt { 2 } + 1 ) } }$
(3) $\frac { 1 } { 2 } \sqrt { \frac { G M } { R } (2 \sqrt { 2 } - 1)}$
(4) $\sqrt { \frac { G M } { R } }$
Q61 Roots of polynomials Determine coefficients or parameters from root conditions View
The number of pairs $a , b$ of real numbers, such that whenever $\alpha$ is a root of the equation $x ^ { 2 } + a x + b = 0 , \quad \alpha ^ { 2 } - 2$ is also a root of this equation, is :
(1) 6
(2) 8
(3) 4
(4) 2
Q62 Combinations & Selection Geometric Combinatorics View
Let $P _ { 1 } , \quad P _ { 2 } \ldots , \quad P _ { 15 }$ be 15 points on a circle. The number of distinct triangles formed by points $P _ { i } , \quad P _ { j } , \quad P _ { k }$ such that $i + j + k \neq 15$, is :
(1) 455
(2) 419
(3) 12
(4) 443
Q63 Sequences and Series Evaluation of a Finite or Infinite Sum View
Let $S _ { n } = 1 \cdot ( n - 1 ) + 2 \cdot ( n - 2 ) + 3 \cdot ( n - 3 ) + \ldots + ( n - 1 ) \cdot 1 , \quad n \geqslant 4$. The sum $\sum _ { n = 4 } ^ { \infty } \frac { 2 S _ { n } } { n ! } - \frac { 1 } { ( n - 2 ) ! }$ is equal to :
(1) $\frac { e - 2 } { 6 }$
(2) $\frac { e - 1 } { 3 }$
(3) $\frac { e } { 6 }$
(4) $\frac { \mathrm { e } } { 3 }$
Q64 Arithmetic Sequences and Series Telescoping or Non-Standard Summation Involving an AP View
Let $a _ { 1 } , a _ { 2 } , \ldots , a _ { 21 }$ be an A.P. such that $\sum _ { n = 1 } ^ { 20 } \frac { 1 } { a _ { n } a _ { n + 1 } } = \frac { 4 } { 9 }$. If the sum of this A.P. is 189 , then $\mathrm { a } _ { 6 } \mathrm { a } _ { 16 }$ is equal to :
(1) 57
(2) 48
(3) 36
(4) 72
Q65 Quadratic trigonometric equations View
If $n$ is the number of solutions of the equation $2 \cos x \left(4 \sin \frac { \pi } { 4 } + x \sin \frac { \pi } { 4 } - x\right) - 1 = 1 , x \in [0 , \pi]$ and $S$ is the sum of all these solutions, then the ordered pair $(n , S)$ is :
(1) $\left(2 , \frac { 8 \pi } { 9 }\right)$
(2) $\left(3 , \frac { 13 \pi } { 9 }\right)$
(3) $\left(2 , \frac { 2 \pi } { 3 }\right)$
(4) $\left(3 , \frac { 5 \pi } { 3 }\right)$
Q66 Conic sections Chord Properties and Midpoint Problems View
Consider the parabola with vertex $\left(\frac { 1 } { 2 } , \frac { 3 } { 4 }\right)$ and the directrix $y = \frac { 1 } { 2 }$. Let P be the point where the parabola meets the line $x = - \frac { 1 } { 2 }$. If the normal to the parabola at P intersects the parabola again at the point Q, then $(PQ) ^ { 2 }$ is equal to :
(1) $\frac { 25 } { 2 }$
(2) $\frac { 75 } { 8 }$
(3) $\frac { 125 } { 16 }$
(4) $\frac { 15 } { 2 }$
Q67 Circles Intersection of Circles or Circle with Conic View
Let $\theta$ be the acute angle between the tangents to the ellipse $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 1 } = 1$ and the circle $x^2 + y^2 = 3$ at their points of intersection. Then $\tan\theta$ is equal to:
(1) $\frac{4}{\sqrt{3}}$
(2) $\frac{2}{\sqrt{3}}$
(3) $2$
(4) $\frac{5}{2\sqrt{3}}$