According to me this question is unclear but if we thinks that ∊ represents that at the top of the stack there can be anything then only we can say option c is correct ..
But in gate they will not ask such unclear and confusing question...
at state B
there should be following transitions specified..
∱(B,b,Zo)=(B,bZ0) , ∱(B,a,Zo)=(B,aZ0) , ∱(B,b,b)=(B,bb), ∱(B,b,a)=(B,ba),
∱(B,a,a)=(B,aa) , ∱(B,a,b)=(B,ab)
Hope this will clear your doubt...