Power supplied to a particle of mass $2 \ kg$ varies with time as $P = \frac{3t^2}{2} \ W$. Here,$t$ is in $s$. If the velocity of the particle at $t = 0$ is $v = 0$,the velocity of the particle at time $t = 2 \ s$ will be ............. $m/s$.

$A$ source of sound of frequency $640 ~Hz$ is moving at a velocity of $\frac{100}{3} ~m/s$ along a road,and is at an instant $30 ~m$ away from a point $A$ on the road (as shown in figure). $A$ person standing at $O$,$40 ~m$ away from the road,hears sound of apparent frequency $v^{\prime}$. The value of $v^{\prime}$ is (velocity of sound $= 340 ~m/s$). (in $~Hz$)

Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in a circular orbit of radius $R$ around the sun will be proportional to

Which of the following substances imparts a green color to the burner flame?

Thermite is a mixture of iron oxide and which of the following?

If $\frac{dy}{dx} = \frac{y + x \tan(\frac{y}{x})}{x}$,then $\sin(\frac{y}{x})$ is equal to