Consider the following languages. $$L_1 = \{a^p \mid p \text{ is a prime number}\}$$ $$L_2 = \{a^n b^m c^{2m} \mid n \ge 0, m \ge 0\}$$ $$L_3 = \{a^n b^n c^{2n} \mid n \ge 0\}$$ $$L_4 = \{a^n b^n \mid n \ge 1\}$$ Which of the following are CORRECT? I. $L_1$ is context-free but not regular. II. $L_2$ is not context-free. III. $L_3$ is not context-free but recursive. IV. $L_4$ is deterministic context-free.

Consider the following languages. L1 = \ap p is a prime number\ L2 = \an bm c2m n 0, m 0\ L3 = \an bn c2n n 0\ L4 = \an bn n 1\ Which of the following are CORRECT? I. L1 is context-free but not regular. II. L2 is not context-free. III. L3 is not context-free but recursive. IV. L4 is deterministic context-free.

Topic-wise GATE CS PYQs with verified steps