$A$ swimmer can swim with a velocity of $12 \, km/h$ in still water. The water flowing in a river has a velocity of $6 \, km/h$. The angle with respect to the direction of flow of the river water at which the swimmer should swim in order to reach the point on the other bank just opposite to his starting point is ........$^{\circ}$. (Round off to the Nearest Integer)

Two cities $X$ and $Y$ are connected by a regular bus service with a bus leaving in either direction every $T$ min. $A$ girl is driving a scooty with a speed of $60 \ km/h$ in the direction $X$ to $Y$ and notices that a bus goes past her every $30$ minutes in the direction of her motion,and every $10$ minutes in the opposite direction. Choose the correct option for the period $T$ of the bus service and the speed (assumed constant) of the buses.

$A$ person aiming to reach the exactly opposite point on the bank of a stream is swimming with a speed of $0.5\, m/s$ at an angle of $120^\circ$ with the direction of flow of water. The speed of water in the stream is..........$m/s$.

Two cars are moving in the same direction with the same speed $30 \, km/hr$. They are separated by a distance of $5 \, km$. The speed of a car moving in the opposite direction,if it meets these two cars at an interval of $4 \, minutes$,will be.......$km/hr$.

On a long horizontal belt,a child runs to and fro with a speed of $9\,km/h$ (with respect to the belt) between his father and mother located $50\,m$ apart on the moving belt. The belt moves with a speed of $4\,km/h.$ For an observer on the platform,the speed of the child in the direction of motion of the belt is.........$km/h$.

$A$ man standing on a road holds his umbrella at $30^\circ$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \, km/h$. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the moving man will be: