A beam of light is incident on a glass plate at an angle of $$60^{\circ}$$. The reflected ray is polarized. If angle of incidence is $$45^{\circ}$$ then angle of refraction is

Consider a light planet revolving around a massive star in a circular orbit of radius '$$r$$' with time period '$$T$$'. If the gravitational force of attraction between the planet and the star is proportional to $$\mathrm{r}^{\frac{7}{2}}$$, then $$\mathrm{T}^2$$ is proportional to

A potentiometer wire has length of $$5 \mathrm{~m}$$ and resistance of $$16 \Omega$$. The driving cell has an e.m.f. of $$5 \mathrm{~V}$$ and an internal resistance of $$4 \Omega$$. When the two cells of e.m.f.s $$1.3 \mathrm{~V}$$ and $$1.1 \mathrm{~V}$$ are connected so as to assist each other and then oppose each other, the balancing lengths are respectively

Four massless springs whose force constants are $$2 \mathrm{~K}, 2 \mathrm{~K}, \mathrm{~K}$$ and $$2 \mathrm{~K}$$ respectively are attached to a mass $$\mathrm{M}$$ kept on a frictionless plane as shown in figure, If mass $$M$$ is displaced in horizontal direction then frequency of oscillating system is