Please refer to the MCQ Questions for Class 11 Mathematical Reasoning Maths Chapter 14 with Answers. The following Mathematical Reasoning Class 11 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 11. Our experts have designed MCQ Questions for Class 11 Mathematical Reasoning with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 11 Mathematics

## Mathematical Reasoning Class 11 MCQ Questions with Answers

See below Mathematical Reasoning Class 11 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

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

(a) Open the door.

(b) Do your home work.

(c) Switch on the fan.

(d) Two plus two is four.

**Answer**

D

**Question. 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 x^{2} is not even.

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

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

**Answer**

B

**Question: The logically equivalent proposition of p ⇔ q is**

(a) (p ∧ q ) ν (p ∧ q)

(b) (p ⇒ q) ∧ (q ⇒ p)

(c) (p ∧ q) ν (q ⇒ p)

(d) (p ∧ q) ⇒ (p ν q)

**Answer**

B

**Question: A proposition is called a tautology, if it is**

(a) always T

(b) always F

(c) sometimes T, sometimes F

(d) None of the above

**Answer**

A

**Question: Let p and q be two statements, then (p v q ) v ~ p is**

(a) tautology

(b) contradiction

(c) Both (a) and

(b) (d) None of these

**Answer**

C

**Question: Which of the following is always true?**

**Answer**

B

**Question: The propositions ( p ⇒ ~ p) ∧ (~ p ⇒ p) is**

(a) Tautology and contradiction

(b) Neither tautology nor contradiction

(c) Contradiction

(d) Tautology

**Answer**

C

**Question: The statement p v ~ p is**

(a) tautology

(b) contradiction

(c) neither a tautology nor a contradiction

(d) None of the above

**Answer**

A

**Question: If p and q are two statements, then statement p ⇒ q ∧ q~ q is**(a) tautology

(b) contradiction

(c) neither tautology nor contradiction

(d) None of the above

**Answer**

C

**Question: The negation of the compound proposition is**

**Answer**

A

**Question: If p and q are two statements, then ~(p ∧ q) v~ (q⇔ p) is**

(a) tautology

(b) contradiction

(c) neither tautology nor contradiction

(d) either tautology or contradiction

**Answer**

C

**Question: The proposition (p ⇒ ~p) ∧ (~p ⇒ p) is**

(a) contigency

(b) neither Tautology nor Contradiction

(c) contradiction

(d) tautology

**Answer**

C

**Question: The proposition S : (p ⇒ q) ⇒ (~p v ~ q ) is 57**

(a) a Tautology

(b) a Contradiction

(c) either (a) or (b)

(d) neither (a) nor (b)

**Answer**

A

**Question: If p and q are two statements, then (p⇒q) ⇔ (~q ⇒ ~ p) is a**

(a) contradiction

(b) tautology

(c) neither (a) nor (b)

(d) None of these

**Answer**

B

**Question: The statement(p ⇒q ) ⇔ (~ p ∧ q is a**

(a) tautology

(b) contradiction

(c) neither

(a) nor (b)

(d) None of these

**Answer**

C

**Question: The proposition S:(p ⇒q) ⇒ (~ p v q) ) is**

(a) a tautology

(b) a contradiction

(c) either (a) or (b)

(d) neither (a) nor (b)

**Answer**

A

**Question: Let p and q be two statements. Then, (~ p v q) ∧ (~ p ∧ ~ q) is a**

(a) tautology

(b) contradiction

(c) neither tautology nor contradiction

(d) both tautology and contradiction

**Answer**

C

**Question: (p ∧ ~q) ∧ (~ p ∧ q) is**

(a) a tautology

(b) a contradiction

(c) both a tautology and a contradiction

(d) neither a tautology nor a contradiction

**Answer**

B

**Question. 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**

C

**Question. Which of the following statement is a conjunction? **

(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**

D

**Question. The contrapositive of the statement, ‘ If I do not secure good marks then I cannot go for engineering’, is **

(a) If I secure good marks, then I go for engineering.

(b) If I go for engineering then I secure good marks.

(c) If I cannot go for engineering then I donot secure good marks.

(d) none.

**Answer**

B

**Question. The converse of the statement if x < y then x ^{2} < y^{2}, is **

(a) If x is not less then y then x

^{2}is not less than y

^{2}

(b) If x

^{2}< y

^{2}then x < y

(c) If x

^{2}³ y

^{2}then x ³ y

(d) none

**Answer**

B

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

“If Billu secure good marks, then he will get a bicycle.”

(a) If Billu will not get bicycle, then he will not secure good marks.

(b) If Billu will get a bicycle, then he will secure good marks.

(c) If Billu will get a bicycle, then he will not secure good marks.

(d) If Billu will not get a bicycle, then he will secure good marks.

**Answer**

B

**Question. The connective in the statement : **

“2 + 7 > 9 or 2 + 7 < 9” is

(a) and

(b) or

(c) >

(d) <

**Answer**

B

**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. Which of the following is a statement? **

(a) May you live long!

(b) May God bless you!

(c) The sun is a star.

(d) Hurrah! we have won the match.

**Answer**

C

**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. If p, q, r are simple propositions, then **

(p ∧ q) ∧ (q ∧ r) is true then,

(a) p, q, r are all false

(b) p, q, r are all true

(c) p, q are true and r is false

(d) p is true and q and r are false

**Answer**

B

**Question. p ⇒ q can also be written as **

(a) p ⇒ ~ q

(b) ~ p ∨ q

(c) ~ q ⇒ ~ p

(d) None of these

**Answer**

B

**Question. The negation of the statement **

“A circle is an ellipse” is

(a) An ellipse is a circle.

(b) An ellipse is not a circle.

(c) A circle is not an ellipse.

(d) A circle is an ellipse.

**Answer**

C

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

(a) Roses are red

(b) New Delhi is in India

(c) Every square is a rectangle

(d) Alas! I have failed

**Answer**

D

**Question. Which of the following is an open statement? **

(a) Good morning to all

(b) Please do me a favour

(c) Give me a glass of water

(d) x is a natural number

**Answer**

D

**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 trianle is 180 degrees

**Answer**

C

**Question. Which of the following is a statement in logic? **

(a) He is running.

(b) x + 3 = 10 , x ÎI

(c) Are you regular in doing your homework?

(d) The sum of an even and odd integer is odd.

**Answer**

D

**Question. If p, q, r are simple propositions, then (p ∧ q) ∧ (q ∧ r) is true then **

(a) p, q, r are all false

(b) p, q, r are all true

(c) p, q are true and r is false

(d) p is true and q and r are false

**Answer**

B

**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. ~ p ∧ q is logically equivalent to **

(a) p→ q

(b) q → p

(c) ~ (p→q)

(d) ~ (q→ p)

**Answer**

D

**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

**Answer**

C

**Question. If : p Raju is tall and q: Raju is intelligent, thenthe symbolic statement ~ p∨ q means **

(a) Raju is not tall or he is intelligent.

(b) Raju is tall or he is intelligent

(c) Raju is not tall and he is intelligent

(d) Raju is not tall implies he is intelligent

**Answer**

A

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

(a) p∨ (~ q)

(b) p∨ q

(c) p ∧ (~ q)

(d) ~ p ∧ ~ q

**Answer**

A

**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. (~ (~ p)) ∧ q is equal to **

(a) ~ p ∧ q

(b) p ∧ q

(c) p ∧ ~ q

(d) ~ p ∧ ~ q

**Answer**

B

**Question. 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**

C

**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

**Answer**

D

**Question. Let p: I am brave, **

q: I will climb the Mount Everest.

The symbolic form of a statement,

‘I am neither brave nor I will climb the mount Everest’ is

(a) p ∧ q

(b) ~ (p ∧ q)

(c) ~ p ∧ ~ q

(d) ~ p∧ q

**Answer**

C

**Question. Let p : A quadrilateral is a parallelogram q : The opposite side are parallel **

Then the compound proposition

‘A quadrilateral is a parallelogram if and only if the opposie sides are parellel’ is represented by

(a) p ∨ q

(b) p → q

(c) p ∧ q

(d) p ↔ q

**Answer**

D