$A$ pump is required to lift $1000 \, kg$ of water per minute from a well of depth $10 \, m$ and eject it with a speed of $10 \, m/s$. The horsepower of the engine needed is: (Assume $g = 10 \, m/s^2$)

Two men with weights in the ratio $4:3$ run up a staircase in time in the ratio $12:11$. The ratio of power of the first to that of second is

$A$ particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement $(s)$ - time $(t)$ graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale)

$A$ man does a given amount of work in $10 \ s$. Another man does the same amount of work in $20 \ s$. The ratio of the output power of the first man to the second man is:

$A$ car of mass $m$ has an engine which can deliver power $P$. The minimum time in which the car can be accelerated from rest to a speed $v$ is .............

$A$ force of $(60 \hat{i} + 15 \hat{j} - 3 \hat{k}) \text{ N}$ produces a velocity of $(2 \hat{i} - 4 \hat{j} + 5 \hat{k}) \text{ m/s}$ in a particle. The value of power at that time will be: (in $\text{ W}$)