Please refer to MCQ Questions Chapter 14 Mathematical Reasoning Class 11 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 11 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 11 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 14 Mathematical Reasoning in Class 11 Mathematics provided below to get more marks in exams.

**Chapter 14 Mathematical Reasoning** **MCQ Questions**

Please refer to the following **Chapter 14 Mathematical Reasoning** ** MCQ Questions Class 11 Mathematics** with solutions for all important topics in the chapter.

**MCQ Questions Answers for Chapter 14 Mathematical Reasoning** **Class 11 Mathematics**

**Question. In mathematical language, the reasoning is of ––––––––– types.**

(a) one

(b) two

(c) three

(d) four

**Answer**

B

**Question. If p, q are true and r is false statement, then which of the following is true statement?**

(a) (p ∧ q) ∨ r is F

(b) (p ∧ q) → r is T

(c) (p ∨ q) ∧ (p ∨ r) is T

(d) (p → q) ↔ (p → r) is T

**Answer**

C

**Question. A compound statement p and q is true only when**

(a) p is true

(b) q is true

(c) both p and q are true

(d) none of p and q is true

**Answer**

C

**Question. If p and q are true statement and r, s are false statements, then the truth value of ~[(p∧~r) ∨ (~q ∨ s)] is**

(a) true

(b) false

(c) false if p is true

(d) none

**Answer**

B

**Question. Which of the following statement is false?**

(a) A quadratic equation has always a real root

(b) The number of ways of seating 2 persons in two chairs out of n persons is P(n, 2)

(c) The cube roots of unity are in GP

(d) None of the above

**Answer**

A

**Question. Which of the following is not a statement?**

(a) Every set is a finite set

(b) 8 is less than 6

(c) Where are you going?

(d) The sum of interior angles of a triangle is 180 degrees

**Answer**

C

**Question. ~ ((~ p) ∧ q) is equal to**

(a) p∨ (~ q)

(b) p∨ q

(c) p ∧ (~ q)

(d) ~ p ∧ ~ q

**Answer**

A

**Question. The connective in the statement : ****“2 + 7 > 9 or 2 + 7 < 9” is**

(a) and

(b) or

(c) >

(d) <

**Answer**

B

**Question. Consider the following statements****p : A tumbler is half empty.****q : A tumbler is half full.****Then, the combination form of “p if and only if q” is**

(a) a tumbler is half empty and half full

(b) a tumbler is half empty if and only if it is half full

(c) Both (a) and (b)

(d) None of the above

**Answer**

B

**Question. The negation of a statement is said to be a ___________**

(a) statement

(b) sentence

(c) negation

(d) ambiguous

**Answer**

A

**Question. If p ⇒(q ∨ r) is false, then the truth values of p, q, r are respectively**

(a) T, F, F

(b) F, F, F

(c) F, T, T

(d) T, T, F

**Answer**

A

**Question. 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**

C

**Question. The false statement in the following is**

(a) p ∧ (~ p) is contradiction

(b) (p ⇒ q) ⇔ (~ q ⇒ ~ p) is a contradiction

(c) ~ (~ p)⇔ p is a tautology

(d) p∨ (~ p)⇔is a tautology

**Answer**

B

**Question. The negation of the statement :****“Rajesh or Rajni lived in Bangalore” is**

(a) Rajesh did not live in Bangalore or Rajni lives in Bangalore.

(b) Rajesh lives in Bangalore and Rajni did not live in Bangalore.

(c) Rajesh did not live in Bangalore and Rajni did not live in Bangalore.

(d) Rajesh did not live in Bangalore or Rajni did not live in Bangalore.

**Answer**

C

**Question. Which of the following is not a negation of the statement “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**

C

**Question. Which of the following is not a statement?**

(a) Please do me a favour

(b) 2 is an even integer

(c) 2 + 1 = 3

(d) The number 17 is prime

**Answer**

A

**Question. The sentence “New Delhi is in India”, is**

(a) a statement

(b) not a statement

(c) may be statement or not

(d) None of the above

**Answer**

A

**Question. The connective in the statement :****“Earth revolves round the Sun and Moon is a satellite of earth” is**

(a) or

(b) Earth

(c) Sun

(d) and

**Answer**

D

**Question. The false statement in the following is**

(a) p ∧(~ p) is contradiction

(b) (p ⇒ q) ⇔ (~ q ⇒ ~ p) is a contradiction

(c) ~ (~ p) ⇔ p is a tautology

(d) p ∨ (~ p) ⇔ is a tautology

**Answer**

B

**Question. The sentence “There are 35 days in a month” is**

(a) a statement

(b) not a statement

(c) may be statement or not

(d) None of these

**Answer**

A

**ASSERTION – REASON TYPE QUESTIONS**

**(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.****(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion****(c) Assertion is correct, reason is incorrect****(d) Assertion is incorrect, reason is correct.**

**Question. Assertion: “Mathematics is difficult”, is a statement.****Reason: A sentence is a statement, if it is either true or false but not both.**

**Answer**

D

**Question. Assertion : The denial of a statement is called negation of the statement.****Reason : A compound statement is a statement which can not be broken down into two or more statements. **

**Answer**

C

**Question. Assertion: The compound statement with ‘And’ is true if all its component statements are true.****Reason: The compound statement with ‘And’ is false if any of its component statements is false. **

**Answer**

B

**Question. Assertion: ~ (p **→** q) ≡ p ∧ ~ q****Reason: ~ (p** ↔** q) ≡ (p ∨ ~ q) ∧ (q ∧ ~ p) **

**Answer**

C

**Question. Assertion : The negation of (p ∨ ~ q) ∧ q is (~ p ∧ q) ∨ ~ q.****Reason : ~ (p** →** q) ≡ p ∧ ~ q **

**Answer**

B

**Question. Assertion: ~ ( p **↔ **~ q) is equivalent to p **↔ **q .****Reason: ~ ( p **↔ **~ q) is a tautology**

**Answer**

C

**Question. Assertion: The contrapositive of (p ∨ q)** →** r is ~ r** →** ~ p ∧ ~ q.****Reason: If (p ∧ ~ q)** →** (~ p ∨ r) is a false statement, then respective truth values of p, q and r are F, T, T. **

**Answer**

C

**Question. Assertion: ~ (p ∨ q ) ≡ ~ p ∧ ~ q****Reason: ~ (p ∧ q) ≡ ~ p ∨ ~ q **

**Answer**

B

**Question. Assertion: If p** →** (~ p ∨ q) is false, the truth values of p and q are respectively F, T.****Reason: The negation of p** →** (~p ∨ q) is p ∧ ~ q. **

**Answer**

D

**Question. Assertion: The sentence “8 is less than 6” is a statement. ****Reason: A sentence is called a statement, if it is either true or false but not both. **

**Answer**

A