Q1: 1. Which of the following best describes computability in Theory of Computation?

• A) The ability to determine if a problem can be solved by an algorithm
• B) The ability to solve any computational problem
• C) The ability to compute complex mathematical functions
• D) The ability to store and process data efficiently

Q2: 2. In the context of computability, which of the following is an example of an undecidable problem?

• A) Sorting a list of integers in ascending order
• B) Determining if a given program will halt on a given input
• C) Finding the shortest path between two nodes in a graph
• D) Calculating the determinant of a matrix

Q3: 3. What is the main goal of decidability in Theory of Computation?

• A) To develop algorithms that can solve any computational problem
• B) To determine the limits of computation and what can be computed
• C) To optimize the efficiency of algorithms
• D) To design programming languages for specific applications

Q4: 4. Which of the following statements is true regarding decidable problems?

• A) Decidable problems can always be solved using a simple algorithm
• B) Decidable problems have a clear and definite solution
• C) Decidable problems are always easier to solve than undecidable problems
• D) Decidable problems are limited to theoretical scenarios only

Q5: 5. Consider the real-life problem of determining whether a given chess position is a checkmate. Is this problem decidable or undecidable?

• A) Decidable
• B) Undecidable
• C) Depends on the complexity of the chess position
• D) Not enough information to determine

Q6: 6. Which of the following is an example of an undecidable problem in the context of computability?

• A) Finding the average of a list of numbers
• B) Checking if a given number is prime
• C) Determining if a given program will output a specific value
• D) Sorting a list of names in alphabetical order

Q7: 7. In the Theory of Computation, decidability refers to the ability to

• A) Solve any computational problem efficiently
• B) Determine if a problem can be solved by an algorithm
• C) Process data using advanced algorithms
• D) Store and retrieve information accurately

Q8: 8. Which of the following statements best describes undecidable problems?

• A) Undecidable problems have a unique solution that can be computed
• B) Undecidable problems cannot be solved by any algorithm
• C) Undecidable problems are always related to complex mathematical calculations
• D) Undecidable problems are limited to theoretical scenarios

Q9: 9. Consider a real-life problem of verifying the correctness of a program that simulates weather patterns. Is this problem decidable or undecidable?

• A) Decidable
• B) Undecidable
• C) Depends on the complexity of the program
• D) Not enough information to determine

Q10: 10. Which of the following is an example of a decidable problem in the context of computability?

• A) Finding the square root of a negative number
• B) Checking if a given string is a palindrome
• C) Solving a system of linear equations
• D) Generating a random number

Q11: 11. In the Theory of Computation, computability refers to the

• A) Ability to solve any computational problem efficiently
• B) Ability to determine if a problem can be solved by an algorithm
• C) Process of optimizing algorithms for faster computation
• D) Design of hardware components for computing tasks

Q12: 12. Which of the following is a characteristic of decidable problems?

• A) They always have a finite number of solutions
• B) They can be solved by any programming language
• C) They have a clear and definite solution that can be computed
• D) They are limited to simple computational tasks

Q13: 13. Consider the real-life problem of determining the validity of a given logical statement. Is this problem decidable or undecidable?

• A) Decidable
• B) Undecidable
• C) Depends on the complexity of the logical statement
• D) Not enough information to determine

Q14: 14. Which of the following best describes undecidable problems in the Theory of Computation?

• A) Problems that have multiple solutions
• B) Problems that cannot be solved by any algorithm
• C) Problems that require advanced computational techniques
• D) Problems that are limited to specific domains

Q15: 15. In the context of computability, an undecidable problem is one for which

• A) A correct solution exists but cannot be computed
• B) No algorithm can be constructed to always provide a correct answer
• C) The problem is too complex to be understood by humans
• D) The problem requires extensive computational resources to solve

Q16: 16. Which of the following statements is true regarding decidability in Theory of Computation?

• A) Decidability implies that a problem can be solved by any means
• B) Decidability is about determining the solvability of a problem by an algorithm
• C) Decidability is only relevant for mathematical problems
• D) Decidability guarantees a unique solution for every problem

Q17: 17. Consider a real-life problem of verifying the correctness of a computer program that predicts stock market trends. Is this problem decidable or undecidable?

• A) Decidable
• B) Undecidable
• C) Depends on the accuracy of the predictions
• D) Not enough information to determine

Q18: 18. Which of the following is an example of a decidable problem in the Theory of Computation?

• A) Determining if a given program will crash on a specific input
• B) Calculating the value of an irrational number
• C) Checking if two given strings are anagrams
• D) Finding the shortest path in a weighted graph

Q19: 19. In the Theory of Computation, decidability is concerned with

• A) Solving computational problems using parallel processing
• B) Determining if a problem can be solved by an algorithm
• C) Developing algorithms for specific applications
• D) Storing and retrieving data efficiently

Q20: 20. Which of the following best defines undecidable problems in the context of computability?

• A) Problems that have no practical applications
• B) Problems that can only be solved by expert programmers
• C) Problems that cannot be solved by any algorithm
• D) Problems that are limited to theoretical discussions

Q21: 21. Consider the real-life problem of verifying the correctness of a machine learning model for predicting customer preferences. Is this problem decidable or undecidable?

• A) Decidable
• B) Undecidable
• C) Depends on the complexity of the model
• D) Not enough information to determine

Q22: 22. Which of the following statements is true regarding computability in the Theory of Computation?

• A) Computability guarantees the efficient solution of any problem
• B) Computability is about determining the solvability of a problem by an algorithm
• C) Computability is limited to mathematical calculations only
• D) Computability ensures that every problem has a unique solution

Q23: 23. In the context of computability, an undecidable problem is one that

• A) Can be solved by any programming language
• B) Has multiple correct solutions
• C) Cannot be solved by any algorithm
• D) Requires extensive computational resources to solve

Q24: 24. Which of the following best describes decidable problems in the Theory of Computation?

• A) Problems that can be solved using trial and error
• B) Problems that have a clear and definite solution that can be computed
• C) Problems that are only relevant for scientific research
• D) Problems that require specialized hardware to solve

Q25: 25. Consider a real-life problem of verifying the correctness of a cryptographic algorithm. Is this problem decidable or undecidable?

• A) Decidable
• B) Undecidable
• C) Depends on the complexity of the algorithm
• D) Not enough information to determine