# MCQ Chapter 14 Mathematical Reasoning Class 11 Mathematics

Please refer to Mathematical Reasoning MCQ Questions Class 11 Mathematics below. These MCQ questions for Class 11 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Mathematical Reasoning will help you to prepare for the exams and get more marks.

## Mathematical Reasoning MCQ Questions Class 11 Mathematics

Please see solved MCQ Questions for Mathematical Reasoning in Class 11 Mathematics. All questions and answers have been prepared by expert faculty of standard 11 based on the latest examination guidelines.

### MCQ Questions Class 11 Mathematics Mathematical Reasoning

Question. The converse of the statement “If x > y, then x + a > y + a” is
(a) If x < y, then x + a < y + a
(b) If x + a > y + a, then x > y
(c) If x < y, then x + a > y + a
(d) If x > y, then x + a < y + a B

B

Question. The contrapositive of statement “If Chandigarh is capital of Punjab, then Chandigarh is in India” is
(a) “If Chandigarh is not in India, then Chandigarh is not the capital of Punjab”.
(b) “If Chandigarh is in India, then Chandigarh is capital of Punjab”.
(c) “If Chandigarh is not capital of Punjab, then Chandigarh is not the capital of India”.
(d) “If Chandigarh is capital of Punjab, then Chandigarh is not in India”.

A

Question. The propositions (p ⇒ ~ p) ∧ (~ p ⇒ p) is
(d) Tautology

C

Question. A compound statement p q is false only when
(a) p is true and q is false
(b) p is false but q is true
(c) at least one of p or q is false
(d) both p and q are false

A

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.

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

D

Question. For the statement “17 is a real number or a positive integer”, the “or” is
(a) inclusive
(b) exclusive
(c) Only (a)
(d) None of these

A

Question. Which of the following is a statement?
(a) Open the door.
(c) Switch on the fan.
(d) Two plus two is four.

D

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 opposite sides are parallel’ is represented by
(a) p ∨ q
(b) p → q
(c) p ∧ q
(d) p ↔ q

D

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)]

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.

A

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

C

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

B

Question. The negation of the statement “ √2 is not a complex number” is
(a) √2 is a rational number
(b) √2 is an irrational number
(c) √2 is a complex number
(d) None of the above

C

Question. If p : Pappu passes the exam,
q : Papa will give him a bicycle.
Then, the statement ‘Pappu passing the exam, implies that his papa will give him a bicycle’ can be symbolically written as
(a) p → q
(b) p ↔ q
(c) p ∧ q
(d) p ∨ q

A

Question. The statement
“If x2 is not even, then x is not even” is converse of the statement
(a) If x2 is odd, then x is even.
(b) If x is not even, then xis not even.
(c) If x is even, then xis even.
(d) If x is odd, then xis even.

B

Question. The inverse of the statement (p ∧ ~ q)r is
(a) ~ (p ∨ ~q) → ~ r
(b) (~p ∧ q) → ~ r
(c) (~p ∨ q) → ~ r
(d) None of these

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

D

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↔(P∧ ~ R))
(b) ~ Q↔~ P ∧ R
(c) ~ (P∧ ~ R)↔Q
(d) ~ P ∧ (Q↔~ R)

A

Question. Negation of the statement (p ∧ r)(r ∨ q) is
(a) ~ (p ∧ r) →~ (r ∨ q)
(b) (~p ∨ ~r) ∨ (r ∨ q)
(c) (p ∧ r) ∧ (r ∧ q)
(d) (p ∧ r) ∧ (~ r ∧ ~q)

D

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.

C

Question. Truth value of the statement ‘It is false that 3 + 3 = 33 or 1 + 2 = 12’ is
(a) T
(b) F
(c) both T and F
(d) 54

A

Question. The statement p: For any real numbers x, y if x = y, then 2x + a = 2y + a when a ∈ Z.
(a) is true
(b) is false
(c) its contrapositive is not true
(d) None of these

A

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.

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

C

STATEMENT TYPE QUESTIONS

Question. Consider the following sentences.
I. She is a Mathematics graduate.
II. There are 40 days in a month.
Choose the correct option.
(a) Only I is a statement.
(b) Only II is a statement.
(c) Both are the statements.
(d) Neither I nor II is statement.

B

Question. Consider the following
I. New Delhi is in Nepal.
II. Every relation is a function.
Choose the correct option.
(a) I and II are statements.
(b) I and III are statements.
(c) II and III are statements.
(d) I, II and III are statements.

A

Question. Consider the following sentences.
I. “Two plus two equals four” is a true statement.
II. “The sum of two positive numbers is positive” is a true statement.
III. “All prime numbers are odd numbers” is a true statement.
Choose the correct option.
(a) Only I is false.
(b) Only II is false.
(c) All I, II and III are false
(d) Only III is false.

D

Question. Consider the following statement.
“If a triangle is equiangular, then it is an obtuse angled triangle.”
This is equivalent to
I. a triangle is equiangular implies that it is an obtuse angled triangle.
II. for a triangle to be obtuse angled triangle it is sufficient that it is equiangular.
Choose the correct option.
(a) Both are correct.
(b) Both are incorrect.
(c) Only I is correct.
(d) Only II is correct.

A

Question. The component statements of the statement “The sky is
blue or the grass is green” are
I. p : The sky is blue.
q : The sky is not blue.
II. p : The sky is blue.
q : The grass is green.
Choose the correct option.
(a) I and II are component statements.
(b) Only I is component statement.
(c) Only II is component statement.
(d) Neither I nor II is component statement.

C

Question. Consider the following statements.
I. If a statement is always true, then the statement is called “tautology”.
II. If a statement is always false, then the statement is called “contradiction”.
Choose the correct option.
(a) Both the statements are false.
(b) Only I is false.
(c) Only II is false.
(d) Both the statements are true.

D

Question. Consider the following sentences.
I. “Two plus three is five” is not a statement.
II. “Every square is a rectangle.” is a statement.
Choose the correct option.
(a) Only I is true.
(b) Only II is true.
(c) Both are true.
(d) Both are false.

A

Question. Consider the following statements
Statement- I: The words “And” and “or” are connectives.
Statement-II: “There exists” and “For all” are called quantifiers.
(a) Only Statement I is true
(b) Only Statement II is true
(c) Both Statement are true
(d) Both Statement are false