A mass suspended from a vertical spring performs S.H.M. of period 0.1 second. The spring is unstretched at the highest point of suspension. Maximum speed of the mass is (Gravitational acceleration $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

For a thin prism, $\delta_1$ is the angle of deviation produced, when prism is placed in air. When the prism is immersed in water, the angle of deviation produced is $\delta_2$. Given ${ }_{\mathrm{a}} \mu_{\mathrm{g}}=\frac{3}{2}$ and ${ }_{\mathrm{a}} \mu_{\mathrm{w}}=\frac{4}{3}$. The ratio $\delta_2: \delta_1$ is

For a common emitter transistor, if $\frac{I_{\mathrm{C}}}{I_{\mathrm{E}}}=0.95$, then the current gain is

A string of mass $0.1 \mathrm{kgm}^{-1}$ has length 0.9 m . It is fixed at both ends and stretched such that it has a tension of 40 N . The string vibrates in three segments with amplitude 0.3 cm . The amplitude (maximum) of the particle velocity is (in $\mathrm{m} / \mathrm{s}$)