Which of the following statements is true?
Answer is (B).
(A) is wrong as a language can be context free even if it is being accepted by non-deterministic PDA for ex- $\{ ww^r: w \in \Sigma^*$ and $w^r$ is reverse of $w\}$
(C) and (D) not always true as Context free languages are not closed under Complement or Intersection.
I think example of A is wrong ... it will be { WWr : W ∈(a,b)+ and Wr is reverse} ... correct me if i am wrong ...
Edit : { WWr : W ∈(a,b)* and Wr is reverse} ... both r npda .... My mistake ...
Answer is only (B) because Deterministic push down automata can recognize only deterministic context free languages and cannot recognize non- deterministic context free languages.
Non Deterministic push down automata can recognize all the context free languages(both deterministic and non- deterministic).
You can also refer similar GATE question https://gateoverflow.in/3650/gate2004-it-9?show=4336#a4336.
The statement in your answer should have been this - "(A) is wrong as a language can be context-free even if it is being not accepted by deterministic PDA for e.g., ...". We don't care whether a CFL is accepted by a non-deterministic PDA or not. Here we concentrate on Deterministic PDA. The key concept here is NDPA ≠ DPDA, i.e., to say NDPA is more powerful than DPDA.