Drops of water fall from the roof of a building $9 \mathrm{m}$ high at regular intervals of time, the first drop reaching the ground at the same instant fourth drop starts to fall. What are the distances of the second and third drops from the roof

A disc in which several grooves are cut along the chord drawn from  a point '$\mathrm{A}$', is arranged in a vertical plane, several particles starts slipping from '$\mathrm{A}$' along the grooves simultaneously. Assuming friction and resistance negligible,the time taken in reaching the edge of disc will be:

Two boats $A$ and $B$ are moving along perpendicular paths in a still lake at night. Boat $A$ move with a speed of $3{\mathrm{MS}}^{-1}$ and boat $B$ moves with a speed of $4{\mathrm{MS}}^{-1}$ in the direction such that they collide after sometime. At $t=0,$ the boats are $300\mathrm{m}$ apart. the ratio of distance travelled by boat $A$ to the distance travelled by boat $B$ at the instant of collision is:

A trolley is moving horizontally with a constant velocity of  $v m{s}^{-1}$ $\mathrm{w}.\mathrm{r}.\mathrm{t}.$ earth. $\mathrm{A}$ man starts running from one end of the trolley with a velocity of $1.5{\mathrm{vms}}^{-1}\mathrm{w}.\mathrm{r}.\mathrm{t}.$ to trolley. after reaching the opposite end, the man return back and continues running with a velocity $1.5{\mathrm{vms}}^{-1}\mathrm{w}.\mathrm{r}.\mathrm{t}.$ the trolley in the backward direction. If the length of the trolley is $L$ then the displacement of the man with  respect to earth during the process will be:

A particle $P$ is projected from a point on the surface of smooth inclined plane ( see figure). simultaneously another particle $Q$ is released on the smooth inclined plane from the same position.$P$and $Q$ collide after $t=4$ second. the speed of projection of $P$ is: