Q1: 1. Which of the following statements is true about context-free languages?

• A) They can be recognized by finite automata
• B) They can be recognized by pushdown automata
• C) They can be recognized by Turing machines
• D) They can be recognized by regular expressions

Q2: 2. A real-life problem that can be modeled as a context-free language is

• A) Validating email addresses
• B) Sorting a list of integers
• C) Finding the shortest path in a graph
• D) Calculating the square root of a number

Q3: 3. Which of the following is a property of context-free languages?

• A) Closure under intersection
• B) Closure under complement
• C) Closure under concatenation
• D) Closure under Kleene star

Q4: 4. Consider a language L = {a^n b^n | n ≥ 0}. Is this language a context-free language?

• A) Yes
• B) No
• C) Cannot be determined
• D) None of the above

Q5: 5. A real-life problem that can be solved using context-free languages is

• A) Predicting stock market trends
• B) Parsing arithmetic expressions
• C) Image recognition
• D) Encrypting data

Q6: 6. Which of the following is a limitation of context-free languages?

• A) They cannot handle nested structures
• B) They cannot recognize regular languages
• C) They cannot be generated by context-free grammars
• D) They cannot be used in web development

Q7: 7. The language L = {a^n b^n c^n | n ≥ 0} is

• A) Context-free
• B) Regular
• C) Context-sensitive
• D) None of the above

Q8: 8. In the context of context-free languages, what is the pumping lemma used for?

• A) To prove a language is regular
• B) To prove a language is context-free
• C) To prove a language is context-sensitive
• D) To prove a language is recursively enumerable

Q9: 9. Which of the following automata is most powerful in recognizing context-free languages?

• A) Deterministic finite automaton (DFA)
• B) Non-deterministic finite automaton (NFA)
• C) Pushdown automaton (PDA)
• D) Turing machine

Q10: 10. A context-free grammar is used to describe

• A) Regular languages
• B) Context-free languages
• C) Context-sensitive languages
• D) Recursive enumerable languages

Q11: 11. The language L = {ww^R | w ∈ {a, b}*} is

• A) Context-free
• B) Regular
• C) Context-sensitive
• D) Recursive enumerable

Q12: 12. Which of the following is an example of a context-free language?

• A) {0^n 1^n | n ≥ 0}
• B) {0^n 1^m | n, m ≥ 0}
• C) {0^n 1^m 0^n | n, m ≥ 0}
• D) {0^m 1^n | n, m ≥ 0}

Q13: 13. The language L = {a^n b^m c^m d^n | n, m ≥ 0} is

• A) Context-free
• B) Regular
• C) Context-sensitive
• D) None of the above

Q14: 14. Which of the following operations can change a context-free language into a regular language?

• A) Intersection
• B) Union
• C) Kleene star
• D) Complementation

Q15: 15. A real-life problem that can be represented using context-free grammars is

• A) Spell-checking text documents
• B) Solving differential equations
• C) Detecting fraudulent activities in banking transactions
• D) Generating random numbers

Q16: 16. The language L = {a^n b^n c^n d^n | n ≥ 0} is

• A) Context-free
• B) Regular
• C) Context-sensitive
• D) None of the above

Q17: 17. Which of the following is NOT a property of context-free languages?

• A) Closure under union
• B) Closure under intersection
• C) Closure under concatenation
• D) Closure under Kleene star

Q18: 18. A context-free language can be recognized by

• A) A deterministic Turing machine
• B) A non-deterministic finite automaton
• C) A pushdown automaton
• D) A regular expression

Q19: 19. Consider the language L = {a^n b^m c^m d^n | n, m ≥ 0}. Is this language context-free?

• A) Yes
• B) No
• C) Cannot be determined
• D) None of the above

Q20: 20. Which of the following statements is true about context-free grammars?

• A) They can generate regular languages
• B) They can generate context-sensitive languages
• C) They can generate recursively enumerable languages
• D) They can generate context-free languages

Q21: 21. A real-life problem that can be solved using context-free grammars is

• A) Predicting weather patterns
• B) Parsing XML documents
• C) Solving Sudoku puzzles
• D) Playing video games

Q22: 22. The language L = {a^n b^m | n ≠ m} is

• A) Context-free
• B) Regular
• C) Context-sensitive
• D) None of the above

Q23: 23. Which of the following is a method used to prove that a language is not context-free?

• A) Pumping lemma
• B) Myhill-Nerode theorem
• C) Closure properties
• D) Reduction to halting problem

Q24: 24. A context-free grammar consists of

• A) Terminals, non-terminals, start symbol, and productions
• B) Regular expressions, automata, and states
• C) Transition functions, input alphabet, and final states
• D) Stack, input tape, and transition rules

Q25: 25. The language L = {a^n b^m c^m | n, m ≥ 0} is

• A) Context-free
• B) Regular
• C) Context-sensitive
• D) None of the above