A and B are two concentric spheres If A is given a charge Q while B is earthed as shown in figure :

The field between A and B is not zero

∵ B is grounded, V_B = 0

$\frac{k Q_B}{R}+\frac{k Q_B}{R}=0$  (R = radius of shell B)

$Q_B=-Q_A$

$\sigma_B=-Q$

$\sigma_B=-\frac{Q}{4 \pi R^2}$

But $\sigma_A=\frac{Q}{4 \pi r^2}$

∴ (A) is not correct

Apply Gauss's theorem. Only (C) is correct.