NATIONAL TALENT SEARCH EXAMINATION (NTSE)

A man from the top of a $100 \mathrm{metres}$ high tower sees a car towards the tower at an angle of depression of $30°$. After some time, the angle of depression becomes $60°$. The distance in $\mathrm{metres}$ travelled by the car during this time is

The upper $\frac{3}{4}\mathrm{th}$ portion of a vertical pole subtends an angle ${\tan }^{-1}\left(\frac{3}{5}\right)$ at a point in the horizontal plane through its foot and at a distance $40 \mathrm{m}$ from the foot. A possible height of the vertical pole is:

A person standing on the bank of a river observes that the angle of the top of a tree on the opposite bank of the river is $60°$ and when he retires $40 \mathrm{metres}$ away from the tree the angle of elevation becomes $30°$. The breadth of the river is

A tower stands at the centre of a circular park. $\mathrm{A}$ and $\mathrm{B}$ are two points on the boundary of the park such that $\mathrm{AB} (=a)$ subtends an angle of $60°$ at the foot of the tower, and the angle of elevation of the top of the tower from $\mathrm{A}$ or $\mathrm{B}$ is $30°$. The height of the tower is

An observer on the top of a cliff $200 \mathrm{m}$ above the sea leve;, observes the angles of depression of two ships on opposite sides of the cliff to be $45°$ and $30°$ respectively. Then the distance between the ships if the line joining these points to the base of the cliff is:

The upper part of a tree broken over by the wind makes an angle of $30°$ with the ground and the distance from the root to the point where the top of the tree touches the ground is $10 \mathrm{m}$. Then height of the tree is

An aeroplane flying at the height of $3000 \mathrm{m}$ above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are $60°$ and $45°$ respectively. Then the height of the lower plane from the ground is

Two vertical lamp posts of equal height stand on either side of a road $50 \mathrm{m}$ wide. At a point on the road, between the two lamp posts, the angle of elevation of the tops of the lamp posts are $60°$ and $30°$. Then the height of each post and the position of the point from one post are: