A.repeat (L) = {ww | w ∊ L} //CSL so non-regular Hence Answer is OptionA
B.prefix (L) = {u | ∃v : uv ∊ L}//can be realized by making NFA where all the states are final states.
i.e. L={abc} then Prefix(L)={^,a,ab,abc}
C.suffix (L) = {v | ∃u uv ∊ L}
suffix(L)=Reverse(prefix(Reveres(L))) //we know reverse and prefix closed under regular Hence suffix(L) also regular
i.e. L={abc} then suffix(L)={^,c,bc,abc}
D.half (L) = {u | ∃v : | v | = | u | and uv ∊ L}//https://gateoverflow.in/93981/half-l //Hence Regular
So option A is Ans