Clearly , looking into DFA we can say that C is Dead state.
Using Arden's theoram to find the regular expression :
A = ε + A0 = ε0* = 0*
B = A1 + B1 = 0*1 +B1 = 0*11* = 0*1*
Therefore answer is 0*1*
PS : Ardens theoram -
Let P and Q be two regular expressions.
If P does not contain null string, then R = Q + RP has a unique solution that is R = QP*