The top of a hill observed from the top and bottom of a building of height $h$ is at the angle of elevation $p$ and $q$ respectively. The height of the hill is

The base of a cliff is circular. From the extremities of a diameter of the base,the angles of elevation of the top of the cliff are $30^\circ$ and $60^\circ$. If the height of the cliff is $500 \ m$,then the diameter of the base of the cliff is:

An aeroplane is flying at a constant speed,parallel to the horizontal ground at a height of $5 \text{ km}$. $A$ person on the ground observed that the angle of elevation of the plane is changed from $15^{\circ}$ to $30^{\circ}$ in the duration of $50 \text{ seconds}$. The speed of the plane (in $\text{kmph}$) is:

$A$ ladder rests against a wall making an angle $\alpha$ with the horizontal. The foot of the ladder is pulled away from the wall through a distance $x$,so that it slides a distance $y$ down the wall making an angle $\beta$ with the horizontal. The correct relation is

At a distance $2h$ from the foot of a tower of height $h$,the tower and a pole at the top of the tower subtend equal angles. The height of the pole is:

The shadow of a tower of height $(1 + \sqrt{3}) \text{ m}$ standing on the ground is found to be $2 \text{ m}$ longer when the sun's elevation is $30^{\circ}$ than when the sun's elevation was $...^{\circ}$.