A steel wire of length 81 cm has a mass of $5 \times 10^{-3} \mathrm{~kg}$.

If the wire is under a tension of 50 N , then the speed of transverse waves on the wire is

A light ray incidents on an equilateral prism made of material of refractive index $\sqrt{3}$. Inside the prism, if the light ray moves parallel to the base of the prism, then the angle of incidence of the light ray is

An unpolarised beam of light incidents on a group of three polarising sheets arranged such that the angle between the axes of any two adjascent sheets is $30^{\circ}$. The ratio of the intensities of polarised light emerging from the second and third sheets is

In a region, the electric field is given by $\mathbf{E}=(3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}) \mathrm{NC}^{-1}$. The electric flux through a surface of area $3 \mathrm{~m}^2$ in $y z$-plane is (in SI units)