(A) False.
\(L_1\) is not a regular language. Any language that requires comparing or matching counts across different parts of the string (such as ensuring equality or symmetry) cannot be accepted by a finite automaton. Finite automata have no memory to store and compare such information, hence \(L_1\) is non-regular. Therefore, the statement in option (A) is false.
(B) True.
\(L_1\) is a context-free language since a pushdown automaton can use its stack to keep track of the number of symbols in one part of the string and match them later. Similarly, \(L_2\) is context-free because pushdown automata can recognize patterns involving a string and its reverse by pushing symbols onto the stack and popping them in reverse order. Hence, both languages are context-free, making option (B) true.
(C) True.
\(L_1\) is regular because it follows a simple repetitive structure that can be recognized without additional memory. \(L_2\) is context-free since recognizing a string followed by its reverse requires stack-based memory, which is provided by pushdown automata. Thus, the statement in option (C) is true.
(D) True.
Both \(L_1\) and \(L_2\) are context-free languages as they can be generated by context-free grammars. However, neither language is regular due to the need for matching conditions and reversal properties, which cannot be handled by finite automata. Hence, option (D) is true.