Below you will find **MCQ Questions of Chapter 14 Mathematical Reasoning Class 11 Maths Free PDF Downlo**ad that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 11 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 11 Maths Chapter 14 Mathematical Reasoning with answers

1. A sentence is called a mathematically accepted statement if

(a) it’s true

(b) it’s either true or false but not both.

(c) it’s false

(d) it’s neither true or false

► (b) it’s either true or false but not both.

2. If x = 5 and y = - 2, then x – 2y = 9. The contrapositive of this proposition is

(a) x – 2y = 9 if x = 5 and y = - 2

(b) If x – 2y = 9, x ≠ 5 and y ≠ - 2

(c) If x – 2y = 9, then x ≠ 5 or y ≠ - 2

(d) None of these

► (c) If x – 2y = 9, then x ≠ 5 or y ≠ - 2

3. The negation of the compound statement p∨(∼p∨q) is

(a) (p∧q)∨p

(b) (p∧∼q)∧∼p

(c) (p∧∼q)∨p

(d) (p∧∼q)∨∼p

► (b) (p∧∼q)∧∼p

4. Which of the following is a preposition?

(a) I am an advocate

(b) Delhi is on the Jupiter

(c) A half open door is half closed

(d) None of these

► (b) Delhi is on the Jupiter

5. Let p and q be two propositions. Then the contrapositive of the implication p→q is

(a) ∼q→∼p

(b) ∼p→∼q

(c) ∼q→p

(d) p↔q

► (a) ∼q→∼p

6. There are 25 days in a month. This is

(a) an implication

(b) a quantifier

(c) a compound statement

(d) a statement

► (d) a statement

7. The negation of the proposition “if a quadrilateral is a square, then it is a rhombus “ is

(a) if a quadrilateral is not a square , then it is a rhombus

(b) a quadrilateral is not a square and it is a rhombus

(c) if a quadrilateral is a square , then it is not a rhombus

(d) a quadrilateral is a square and it is not a rhombus

► (d) a quadrilateral is a square and it is not a rhombus

8. The contrapositive of (∼p∧q)→ is

(a) (p∨q)→r

(b) r→(p∨∼q)

(c) (p∧q)→r

(d) None of these

► (b) r→(p∨∼q)

9. The contrapositive of (p∨q)→ r is

(a) ∼r→(p∧q)

(b) ∼r→∼(p∨q)

(c) p→(p∧q)

(d) ∼r→(∼p∧∼q)

► (d) ∼r→(∼p∧∼q)

10. The negation of q∨∼(p∧r) is

(a) ∼q∨(p∨r)

(b) ∼q∧(p∧r)

(c) q∨(p∨r)

(d) ∼q∧(p∨r)

► (b) ∼q∧(p∧r)

11. Which of the following pairs is logically equivalent ?

(a) Contrapositive, Converse

(b) Conditional, Inverse

(c) Inverse, Contrapositive

(d) Conditional, Contrapositive

► (d) Conditional, Contrapositive

12. Let p and q be two prepositions given by p : I play cricket during the holidays, q : I just sleep throughout the day then , the compound statement p ∧ q is

(a) I play cricket during the holidays and just sleep throughout the day

(b) If I play cricket during the holidays, I just sleep throughout the day

(c) I play cricket during the holidays or just sleep throughout the day

(d) I just sleep throughout the day if and only if I play cricket during the holidays

► (a) I play cricket during the holidays and just sleep throughout the day

13. If p and q are mathematical statements, then in order to show that the statement “p and q” is true, we need to show that:

(a) The statement p is true and the statement q is not true

(b) The statement p is false and the statement q is true.

(c) The statement p is true and the statement q is false

(d) The statement p is true and the statement q is true

► (d) The statement p is true and the statement q is true

14. The negation of p∧∼(q∧r) is

(a) ∼p→(q∧r)

(b) p∨(q∧r)

(c) ∼p∨(q∧r)

(d) ∼p→(q∨∼r)

► (c) ∼p∨(q∧r)

15. The contrapositive of 2x + 3 = 9 ⇒ x ≠ 4 is

(a) x ≠ 4, 2x+3 ≠ 9

(b) x = 4, 2x+3 ≠ 9

(c) x = 4, 2x+3 = 9

(d) x ≠ 4, 2x+3 = 9

► (b) x = 4, 2x+3 ≠ 9

16. The proposition (p→∼p)∧(∼p→p) is

(a) a contradiction

(b) a contradiction and a tautology

(c) neither a contradiction nor a tautology

(d) a tautology

► (a) a contradiction

17. The quantifier used in the statement “For every real number x, x is less than x + 5” is:

(a) For every

(b) And

(c) There exist

(d) Or

► (a) For every

18. The proposition p→∼(p∧∼q) is

(a) a contradiction

(b) neither a contradiction nor a tautology

(c) a tautology

(d) none of these

► (b) neither a contradiction nor a tautology

19. p∧(q∧r) is logically equivalent to

(a) (p∨q)∧r

(b) (p∧q)∧r

(c) p→(q∧r)

(d) (p∨q)∨r

► (b) (p∧q)∧r

20. Let p and q be two propositions. Then, the contrapositive of the implication p→q is

(a) p→q

(b) p↔q

(c) ∼p→∼q

(d) ∼q→∼p

► (d) ∼q→∼p

21. Logical equivalent proposition to the proposition ∼(p∨q) is

(a) ∼p↔∼q

(b) ∼p∧∼q

(c) ∼p∨∼q

(d) ∼p→∼q

► (b) ∼p∧∼q

22. Which of the following proposition is a tautology ?

(a) ∼p∧(∼p∨∼q)

(b) ∼q∧(∼p∨∼q)

(c) (∼p∨∼q)∧(p∨∼q)

(d) (∼p∨∼q)∨(p∨∼q)

► (d) (∼p∨∼q)∨(p∨∼q)

Hope the given MCQ Questions will help you in cracking exams with good marks. These **Mathematical Reasoning MCQ Questions** will help you in practising more and more questions in less time.