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?

As a charge Q is placed at center there will be induced charge -Q at inner surface of sphere. hence charge a charge of additional Q is induced on the outer surface of the spherical shell.

$\text{⇒charge density }\frac{2Q}{4\pi r^2}=\frac{Q}{2\pi r^2}$

Just outside S, the charge and shell will act as a 2Q charge placed at C, therefore the field will be double that of just inside the shell.

At any point inside S, the electric field is only due to the charge Q placed at C, hence the electric field is inversely proportional to the square of its distance from C