$A$ passenger sitting in a train $A$ moving at $90\,km/h$ observes another train $B$ moving in the opposite direction for $8\,s$. If the velocity of the train $B$ is $54\,km/h$,then the length of train $B$ is $..........\,m$.

$A$ bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane,the trajectory of the bomb is a:

Two towns $A$ and $B$ are connected by a regular bus service with a bus leaving in either direction every $T$ min. $A$ man cycling with a speed of $20 \,km/h$ from $A$ to $B$ notices that a bus travelling in the direction of his motion goes past him every $18 \,min$ and every $6 \,min$ he notices a bus travelling in the opposite direction go past him. Assuming that the buses travel with a constant speed,find $T$ and the constant speed of the buses.

$A$ man crosses a $320 \ m$ wide river perpendicular to the current in $4 \ minutes$. If in still water he can swim with a speed $5/3$ times that of the current,then the speed of the current,in $m/min$ is

$A$ steam boat goes across a lake and comes back: $(i)$ on a quiet day when the water is still and $(ii)$ on a rough day when there is a uniform current so as to help the journey onward and to impede the journey back. If the speed of the launch,on both days,was same,the time required for the complete journey on the rough day as compared to that on the quiet day,will be

Two particles are moving along two long straight lines,in the same plane,with the same speed $= 20 \, cm/s$. The angle between the two lines is $60^{\circ}$,and their intersection point is $O$. At a certain moment,the two particles are located at distances $3 \, m$ and $4 \, m$ from $O$,and are moving towards $O$. Subsequently,the shortest distance between them will be