MTH202 Quiz 2022 by Knowledge for Us

MTH-202 Quiz File · By Knowledge for us · Attiq Kundi

1. In the proof by contradiction, we lead the assumption to___.

Answer: absurdity

2. The predicate describing the initial state is called____.

Answer: pre-condition of the algorithm

3. An integer n is prime number, if and only if for all positive integers r and s, if n= rs then____.

Answer: r = 1 or s = 1.

Q4. If ‘f’ is a perfect square, then which of the following is the correct representation of ‘r’?

Answer: r = k^2 for some integer k

Q5. Which of the following is not a rational number?

Answer: √𝟕

6. To prove by mathematical induction for 1+2+3+...+n= (n) (n+1)/2 for all positive integers, the basis step is____.

Answer: 1 = (1) (1+1)/2

7. GCD of (8, 12) will be____.

Answer: 4

8. The statement 4n>3n+4 is true when____.

Answer: 𝒏≥𝟐

9. If n is any positive integer then 2n≥ 2 (n+1) is true for all_____.

Answer: 𝒏≥𝟑

10. The sum of (6-7√2) and (6+ 7√2) is____.

Answer: 12

11. The sum of two integers is not an even integer when____.
12. If n is an add integer then ‘3n+2’ is____.

Answer: odd

13. The sum of any rational number and any irrational number is irrational.

Answer: true

14. A proof by___is based on the logical equivalence between a statement and its contrapositive.

Answer: contrapositive

15. For every prime number n, n+2 is prime. Which of the following prime number disproves the above statement.

Answer: n=7

Q16. In basis property the first iteration of the loop is solved for?

Answer: I (0).

17. For all integers n>0 1+2+2^2+___+2^n=___.

Answer: 2^ (n-1)

18. In division algorithm ‘r’ stands for____.

Answer: remainder.

19. If n is any positive integer then the sequence 3+6+9+-----+3n =_____.
20. For all positive real numbers a and b, if a<b, then____.

Answer: a^2 < b^2

Q21. The last step of describing algorithms formally is?

Answer: An end statement

22. If ‘n’ is an odd integer then n^3+n is___

Answer: even

23. Proof by____uses the equivalence p→q = -q→𝑝.

Answer: Contraposition

24. The product of an even and odd integer is____.

Answer: even

25. In the Direct Proof, we show that if the statement p is true, then the statement q is___.

Answer: True

26. (-1)^n = 1 for n = ___. (^ stands for power)

Answer: 4

Q27. Which of the following is true for n = 1?

Answer: 2^ (2n) – 1 by 3

28. Proof by____uses the equivalence p→q =(p⋀−q)→𝑐.

Answer: Contradiction

29. Proof by contradiction is a/an____method of proof.

Answer: Indirect.