B

Step 1: Understanding the system
We have three concentric spherical shells A, B, and C with charges q, 0, and -q, respectively. Shell B is earthed, meaning it is at zero potential.
Step 2: Charge distribution
Since the electric field inside a charged conductor is zero, the charge on shell B must redistribute itself to maintain this condition. Given that shell A has a charge q and shell C has a charge -q, they influence the charge on shell B.
Step 3: Calculating the charge on shell B
The net charge on shell A (+q) induces an equal and opposite charge on the inner surface of shell B. Hence, there will be a -q charge on the inner surface of shell B. Since B is earthed, the total charge on the outer surface of B must balance it out.
Let the charge on the outer surface of shell B be Q_B. The total charge on shell B is zero, hence:
0 = Q_B - q
Therefore,
Q_B = +q.
Step 4: Charge on outer surface of shell C
Since shell C has a charge of -q and the inner surface of shell C must balance the charge on the inner surface of shell B, it must have a charge of +q on its inner surface. Therefore, the total charge on the outer surface of shell C will be:
Q_C = -q (total charge of shell C) - (+q) (induced charge on the inner surface) = -2q.
Conclusion
Thus, the charges appearing on the outer surfaces of shells B and C are +q and -2q, respectively.