A solid conducting sphere of radius a carries charge +Q. It is surrounded by a concentric thick conducting shell of inner radius b and outer radius c…

Field inside the conductor of the shell must vanish, so induced charge on the inner surface is $-Q$ and, since the shell is neutral and isolated, $+Q$ appears on the outer surface: (A) and (B) are true. Potential of the sphere is the sum of contributions from all spherical surfaces: $k\left(\dfrac Qa-\dfrac Qb+\dfrac Qc\right)$, so (C) is true. On earthing, the outer charge flows away, the outer surface is at zero potential and the sphere's potential becomes $kQ\left(\dfrac1a-\dfrac1b\right)$, not with $c$; (D) is false.