A solid conducting sphere of radius 1 cm carries charge +4 nC. It is surrounded concentrically by a thick conducting spherical shell of inner radius…

Gauss's law in the conducting shell material requires zero field, so the inner surface of the shell carries $-4\ \mathrm{nC}$ to cancel the $+4\ \mathrm{nC}$ enclosed. The shell total is $-1\ \mathrm{nC}$, so its outer surface holds $-1-(-4)=+3\ \mathrm{nC}$. Thus (A) is false and (B) is true. The potential of the inner sphere is the sum of three contributions, $V=k\left[\dfrac{q_1}{a}-\dfrac{q_1}{b}+\dfrac{q_1+q_2}{c}\right]=9\times10^{9}\times10^{-7}\,(4-2+1)\ \mathrm{V}=2700\ \mathrm{V}$ (C true). When the shell is earthed its potential is zero, so the outer surface charge leaves (becomes zero) and the inner sphere's potential is $kq_1\left(\dfrac1a-\dfrac1b\right)=9\times10^9\times4\times10^{-9}\times50=1800\ \mathrm{V}$ (D true).