A force acting on a body of mass 5 Kg is $(4 \hat{i}-2 \hat{j}+3 \hat{k}) \mathrm{N}$. If the body is initially at rest then the magnitude of its velocity at the end of 10 second in $\mathrm{m} / \mathrm{s}$ will be

The length of closed and open pipe is same. The ratio of frequency of $\mathrm{n}^{\text {th }}$ overtone for closed pipe to that of open pipe is (Neglect end correction)

An e.m.f. $e=E_0 \cos \omega t$ is applied to a circuit containing $L, C$ and $R$ in series where $X_L=3 R$ and $\mathrm{X}_{\mathrm{C}}=\mathrm{R}$. The average power dissipated in the circuit is

The temperature of an air bubble while rising from bottom to surface of a lake remains constant but diameter is doubled. If pressure on the surface is $h$ meter of mercury column and relative density of mercury is ' $\rho$ ' then the depth of the lake is