If two stones are projected at angles $\theta$ and $(90^{\circ}-\theta)$ respectively with the horizontal with a speed of $20 \ ms^{-1}$. If the second stone rises $10 \ m$ higher than the first stone,then the angle of projection $\theta$ is (acceleration due to gravity $g = 10 \ ms^{-2}$) (in $^{\circ}$)

$A$ particle has initial velocity $(2\hat{i} + 3\hat{j})$ and acceleration $(0.3\hat{i} + 0.2\hat{j})$. The magnitude of velocity after $10\, s$ will be:

The coordinates of a particle moving in a plane are given by $x = a \cos(pt)$ and $y = b \sin(pt)$,where $a, b (b < a)$ and $p$ are positive constants of appropriate dimensions. Then:

$A$ car moving with a certain velocity jumps from an inclined plane placed at one bank of a river and reaches the other bank by attaining a maximum height of $80 \,m$. If the same car, moving with the same velocity, jumps from another inclined plane having a different angle of inclination and reaches the same point on the other bank by attaining a maximum height of $45 \,m$, then the width of the river is: (in $\,m$)

An aircraft is flying at a height of $H$ above the ground at a constant speed $V$. What is the maximum angle subtended at a ground observation point by the aircraft's path after time $T$?

List-$I$ describes four systems,each with two particles $A$ and $B$ in relative motion. List-$II$ gives possible magnitudes of their relative velocities (in $m s^{-1}$) at time $t = \frac{\pi}{3} s$. Which one of the following options is correct?