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

Mathematical Reasoning Class 11 MCQ is one of the best strategies to prepare for the CBSE Class 11 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more Mathematical Reasoning class 11 MCQ which will help them all through their board test.

## Mathematical Reasoning Class 11 MCQ Questions with Answer

Class 11 Math MCQ with answers are given here to Chapter 14 Mathematical Reasoning. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 11 Mathematics syllabus. By Solving these Class 11 MCQs, you will be able to analyze all of the concepts quickly in the Chapter and get ready for the Class 11 Annual exam.

Learn Mathematical Reasoning Class 11 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 11 Mathematical Reasoning MCQ with answers given below.

Question 1 : 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 2: 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 3: 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 4: 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 5: 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 6 : 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)]

B

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 7 : 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 8 : 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 9 : 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 10 : 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

A

Question 11: The propositions (p⇒~ p) Λ (~ p⇒p) is
(d) Tautology

Question 12: 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 13 : 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 14 : 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 15 : ~ (p∨ (~ q)) is equal to
(a) ~ p ∨ q
(b) (~ p) ∧ q
(c) ~ p ∨ ~ p
(d) ~ p ∧ ~ p

B

Whoever needs to take the CBSE Class 11 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 11 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Mathematical Reasoning Class 11 MCQ are ready by the subject specialists themselves.

Question 16 : 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 17 : 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 18 : ~(p → q)→ [(~p) ∨ (~ q)] is
(a) a tautology
(c) neither a tautology nor contradiction
(d) cannot come any conclusion

Question 19 : 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 20 : (p Λ ~ q) Λ (~ p ∨q) is
(b) A tautology
(c) Either (a) or (b)
(d) Neither (a) nor (b)

Question 21 : 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

C

Question 22 : 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 23 : 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 24 : 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 25 : 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 26 : 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)

C

Question 27 : 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 28 : ~ (p ∨ q)∨ (~ p Λ q) is logically equivalent to
(a) ~p
(b) p
(c) q
(d) ~q

Question 29 : 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 30 : 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 31: 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.

D

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