Considering (a+b)*:
L = xww is regular. Since, w can be ϵ and x∈(a+b)∗, making L=Σ∗. i.e.; the set of strings generated by L is {ϵ,a,b,aa,ab,ba,bb,aaa,…}=Σ∗
L = xww^R is also regular.
Considering (a+b)+:
L = xww is CSL. Since x∈(a+b)+ , w cant be ϵ , so string comparison is required.
L = xww^R is NCFL.