A thin-walled spherical conducting shell S of radius R is given charge Q. The same amount of charge is also placed at its center C. Which of the following statements are correct? 

On the outer surface of S, the charge density is $\mathrm{Q}/2{\mathrm{\pi R}}^2$.

The electric field is zero at all points inside S.

At a point just outside S, the electric field is double the field at a point just inside S in the cavity.

At any point inside S (i.e., within its cavity), the electric field is inversely proportional to the square of its distance from C.