$A$ gas balloon is going up with a constant velocity of $10 \text{ m/s}$. When this balloon reached a height of $75 \text{ m}$, a stone is dropped from it and the balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is . . . . . . $\text{m}$. (Take $g = 10 \text{ m/s}^2$)

$A$ stone is dropped into a lake from a tower $500 \ m$ high. The sound of the splash will be heard by the man approximately after ..... $s$. (Take $g = 10 \ m/s^2$ and speed of sound $v = 340 \ m/s$)

Look at the graphs $(a)$ to $(d)$ carefully and state,with reasons,which of these cannot possibly represent one-dimensional motion of a particle.

$A$ train starting from rest first accelerates uniformly up to a speed of $80 \ km/h$ for time $t$,then it moves with a constant speed for time $3t$. The average speed of the train for this duration of journey will be (in $km/h$):

Select the incorrect statement among the following$:-$
$S_1 :$ If the acceleration is zero,a moving particle will perform uniform motion.
$S_2 :$ Motion with constant speed may or may not be uniform motion.
$S_3 :$ If a particle moves on a curved path,its acceleration can never be zero.
$S_4 :$ In successive time intervals,if the average velocities of a particle are equal,then the particle must be moving with uniform velocity.

State whether the following statements are true or false:
$(a)$ Velocity can change without a change in speed.
$(b)$ The total distance covered by a freely falling body in a given time is directly proportional to the time.
$(c)$ $A$ particle is a point object that possesses dimensions.