$A$ particle of mass $M$ starting from rest undergoes uniform acceleration. If the speed acquired in time $T$ is $V$,then the power delivered to the particle in time $T$ is:

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

Which one of the following is a secondary alcohol?

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $T_1 = \frac{4}{5} \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $T_2 = \frac{3}{5} \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,what is its new time period in seconds?

The transition from the state $n = 4$ to $n = 3$ in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition:

$\int_0^\pi \frac{x \tan x}{\sec x+\tan x} d x=$