# Class 11 Mathematics Mathematical Reasoning MCQs

Refer to Class 11 Mathematics Mathematical Reasoning MCQs provided below. CBSE Class 11 Mathematics MCQs with answers available in Pdf for free download. The MCQ Questions for Class 11 Mathematics with answers have been prepared as per the latest syllabus, CBSE books and examination pattern suggested in Class 11 by CBSE, NCERT and KVS. Multiple Choice Questions for Chapter 14 Mathematical Reasoning are an important part of exams for Class 11 Mathematics and if practiced properly can help you to get higher marks. Refer to more Chapter-wise MCQs for CBSE Class 11 Mathematics and also download more latest study material for all subjects

## MCQ for Class 11 Mathematics Chapter 14 Mathematical Reasoning

Class 11 Mathematics students should refer to the following multiple-choice questions with answers for Chapter 14 Mathematical Reasoning in Class 11. These MCQ questions with answers for Class 11 Mathematics will come in exams and help you to score good marks

### Chapter 14 Mathematical Reasoning MCQ Questions Class 11 Mathematics with Answers

Question : Which of the following is not a statement?
(a) 2 is an even integer.
(b) 2 + 1= 3.
(c) The number 17 is prime.
(d) x + 3 = 10, x Î R.

Question : Let p: Kiran passed the examination, q: Kiran is sad
The symbolic form of a statement "It is not true that Kiran passed therfore he is said' is
(a) (~ p → q)
(b) (p → q)
(c) ~ (p → ~ q)
(d) ~ ( p ↔ q)

Question : Consider the following statements
P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as
(a) ~ (Q ↔ (PΛ ~ R))
(b) ~ Q ↔~ P Λ R
(c) ~ (PΛ ~ R) ↔Q
(d) ~ P Λ (Q ↔ ~ R)

Question : The only statement among the following that is a tautology is
(a) A Λ (A ∨ B)
(b) A ∨ (A Λ B)
(c) [A Λ (A → B)] → B
(d) B → [A Λ (A → B)]

Question : If (p ∧ ~ r)⇒(q ∨r) is false and q and r are both false, then p is
(a) True
(b) False
(c) May be true or false
(d) Data sufficient

Question : If p, q, r are statement with truth vales F, T, F respectively then the truth value of p→(q → r) is
(a) false
(b) true
(c) true if p is true
(d) none

Question : In the truth table for the statement ~ ( ~ p ∨ ~ q),the last column has the truth value in the following order
(a) TFFF
(b) TTFT
(c) FTTF
(d) FFFT

Question : In the truth table for the statement ( ~ p → ~ q) ∧( ~ q → ~ p), the last column has the truth value in the following order is
(a) TTTF
(b) FTTF
(c) TFFT
(d) TTTT
(d) (p Λ q) ∨ (~ q Λ ~ r).

Question : Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”
(a) If a number is not a prime then it is odd
(b) If a number is not a prime then it is odd
(c) If a number is not odd then it is not a prime
(d) If a number is not odd then it is a prime

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

Question : Which of the following is true?
(a) p⇒q ≡~ p⇒ ~ q
(b) ~ (p ⇒ ~ q) ≡ ~ p ∧ q
(c) ~ (~ p ⇒ ~ q) ≡ ~ p ∧ q
(d) ~ (~ p ⇔ q) ≡ [~ (p⇒q)∧ ~ (q⇒p)]

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

Question : In the truth table for the statement ( p ∧ q) →(q ∨ ~ p), the last column has the truth value in the following order is
(a) TTFF
(b) FTTT
(c) TFTT
(d) TTTT

Question : ~(p → q)→ [(~p) ∨ (~ q)] is
(a) a tautology
(c) neither a tautology nor contradiction
(d) cannot come any conclusion

Question : Which of the following is a contradiction?
(a) (p Λ q)Λ ~ (p ∨ q)
(b) p∨ (-p Λ q)
(c) (p ⇒ q) ⇒ p
(d) None of these

Question : (p Λ ~ q) Λ (~ p ∨q) is
(b) A tautology
(c) Either (a) or (b)
(d) Neither (a) nor (b)

Question : Which of the following is always true?
(a) (p⇒q) ≡ ~ q⇒~ p
(b) ~ (p ∨ q) ≡ ∨ p ∨ ~ q
(c) ~ (p⇒q) ≡ p Λ ~ q
(d) ~ (p ∨ q) ≡ ~ p Λ ~ q

Question : The propositions (p⇒~ p) Λ (~ p⇒p) is
(d) Tautology

Question : The negation of the statement (p Λ q) → (~ p ∨ r) is
(a) (p Λ q) ∨ (p ∨ ~ r)
(b) (p Λ q) ∨ (p Λ ~ r)
(c) (p Λ q) Λ (p Λ~ r)
(d) p ∨ q

Question : The false statement in the following is
(a) p Λ (~ p) is contradiction
(b) (p⇒q)  ⇔ (~ q⇒~ p) is a contradiction
(c) ~ (~ p) ⇔ p is a tautology
(d) p∨ (~ p) ⇔ is a tautology

Question : If p, q, r are statement with truth values F, T, F respectively then the truth value of (~ p → ~ q) ∨ r is
(a) true
(b) false
(c) false if r is true
(d) false if q is false

Question : ~ (p∨ (~ q)) is equal to
(a) ~ p ∨ q
(b) (~ p) ∧ q
(c) ~ p ∨ ~ p
(d) ~ p ∧ ~ p

Question : The negation of the statement (p∨ q) Λ r is
(a) (~ p ∨ ~ q) ∨ ~ q
(b) (~ p Λ ~ q) ∨ ~ r
(c) ~ (p ∨ q)→ r
(d) pΛq.

Question : ~ (p ∨ q)∨ (~ p Λ q) is logically equivalent to
(a) ~p
(b) p
(c) q
(d) ~q

Question : The negation of (p ∨ q)Λ (p ∨ ~ r) is
(a) (~ p Λ ~ q) ∨ (q Λ ~ r)
(b) (~ p Λ ~ q) ∨ (~ q Λ r)
(c) (~ p Λ ~ q) ∨ (~ q Λ r)
(d) (p Λ q) ∨ (~ q Λ ~ r).

Question : Let S be a non-empty subset of R. Consider the following statement : P : There is a rational number x Î S such that x > 0.
Which of the following statements is the negation of the statement P ?
(a) There is no rational number x Î S such than x < 0.
(b) Every rational number x Î S satisfies x < 0.
(c) x Î S and x < 0 ⇒ x is not rational.
(d) There is a rational number x Î S such that x < 0.

Question : Which of the following is not a statement in logic?
(a) The sum of angles of a quadrilateral is 180°.
(b) Every statement has one truth value.
(c) 3 is an irrational number.
(d) x + 5 = 7, x Î Q.

Question : If p⇒(~ p ∨ q) is false, the truth values of p and q are respectively
(a) F, T
(b) F, F
(c) T, T
(d) T, F

Question : Negation is “2 + 3 = 5 and 8 < 10” is
(a) 2 + 3 ≠ 5 and < 10
(b) 2 + 3 = 5 and 8 (c) 2 + 3 ¹ 5 or 8 (d) None of these

Question : If p⇒(~ p ∨ q) is false, the truth values of p and q are respectively
(a) F, T
(b) F, F
(c) T, T
(d) T, F

Question : Negation of the proposition : If we control population growth, we prosper
(a) If we do not control population growth, we prosper
(b) If we control population growth, we do not prosper
(c) We control population but we do not prosper
(d) We do not control population, but we prosper

Question : The negation of (p ∨ q)Λ (p ∨ ~ r) is
(a) (~ p Λ ~ q) ∨ (q Λ ~ r)
(b) (~ p Λ ~ q) ∨ (~ q Λ r)
(c) (~ p Λ ~ q) ∨ (~ q Λ r)

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### CBSE Class 11 Mathematics Chapter 14 Mathematical Reasoning MCQs

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