If $\overrightarrow{F} = (60 \hat{i} + 15 \hat{j} - 3 \hat{k}) \; N$ and $\overrightarrow{V} = (2 \hat{i} - 4 \hat{j} + 5 \hat{k}) \; m/s$,then the instantaneous power is: (in $; W$)

$A$ body is moved along a straight line by an engine which delivers a constant power. The distance moved by the body in time $t$ is proportional to:

$1\,kWh$ is a unit of power. This statement is true or false? If it is wrong,then correct it.

$A$ pump on the ground floor can pump up water to fill a tank of volume $30 \ m^3$ in $15 \ minutes$. If the tank is $40 \ m$ above the ground and the efficiency of the pump is $30\%$,then the electric power consumed by the pump is ....... $kW$.

An electric pump is used to fill an overhead tank of capacity $9\,m^3$ kept at a height of $10\,m$ above the ground. If the pump takes $5\,minutes$ to fill the tank by consuming $10\,kW$ power,the efficiency of the pump should be : ............... $\%$ (Take $g = 10\,m/s^2$)

$A$ body of mass $m$ starts from rest and moves with uniform acceleration such that it attains a velocity $v$ in time $T$. The instantaneous power delivered to the body as a function of time $t$ is given by: