These Mathematical Reasoning Questions And Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Mathematical Reasoning Questions And Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## Mathematical Reasoning Questions And Answers

1. If (p or q) is false when

(A) p is true and q is false

(B) p is true and q is true

(C) p is false and q is false

(D) p is false and q is true

**Answer:** p is true and q is false

2. p if and only if q is written as

(A) p => q

(B) q => p

(C) p <=> q

(D) q <=> p

**Answer:** p <=> q

3. The compound statement with AND is true if all its component statements are

(A) true

(B) false

(C) either true or false

(D) None of these

**Answer:** true

4. Which of the following is a statement

(A) x is a real number

(B) Switch of the fan

(C) 6 is a natural number

(D) Let me go

**Answer:** 6 is a natural number

5. Which of the following is not a statement

(A) The product of (-1) and 8 is 8

(B) All complex number are real number

(C) Today is windy day

(D) All of the above

**Answer:** All of the above

6. The converse of the statement p ? q is

(A) p ? q

(B) q ? p

(C) ~p ? q

(D) ~q ? p

**Answer:** q ? p

7. Which of the following is the conditional p ? q

(A) q is sufficient for p

(B) p is necessary for q

(C) p only if q

(D) if q then p

**Answer:** p only if q

8. If (p and q) is false then

(A) p is true and q is false

(B) p is false and q is false

(C) p is false and q is true

(D) all of the above

**Answer:** all of the above

9. Which of the following statement is conjuction?

(A) Ram and Shyam are friends.

(B) Both Ram and Shyam are tall.

(C) Both Ram and Shyam are enemies.

(D) None of the above.

**Answer:** None of the above.

10. Which of the following is not a negation of “A natural number is greater than zero”?

(A) A natural number is not greater than zero.

(B) It is false that a natural number is greater than zero.

(C) It is false that a natural number is not greater than zero.

(D) None of the above

**Answer:** It is false that a natural number is not greater than zero.

11. The negation of the statement “The product of 3 and 4 is 9” is

(A) It is false that the product of 3 and 4 is 9.

(B) The product of 3 and 4 is 12.

(C) The product of 3 and 4 is not 12.

(D) It is false that the product of 3 and 4 is not 9.

**Answer:** It is false that the product of 3 and 4 is 9.

12. The contrapositive of statement “If Chandigarh is Capital of Punjab, then Chandigarh is in India” is

(A) If Chandigarh is not in India, then Chandigarh is not the Capital of Punjab.

(B) If Chandigarh is in India, then Chandigarh is Capital of Punjab.

(C) If Chandigarh is not Capital of Punjab, then Chandigarh is not Capital of India.

(D) If Chandigarh is Capital of Punjab, then Chandigarh not in India.

**Answer:** If Chandigarh is not in India, then Chandigarh is not the Capital of Punjab.

13. The statement “If x^{2} is not even, then x is not even” is converse of the statement.

(A) If x^{2} is odd, then x is even.

(B) If x is not even, then x2 is not even.

(C) If x is even, then x2 is even.

(D) If x is odd, then x2 is even.

**Answer:** If x is not even, then x2 is not even.

14. The contrapositive of the statement “If p, then q”, is

(A) If q, then p

(B) If p, then ~ q

(C) If ~ q, then ~ p

(D) If ~ p then ~ q

**Answer:** If ~ q, then ~ p

15. The converse of the statement “If Sun is not shining, then Sky is filled with clouds” is

(A) If Sky is filled with clouds, then the Sun is not shining.

(B) If Sun is shining, then Sky is filled with clouds.

(C) If Sky is clear, then Sun is shining.

(D) If Sun is not shining, then Sky is not filled with clouds.

**Answer:** If Sky is filled with clouds, then the Sun is not shining.

16. The converse of the statement “If x > y, then x + a > y + a” is

(A) If x < y, then x + a < y + a

(B) If x + a > y + a, then x > y

(C) If x < y, then x + a > y + a

(D) If x > y, then x + a < y + a

**Answer:** If x + a > y + a, then x > y

17. The contrapositive of the statement “If 7 is greater than 5, then 8 is greater than 6” is

(A) If 8 is greater than 6, then 7 is greater than 5.

(B) If 8 is not greater than 6, then 7 is greater than 5.

(C) If 8 is not greater than 6, then 7 is not greater than 5.

(D) If 8 is greater than 6, then 7 is not greater than 5.

**Answer:** If 8 is not greater than 6, then 7 is not greater than 5.

18. The negation of the statement “101 is not a multiple of 3” is

(A) 101 is a multiple of 3.

(B) 101 is a multiple of 2.

(C) 101 is an odd number.

(D) 101 is an even number.

**Answer:** 101 is a multiple of 3.

19. The negation of the statement “Rajesh or Rajni lived in Bengaluru” is

(A) Rajesh did not live in Bengaluru or Rajni lives in Bengaluru.

(B) Rajesh live in Bengaluru and Rajni did not live in Bengaluru.

(C) Rajesh did not live in Bengaluru and Rajni did not live in Bengaluru.

(D) Rajesh did not live in Bengaluru or Rajni did not live in Bengaluru.

**Answer:** Rajesh did not live in Bengaluru and Rajni did not live in Bengaluru.

20. The negative of the statement “Plants take in CO_{2} and give out O_{2}” is

(A) Plants do not take in CO_{2} and do not give out O_{2}.

(B) Plants do not take in CO_{2} or do not give out O_{2}.

(C) Plants take in CO_{2} and do not give out O_{2}.

(D) Plants take in CO_{2} or do not give out O_{2}.

**Answer:** Plants do not take in CO_{2} or do not give out O_{2}.