JEE MainsJEE AdvanceBITSAT

JEE Mains | PYQ

1.A swimmer wants to cross a river from point A to point B. Line AB makes an angle of \( 30^\circ \) with flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle \( \theta \) with the line AB should be ______\( ^\circ \), so that the swimmer reaches point B. 

A ball is thrown up with a certain velocity so that it reaches a height '\( h \)'. Find the ratio of the two different times of the ball reaching \( \dfrac{h}{3} \) in both the directions.

The velocity-displacement graph of a particle is shown in the figure.

The acceleration-displacement graph of the same particle is represented by:

A car accelerates from rest at a constant rate \( \alpha \) for some time after which it decelerates at a constant rate \( \beta \) to come rest. If the total time elapsed is \( t \) seconds, the total distance travelled is:

The instantaneous velocity of a particle moving in a straight line is given as \( v = \alpha t + \beta t^{2} \), where \( \alpha \) and \( \beta \) are constants. The distance travelled by the particle between \( 1 \, \text{s} \) and \( 2 \, \text{s} \) is:

A rubber ball is released from a height of \( 5 \, \text{m} \) above the floor. It bounces back repeatedly, always rising to \( \dfrac{81}{100} \) of the height through which it falls. Find the average speed of the ball. (Take \( g = 10 \, \text{m s}^{-2} \))

A body of mass \( 2 \, \text{kg} \) moves under a force of \( (2\hat{i} + 3\hat{j} + 5\hat{k} )\, \text{N} \). It starts from rest and was at the origin initially. After \( 4 \, \text{s} \), its new coordinates are \( (8, b, 20) \). The value of \( b \) is ______. (Round off to the Nearest Integer)

The relation between time \( t \) and distance \( x \) for a moving body is given as \( t = m x^2 + n x \), where \( m \) and \( n \) are constants. The retardation of the motion is: (Where \( v \) stands for velocity)

A force \( \vec{F} = (40\hat{i} + 10\hat{j}) \, \text{N} \) acts on a body of mass \( 5 \, \text{kg} \). If the body starts from rest, its position vector \( \vec{r} \) at time \( t = 10 \, \text{s} \), will be:

A particle is moving with constant acceleration ‘\( a \)’. Following graph shows \( v^2 \) versus \( x \) (displacement) plot. The acceleration of the particle is ______ \( \mathrm{m/s^2} \).

A player kicks a football with an initial speed of \( 25 \, \text{ms}^{-1} \) at an angle of \( 45^\circ \) from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion?
(Take : \( g = 10 \, \text{ms}^{-2} \))

If the velocity of a body related to displacement \( x \) given by \( v=\sqrt{5000+24x} \, \mathrm{m/s} \), then the acceleration of the body is __________ \( \mathrm{m/s^2} \).

Water droplets are coming from an open tap at a particular rate, The spacing between a droplet observed at \( 4^{\text{th}} \) second after its fall to the next droplet is \( 34.3 \ \text{m} \). At what rate the droplets are coming from the tap? (Take \( g=9.8 \ \text{m}/\text{s}^{2} \))