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A ball is released from a height h. If $$t_{1}$$ and $$t_{2}$$ be the time required to complete first half and second ha...
JEE Main 2022 (Online) 29th July Evening Shift
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A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest pos...
JEE Main 2022 (Online) 29th July Evening Shift
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If $$\mathrm{t}=\sqrt{x}+4$$, then $$\left(\frac{\mathrm{d} x}{\mathrm{~d} t}\right)_{\mathrm{t}=4}$$ is :
JEE Main 2022 (Online) 29th July Morning Shift
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A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the tim...
JEE Main 2022 (Online) 29th July Morning Shift
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At time $$t=0$$ a particle starts travelling from a height $$7 \hat{z} \mathrm{~cm}$$ in a plane keeping z coordinate co...
JEE Main 2022 (Online) 28th July Evening Shift
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A NCC parade is going at a uniform speed of $$9 \mathrm{~km} / \mathrm{h}$$ under a mango tree on which a monkey is sitt...
JEE Main 2022 (Online) 28th July Morning Shift
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The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing ...
JEE Main 2022 (Online) 27th July Evening Shift
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A bullet is shot vertically downwards with an initial velocity of $$100 \mathrm{~m} / \mathrm{s}$$ from a certain height...
JEE Main 2022 (Online) 27th July Morning Shift
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Two projectiles are thrown with same initial velocity making an angle of $$45^{\circ}$$ and $$30^{\circ}$$ with the hor...
JEE Main 2022 (Online) 26th July Evening Shift
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Two projectiles thrown at $$30^{\circ}$$ and $$45^{\circ}$$ with the horizontal respectively, reach the maximum height i...
JEE Main 2022 (Online) 26th July Morning Shift
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A ball is projected from the ground with a speed 15 ms$$-$$1 at an angle $$\theta$$ with horizontal so that its range an...
JEE Main 2022 (Online) 25th July Evening Shift
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Two projectiles P1 and P2 thrown with speed in the ratio $$\sqrt3$$ : $$\sqrt2$$, attain the same height during their mo...
JEE Main 2022 (Online) 30th June Morning Shift
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At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms$$-$$2. At t = 20 ...
JEE Main 2022 (Online) 30th June Morning Shift
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A projectile is projected with velocity of 25 m/s at an angle $$\theta$$ with the horizontal. After t seconds its inclin...
JEE Main 2022 (Online) 24th June Morning Shift
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Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by...
JEE Main 2022 (Online) 25th June Evening Shift
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Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Two ...
JEE Main 2022 (Online) 25th June Evening Shift
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A girl standing on road holds her umbrella at 45$$^\circ$$ with the vertical to keep the rain away. If she starts runnin...
JEE Main 2022 (Online) 27th June Morning Shift
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A projectile is launched at an angle '$$\alpha$$' with the horizontal with a velocity 20 ms$$-$$1. After 10 s, its incli...
JEE Main 2022 (Online) 27th June Morning Shift
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Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as $${v_2} = {n \over {{m^2}}}{v_1}$$ and ...
JEE Main 2022 (Online) 28th June Evening Shift
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A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?
JEE Main 2022 (Online) 29th June Evening Shift
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A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t ...
JEE Main 2022 (Online) 29th June Evening Shift
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Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is throw...
JEE Main 2022 (Online) 29th June Morning Shift
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The ranges and heights for two projectiles projected with the same initial velocity at angles 42$$^\circ$$ and 48$$^\cir...
JEE Main 2021 (Online) 1st September Evening Shift
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A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the groun...
JEE Main 2021 (Online) 31st August Morning Shift
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A player kicks a football with an initial speed of 25 ms$$-$$1 at an angle of 45$$^\circ$$ from the ground. What are the...
JEE Main 2021 (Online) 27th August Evening Shift
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Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m. The drops fall at a regular in...
JEE Main 2021 (Online) 27th August Evening Shift
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A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb ...
JEE Main 2021 (Online) 26th August Evening Shift
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A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times o...
JEE Main 2021 (Online) 27th July Morning Shift
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The instantaneous velocity of a particle moving in a straight line is given as $$V = \alpha t + \beta {t^2}$$, where $$\...
JEE Main 2021 (Online) 25th July Evening Shift
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A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon whe...
JEE Main 2021 (Online) 25th July Evening Shift
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The relation between time t and distance x for a moving body is given as t = mx2 + nx, where m and n are constants. The ...
JEE Main 2021 (Online) 25th July Evening Shift
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Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th second af...
JEE Main 2021 (Online) 25th July Morning Shift
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A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t1. ...
JEE Main 2021 (Online) 20th July Evening Shift
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A butterfly is flying with a velocity $$4\sqrt 2 $$ m/s in North-East direction. Wind is slowly blowing at 1 m/s from No...
JEE Main 2021 (Online) 20th July Morning Shift
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The velocity $$-$$ displacement graph of a particle is shown in the figure.The acceleration $$-$$ displacement graph of ...
JEE Main 2021 (Online) 18th March Evening Shift
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The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :
JEE Main 2021 (Online) 18th March Morning Shift
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A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to $${{81} \ov...
JEE Main 2021 (Online) 17th March Evening Shift
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The velocity of a particle is v = v0 + gt + Ft2. Its position is x = 0 at t = 0; then its displacement after time (t = 1...
JEE Main 2021 (Online) 17th March Evening Shift
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A car accelerates from rest at a constant rate $$\alpha$$ for some time after which it decelerates at a constant rate $$...
JEE Main 2021 (Online) 17th March Morning Shift
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A mosquito is moving with a velocity $$\overrightarrow v = 0.5{t^2}\widehat i + 3t\widehat j + 9\widehat k$$ m/s and ac...
JEE Main 2021 (Online) 16th March Evening Shift
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The velocity-displacement graph describing the motion of bicycle is shown in the figure.The acceleration-displacement gr...
JEE Main 2021 (Online) 16th March Morning Shift
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The trajectory of a projectile in a vertical plane is y = $$\alpha$$x $$-$$ $$\beta$$x2, where $$\alpha$$ and $$\beta$$ ...
JEE Main 2021 (Online) 26th February Evening Shift
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A scooter accelerates from rest for time t1 at constant rate a1 and then retards at constant rate a2 for time t2 and com...
JEE Main 2021 (Online) 26th February Evening Shift
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A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall f...
JEE Main 2021 (Online) 25th February Evening Shift
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An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment ...
JEE Main 2021 (Online) 25th February Morning Slot
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If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?...
JEE Main 2021 (Online) 24th February Morning Slot
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When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees t...
JEE Main 2020 (Online) 6th September Evening Slot
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The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 ...
JEE Main 2020 (Online) 5th September Evening Slot
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A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1, a girl standing at a ...
JEE Main 2020 (Online) 5th September Morning Slot
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A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped f...
JEE Main 2020 (Online) 5th September Morning Slot
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Starting from the origin at time t = 0, with initial velocity 5$$\widehat j$$ ms-1 , a particle moves in the x-y plane w...
JEE Main 2020 (Online) 4th September Morning Slot
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Train A and train B are running on parallel tracks in the opposite directions with speeds of 36 km/hour and 72 km/hour, ...
JEE Main 2020 (Online) 2nd September Morning Slot
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A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height $${h...
JEE Main 2020 (Online) 4th September Morning Slot
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A particle starts from the origin at t = 0 with an initial velocity of 3.0 $$\widehat i$$ m/s and moves in the x-y plane...
JEE Main 2020 (Online) 9th January Evening Slot
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A particle moves such that its position vector $$\overrightarrow r \left( t \right) = \cos \omega t\widehat i + \sin \om...
JEE Main 2020 (Online) 8th January Evening Slot
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Two particles are projected from the same point with the same speed u such that they have the same range R, but differen...
JEE Main 2019 (Online) 12th April Evening Slot
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A particle is moving with speed v = b$$\sqrt x $$ along positive x-axis. Calculate the speed of the particle at time t =...
JEE Main 2019 (Online) 12th April Evening Slot
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The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x2 . If it were launched at an angle ...
JEE Main 2019 (Online) 12th April Morning Slot
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A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a dist...
JEE Main 2019 (Online) 12th April Morning Slot
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A plane is inclined at an angle $$\alpha $$ = 30° with respect to the horizontal. A particle is projected with a speed u...
JEE Main 2019 (Online) 10th April Evening Slot
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A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by...
JEE Main 2019 (Online) 10th April Morning Slot
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The position vector of a particle changes with time according to the relation $$\overrightarrow r (t) = 15{t^2}\widehat ...
JEE Main 2019 (Online) 9th April Evening Slot
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The position of a particle as a function of time t, is given byx(t) = at + bt2 – ct3 where a, b and c are constants. Whe...
JEE Main 2019 (Online) 9th April Evening Slot
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The stream of a river is flowing with a speed of 2km/h. A swimmer can swim at a speed of 4km/h. What should be the direc...
JEE Main 2019 (Online) 9th April Morning Slot
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A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all ...
JEE Main 2019 (Online) 8th April Evening Slot
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Ship A is sailing towards north-east with velocity $$\mathop v\limits^ \to = 30\mathop i\limits^ \wedge + 50\mathop ...
JEE Main 2019 (Online) 8th April Morning Slot
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A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a spee...
JEE Main 2019 (Online) 12th January Morning Slot
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A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with ground le...
JEE Main 2019 (Online) 12th January Morning Slot
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A particle moves from the point $$\left( {2.0\widehat i + 4.0\widehat j} \right)$$ m, at t = 0, with an initial velocity...
JEE Main 2019 (Online) 11th January Evening Slot
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A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect ...
JEE Main 2019 (Online) 10th January Evening Slot
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Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they ar...
JEE Main 2019 (Online) 10th January Morning Slot
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The position co-ordinates of a particle moving in a 3-D coordinate system is given by x = a cos$$\omega $$t y = a sin$$...
JEE Main 2019 (Online) 9th January Evening Slot
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In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a spe...
JEE Main 2019 (Online) 9th January Evening Slot
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A particle is moving with a velocity $$\overrightarrow v \, = K(y\widehat i + x\widehat j),$$ where K is a constant. Th...
JEE Main 2019 (Online) 9th January Morning Slot
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A man in a car at location Q on a straight highway is moving with speed $$\upsilon $$. He decides to reach a point P in ...
JEE Main 2018 (Online) 15th April Evening Slot
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The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travell...
JEE Main 2018 (Online) 15th April Morning Slot
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An automobile, travelling at $$40\,$$ km/h, can be stopped at a distance of $$40\,$$ m by applying brakes. If the same a...
JEE Main 2018 (Online) 15th April Morning Slot
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All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.
JEE Main 2018 (Offline)
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A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different...
JEE Main 2017 (Online) 9th April Morning Slot
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Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?
JEE Main 2017 (Online) 8th April Morning Slot
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A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?
JEE Main 2017 (Offline)
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Two stones are thrown up simultaneously from the edge of a cliff $$240$$ $$m$$ high with initial speed of $$10$$ $$m/s$$...
JEE Main 2015 (Offline)
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From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit...
JEE Main 2014 (Offline)
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A projectile is given an initial velocity of $$\left( {\widehat i + 2\widehat j} \right)$$ m/s, where $${\widehat i}$$ i...
JEE Main 2013 (Offline)
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A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same ...
AIEEE 2012
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An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by : $${{dv} \over {dt}} = - 2.5\sqrt v $$ w...
AIEEE 2011
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A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the...
AIEEE 2011
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A small particle of mass $$m$$ is projected at an angle $$\theta $$ with the $$x$$-axis with an initial velocity $${v_0}...
AIEEE 2010
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A particle is moving with velocity $$\overrightarrow v = k\left( {y\widehat i + x\widehat j} \right)$$, where K is a co...
AIEEE 2010
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Consider a rubber ball freely falling from a height $$h=4.9$$ $$m$$ onto a horizontal elastic plate. Assume that the du...
AIEEE 2009
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A particle has an initial velocity $$3\widehat i + 4\widehat j$$ and an acceleration of $$0.4\widehat i + 0.3\widehat j$...
AIEEE 2009
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A body is at rest at $$x=0.$$ At $$t=0,$$ it starts moving in the positive $$x$$-direction with a constant acceleration....
AIEEE 2008
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The velocity of a particle is v = v0 + gt + ft2. If its position is x = 0 at t = 0, then its displacement after unit tim...
AIEEE 2007
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A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' that varies ...
AIEEE 2006
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The relation between time t and distance x is t = ax2 + bx where a and b are constants. The acceleration is
AIEEE 2005
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A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The ave...
AIEEE 2005
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A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and...
AIEEE 2005
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A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point and at the same instant p...
AIEEE 2004
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An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice a...
AIEEE 2004
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A projectile can have the same range 'R' for two angles of projection. If T1 and T2 be the time of flights in the two ca...
AIEEE 2004
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A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the posit...
AIEEE 2004
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The co-ordinates of a moving particle at any time 't' are given by x = $$\alpha $$t3 and y = βt3. The speed to the parti...
AIEEE 2003
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A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of $$30^\circ $$ with...
AIEEE 2003
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A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving at a spee...
AIEEE 2003
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Speeds of two identical cars are $$u $$ and $$4$$$$u $$ at the specific instant. The ratio of the respective distances i...
AIEEE 2002
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From a building two balls A and B are thrown such that A is thrown upwards and B downwards ( both vertically with the s...
AIEEE 2002
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An object is projected in the air with initial velocity u at an angle $$\theta$$. The projectile motion is such that the...
JEE Main 2022 (Online) 29th July Morning Shift
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A ball is thrown vertically upwards with a velocity of $$19.6 \mathrm{~ms}^{-1}$$ from the top of a tower. The ball stri...
JEE Main 2022 (Online) 28th July Evening Shift
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Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its ...
JEE Main 2022 (Online) 27th July Evening Shift
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A ball of mass m is thrown vertically upward. Another ball of mass $$2 \mathrm{~m}$$ is thrown at an angle $$\theta$$ wi...
JEE Main 2022 (Online) 27th July Morning Shift
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If the initial velocity in horizontal direction of a projectile is unit vector $$\hat{i}$$ and the equation of trajector...
JEE Main 2022 (Online) 26th July Morning Shift
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A particle is moving in a straight line such that its velocity is increasing at 5 ms$$-$$1 per meter. The acceleration o...
JEE Main 2022 (Online) 25th July Evening Shift
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A car is moving with speed of $$150 \mathrm{~km} / \mathrm{h}$$ and after applying the break it will move $$27 \mathrm{~...
JEE Main 2022 (Online) 25th July Morning Shift
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From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertic...
JEE Main 2022 (Online) 24th June Morning Shift
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A body is projected from the ground at an angle of 45$$^\circ$$ with the horizontal. Its velocity after 2s is 20 ms$$-$$...
JEE Main 2022 (Online) 24th June Evening Shift
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A ball is projected vertically upward with an initial velocity of 50 ms$$-$$1 at t = 0s. At t = 2s, another ball is proj...
JEE Main 2022 (Online) 26th June Evening Shift
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A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal t...
JEE Main 2022 (Online) 26th June Morning Shift
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A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms$$-$$1. When it passes directly overhea...
JEE Main 2022 (Online) 26th June Morning Shift
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A car covers AB distance with first one-third at velocity v1 ms$$-$$1, second one-third at v2 ms$$-$$1 and last one-thir...
JEE Main 2022 (Online) 28th June Evening Shift
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A particle is moving with constant acceleration 'a'. Following graph shows v2 versus x(displacement) plot. The accelerat...
JEE Main 2021 (Online) 31st August Evening Shift
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If the velocity of a body related to displacement x is given by $$\upsilon = \sqrt {5000 + 24x} $$ m/s, then the accele...
JEE Main 2021 (Online) 27th August Morning Shift
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Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at...
JEE Main 2021 (Online) 26th August Morning Shift
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A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30$$^\circ$$ with the flow of river....
JEE Main 2021 (Online) 27th July Evening Shift
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Three particles P, Q and R are moving along the vectors $$\overrightarrow A = \widehat i + \widehat j$$, $$\overrightar...
JEE Main 2021 (Online) 22th July Evening Shift
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A person is swimming with a speed of 10 m/s at an angle of 120$$^\circ$$ with the flow and reaches to a point directly o...
JEE Main 2021 (Online) 18th March Morning Shift
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A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction ...
JEE Main 2021 (Online) 16th March Evening Shift
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The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during ...
JEE Main 2020 (Online) 4th September Evening Slot
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The distance x covered by a particle in one dimensional motion varies with time t as x2 = at2 + 2bt + c. If the accelera...
JEE Main 2020 (Online) 9th January Morning Slot
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A ball is dropped from the top of a 100 m high tower on a planet. In the last $${1 \over 2}s$$ before hitting the ground...
JEE Main 2020 (Online) 8th January Evening Slot
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A particle is moving along the x-axis with its coordinate with the time 't' given be x(t) = 10 + 8t – 3t2. Another parti...
JEE Main 2020 (Online) 8th January Morning Slot
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