$A$ train of $150 \; m$ length is going towards the north direction at a speed of $10 \; m/s$. $A$ parrot flies at a speed of $5 \; m/s$ towards the south direction parallel to the railway track. The time taken by the parrot to cross the train is: (in $; s$)

Two cars $A$ and $B$ are moving with the same speed of $45\,km/h$ along the same direction. If a third car $C$ coming from the opposite direction with a speed of $36\,km/h$ meets the two cars in an interval of $5\,min$,the distance of separation between the two cars $A$ and $B$ should be.......$km$.

The maximum speed of a boat in still water is $27 \,km/h$. Now this boat is moving downstream in a river flowing at $9 \,km/h$. $A$ man in the boat throws a ball vertically upwards with a speed of $10 \,m/s$. The range of the ball as observed by an observer at rest on the river bank is . . . . . . $cm$. (Take $g = 10 \,m/s^2$)

Two particles $A$ and $B$ move with constant velocities $\vec{v}_1$ and $\vec{v}_2$. At the initial moment,their position vectors are $\vec{r}_1$ and $\vec{r}_2$ respectively. The condition for particles $A$ and $B$ to collide is:

$A$ man is running at a speed of $5 \, m/s$. The rain drops appear to be falling at an angle of $45^{\circ}$ from the vertical. If the rain drops are actually falling vertically downwards,then the velocity of the rain drops (in $m/s$) is:

Two particles $P_1$ and $P_2$ are moving with velocities $v_1$ and $v_2$ respectively. Which of the following statements about their relative velocity $v_{12}$ is true?