jee-main

Papers (191)
2026
session1_21jan_shift1 13 session1_21jan_shift2 9 session1_22jan_shift1 16 session1_22jan_shift2 10 session1_23jan_shift1 11 session1_23jan_shift2 7 session1_24jan_shift1 14 session1_24jan_shift2 10 session1_28jan_shift1 10 session1_28jan_shift2 9
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 session2_02apr_shift1 31 session2_02apr_shift2 36 session2_03apr_shift1 35 session2_03apr_shift2 35 session2_04apr_shift1 37 session2_04apr_shift2 33 session2_07apr_shift1 32 session2_07apr_shift2 32 session2_08apr_shift1 36 session2_08apr_shift2 35
2024
session1_01feb_shift1 5 session1_01feb_shift2 21 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 28 session1_29jan_shift2 29 session1_30jan_shift1 20 session1_30jan_shift2 29 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 5 session2_04apr_shift2 28 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 21 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 29 session2_09apr_shift1 8 session2_09apr_shift2 30
2023
session1_01feb_shift1 28 session1_01feb_shift2 3 session1_24jan_shift1 11 session1_24jan_shift2 11 session1_25jan_shift1 29 session1_25jan_shift2 29 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 5 session1_30jan_shift2 27 session1_31jan_shift1 28 session1_31jan_shift2 15 session2_06apr_shift1 5 session2_06apr_shift2 16 session2_08apr_shift1 29 session2_08apr_shift2 13 session2_10apr_shift1 29 session2_10apr_shift2 16 session2_11apr_shift1 6 session2_11apr_shift2 8 session2_12apr_shift1 26 session2_13apr_shift1 24 session2_13apr_shift2 24 session2_15apr_shift1 19
2022
session1_24jun_shift1 19 session1_24jun_shift2 25 session1_25jun_shift1 14 session1_25jun_shift2 14 session1_26jun_shift1 29 session1_26jun_shift2 24 session1_27jun_shift1 4 session1_27jun_shift2 29 session1_28jun_shift1 13 session1_29jun_shift1 20 session1_29jun_shift2 4 session2_25jul_shift1 29 session2_25jul_shift2 20 session2_26jul_shift1 29 session2_26jul_shift2 23 session2_27jul_shift1 28 session2_27jul_shift2 29 session2_28jul_shift1 11 session2_28jul_shift2 29 session2_29jul_shift1 17 session2_29jul_shift2 18
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
session1_07jan_shift1 28 session1_07jan_shift2 20 session1_08jan_shift1 5 session1_08jan_shift2 11 session1_09jan_shift1 26 session1_09jan_shift2 16 session2_02sep_shift1 18 session2_02sep_shift2 16 session2_03sep_shift1 23 session2_03sep_shift2 8 session2_04sep_shift1 14 session2_04sep_shift2 27 session2_05sep_shift1 22 session2_05sep_shift2 29 session2_06sep_shift1 11 session2_06sep_shift2 10
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
02apr 30 08apr 30 09apr 34
2016
03apr 28 09apr 29 10apr 30
2015
04apr 29 10apr 29 11apr 8
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
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
2005 jee-main_2005.pdf

25 maths questions

Q1 SUVAT in 2D & Gravity Vector Word Problem / Physical Application View
A particle is moving eastwards with a velocity of $5 \mathrm{~m}/\mathrm{s}$ in 10 seconds the velocity changes to $5 \mathrm{~m}/\mathrm{s}$ northwards. The average acceleration in this time is
(1) $\frac{1}{\sqrt{2}} \mathrm{~m}/\mathrm{s}^2$ towards north-east
(2) $\frac{1}{2} \mathrm{~m}/\mathrm{s}^2$ towards north.
(3) zero
(4) $\frac{1}{\sqrt{2}} \mathrm{~m}/\mathrm{s}^2$ towards north-west
Q3 Variable acceleration (1D) Inverse/implicit relationship between position and time View
The relation between time $t$ and distance x is $\mathrm{t} = a\mathrm{x}^2 + \mathrm{bx}$ where a and b are constants. The acceleration is
(1) $-2abv^2$
(2) $2bv^3$
(3) $-2av^3$
(4) $2av^2$
Q4 Constant acceleration (SUVAT) Acceleration then deceleration (two-phase motion) View
A car starting from rest accelerates at the rate $f$ through a distance $S$, then continues at constant speed for time $t$ and then decelerates at the rate $f/2$ to come to rest. If the total distance traversed is 15 S, then
(1) $S = ft$
(2) $\mathrm{S} = 1/6\, \mathrm{ft}^2$
(3) $\mathrm{S} = 1/2\, \mathrm{ft}^2$
(4) None of these
Q5 Constant acceleration (SUVAT) Real-world SUVAT application problem View
A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at $2 \mathrm{~m}/\mathrm{s}^2$. He reaches the ground with a speed of $3 \mathrm{~m}/\mathrm{s}$. At what height, did he bail out?
(1) 91 m
(2) 182 m
(3) 293 m
(4) 111 m
Q6 Constant acceleration (SUVAT) Two bodies meeting or catching up View
Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f'$ respectively. If $A$ takes $m$ sec. more than $B$ and describes '$n$' units more than $B$ in acquiring the same speed then
(1) $\left(f - f'\right)m^2 = ff'n$
(2) $\left(f + f'\right)m^2 = ff'n$
(3) $\frac{1}{2}\left(f + f'\right)m = ff'n^2$
(4) $\left(f' - f\right)n = \frac{1}{2}ff'm^2$
Q7 Moments View
$A$ and $B$ are two like parallel forces. A couple of moment H lies in the plane of $A$ and $B$ and is contained with them. The resultant of $A$ and $B$ after combining is displaced through a distance
(1) $\frac{2\mathrm{H}}{\mathrm{A}-\mathrm{B}}$
(2) $\frac{H}{A+B}$
(3) $\frac{H}{2(A+B)}$
(4) $\frac{H}{A-B}$
Q8 Projectiles Range and Complementary Angle Relationships View
A projectile can have the same range R for two angles of projection. If $\mathrm{t}_1$ and $\mathrm{t}_2$ be the times of flights in the two cases, then the product of the two time of flights is proportional to
(1) $R^2$
(2) $1/R^2$
(3) $1/R$
(4) R
Q9 Projectiles Velocity or Momentum at a Given Time View
A particle is projected from a point O with velocity $u$ at an angle of $60^\circ$ with the horizontal. When it is moving in a direction at right angles to its direction at $O$, its velocity then is given by
(1) $\frac{u}{3}$
(2) $\frac{u}{2}$
(3) $\frac{2u}{3}$
(4) $\frac{u}{\sqrt{3}}$
Q10 Friction Sliding on Inclined Plane (Kinematic) View
A smooth block is released at rest on a $45^\circ$ incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
(1) $\mu_\mathrm{k} = 1 - \frac{1}{\mathrm{n}^2}$
(2) $\mu_\mathrm{k} = \sqrt{1 - \frac{1}{\mathrm{n}^2}}$
(3) $\mu_s = 1 - \frac{1}{n^2}$
(4) $\mu_s = \sqrt{1 - \frac{1}{n^2}}$
Q11 Friction Inclined Plane with Smooth and Rough Sections (Energy/Work) View
The upper half of an inclined plane with inclination $\phi$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
(1) $2\sin\phi$
(2) $2\cos\phi$
(3) $2\tan\phi$
(4) $\tan\phi$
Q12 Forces, equilibrium and resultants View
A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration a to keep the block stationary. Then a is equal to
(1) $g/\tan\alpha$
(2) $g\operatorname{cosec}\alpha$
(3) g
(4) $g\tan\alpha$
Q13 Constant acceleration (SUVAT) Acceleration of a Block Under Applied Force with Kinetic Friction View
A particle of mass 0.3 kg is subjected to a force $F = -kx$ with $k = 15 \mathrm{~N}/\mathrm{m}$. What will be its initial acceleration if it is released from a point 20 cm away from the origin?
(1) $3 \mathrm{~m}/\mathrm{s}^2$
(2) $15 \mathrm{~m}/\mathrm{s}^2$
(3) $5 \mathrm{~m}/\mathrm{s}^2$
(4) $10 \mathrm{~m}/\mathrm{s}^2$
Q14 Constant acceleration (SUVAT) Flat Curve with Friction (Unbanked Road) View
Consider a car moving on a straight road with a speed of $100 \mathrm{~m}/\mathrm{s}$. The distance at which car can be stopped is $[\mu_\mathrm{k} = 0.5]$
(1) 800 m
(2) 1000 m
(3) 100 m
(4) 400 m
Q15 Circular Motion 1 Rolling body energy and incline problems View
An annular ring with inner and outer radii $R_1$ and $R_2$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $F_1/F_2$ is
(1) $\frac{R_2}{R_1}$
(2) $\left(\frac{R_1}{R_2}\right)^2$
(3) 1
(4) $\frac{R_1}{R_2}$
Q16 Constant acceleration (SUVAT) Energy conservation with friction or dissipative forces View
A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?
(1) 3.0 cm
(2) 2.0 cm
(3) 1.5 cm
(4) 1.0 cm
Q17 Work done and energy Rolling body energy and incline problems View
A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is
(1) $40 \mathrm{~m}/\mathrm{s}$
(2) $20 \mathrm{~m}/\mathrm{s}$
(3) $10 \mathrm{~m}/\mathrm{s}$
(4) $10\sqrt{30} \mathrm{~m}/\mathrm{s}$
Q18 Power and driving force View
A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function time is given by
(1) $\frac{mv^2}{T^2} \cdot t$
(2) $\frac{mv^2}{T^2} \cdot t^2$
(3) $\frac{1}{2}\frac{\mathrm{mv}^2}{\mathrm{T}^2} \cdot \mathrm{t}$
(4) $\frac{1}{2}\frac{\mathrm{mv}^2}{\mathrm{T}^2} \cdot \mathrm{t}^2$
Q19 Centre of Mass 1 View
A body $A$ of mass $M$ while falling vertically downwards under gravity breaks into two parts; a body B of mass $1/3\,M$ and a body C of mass $2/3\,M$. The centre of mass of bodies B and C taken together shifts compared to that of body A towards
(1) depends on height of breaking
(2) does not shift
(3) body C
(4) body B
Q20 Momentum and Collisions Collision with Spring System View
The block of mass $M$ moving on the frictionless horizontal surface collides with a spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is
(1) $\sqrt{\mathrm{MK}}\,\mathrm{L}$
(2) $\frac{\mathrm{KL}^2}{2\mathrm{M}}$
(3) zero
(4) $\frac{ML^2}{\mathrm{K}}$
Q21 Oblique and successive collisions View
A mass '$m$' moves with a velocity $v$ and collides inelastically with another identical mass. After collision the $1^{\text{st}}$ mass moves with velocity $v/\sqrt{3}$ in a direction perpendicular to the initial direction of motion. Find the speed of the $2^{\text{nd}}$ mass after collision
(1) v
(2) $\sqrt{3}\,v$
(3) $2v/\sqrt{3}$
(4) $v/\sqrt{3}$
Q22 Moments View
The moment of inertia of a uniform semicircular disc of mass $M$ and radius $r$ about a line perpendicular to the plane of the disc through the centre is
(1) $\frac{1}{4}\mathrm{Mr}^2$
(2) $\frac{2}{5}\mathrm{Mr}^2$
(3) $\mathrm{Mr}^2$
(4) $\frac{1}{2}\mathrm{Mr}^2$
Q23 Moments View
A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $F$ is applied at the point $P$ parallel to $AB$, such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$
(1) $\frac{2}{3}\ell$
(2) $\frac{3}{2}\ell$
(3) $\frac{4}{3}\ell$
(4) $\ell$
Q34 Simple Harmonic Motion View
The function $\sin^2(\omega t)$ represents
(1) a periodic, but not simple harmonic motion with a period $2\pi/\omega$
(2) a periodic, but not simple harmonic motion with a period $\pi/\omega$
(3) a simple harmonic motion with a period $2\pi/\omega$
(4) a simple harmonic motion with a period $\pi/\omega$
Q35 Simple Harmonic Motion View
Two simple harmonic motions are represented by the equation $\mathrm{y}_1 = 0.1\sin\left(100\pi t + \frac{\pi}{3}\right)$ and $y_2 = 0.1\cos\pi t$. The phase difference of the velocity of particle 1 w.r.t. the velocity of the particle 2 is
(1) $-\pi/6$
(2) $\pi/3$
(3) $-\pi/3$
(4) $\pi/6$
Q36 Simple Harmonic Motion View
If a simple harmonic motion is represented by $\frac{d^2x}{dt^2} + \alpha x = 0$, its time period is
(1) $\frac{2\pi}{\alpha}$
(2) $\frac{2\pi}{\sqrt{\alpha}}$
(3) $2\pi\alpha$
(4) $2\pi\sqrt{\alpha}$