$A$ and $B$ are concentric conducting spherical shells. $A$ is given a positive charge while $B$ is earthed. Then :-
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The charge on sphere $B$ due to ground potential of zero is $-Q$ on the inner surface. Charge density on $A$ is $Q / 4 \pi r_{A}^{2}$ and that of $B$ is $-Q / 4 \pi r_{B}^{2} .$ So two charge densities are not equal.
option $A$ is incorrect.
The two sphere system act as the concentric sphere capacitor.
By Gauss'law, The electric field is zero inside $A$ and outside the $B$.
But it is $non-zero$ between $A$ and $B$.
So option $\mathrm{B}$ and $\mathrm{D}$ are incorrect.
option $C$ is incorrect.
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