MCQ Questions For Class 11 Mathematical Reasoning with Answers

Students can refer to the following Mathematical Reasoning MCQ Questions for Class 11 Maths with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here a collection of multiple choice questions for Mathematical Reasoning Class 11 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

Mathematical Reasoning MCQ Questions for Class 11 Maths with Answers

We have provided below Mathematical Reasoning MCQ Questions for Class 11 Maths with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Mathematical Reasoning MCQs in Class 11 Mathematics pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

Question. Statement ( 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

Question: Which of the following is not a statement?
(a) Smoking is injurious to health
(b) 2 + = 2 4
(c) 2 is the only even prime number
(d) Come here   

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 

Question: The negation of the “statement, 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) if a quadrilateral is a square, then it is not a rhombus
(c) a quadrilateral is a square and it is not a rhombus
(d) a quadrilateral is not a square and it is a rhombus 

Question: The conditional statement of “You will get a sweet dish after the dinner” is
(a) If you take the dinner, then you will get a sweet dish
(b) If you take the dinner, you will get a sweet dish
(c) You get a sweet dish if and only if you take the dinner
(d) None of the above 

Question: Which of the following is a statement?
(a) x is a real number
(b) Switch off the fan
(c) 6 is a natural number
(d) Let me go 

Question: Which of the following is not logically equivalent to the following proposition?
“A real number is either rational or irrational”
(a) If a number is neither rational nor irrational, then it is not real
(b) If a number is not a rational or not an irrational, then it is not real
(c) If a number is not real, then it is neither rational or irrational
(d) If a number is real, then it is rational or irrational

Question: The negation of the statement “72 is divisible by 2 and 3” is
(a) 72 is not divisible by 2 or 72 is not divisible by 3
(b) 72 is not divisible by 2 and 72 is not divisible by 3
(c) 72 is divisible by 2 and 72 is not divisible by 3
(d) 72 is not divisible by 2 and 72 is divisible by 3 

Question: Which of the following is not a proposition ?
(a) √3 is a prime
(b) √2 is irrational
(c) Mathematics is interesting
(d) 5 is an even integer 

Question: Let R be the set of real numbers and x∈ R . Then, x +3= 8 is
(a) open statement
(b) a true statement
(c) false statement
(d) None of these 

Question: Which of the following is an open statement
(a) x is a natural number
(b) Give me a glass of water
(c) Wish you best of luck
(d) Good morning to all 

Question. Which of the following sentences is/are not statements? 
(a) There are 35 days in a month.
(b) Mathematics is difficult.
(c) The square of a number is an even number.    
(d) The side of a quadrilateral have equal lengths.

Question. The statement ~ (~ p ∨ ~ q) is
(a) tautology
(b) contradiction
(c) contigency
(d) None of these

Question. Which of the following is wrong statement?
(a) p → q is logically equivalent to ~ p ∨ q
(b) If the truth values of p, q, r are T, F, T respectively, then the truth value of (p ∨ q) ∧ (q ∨ r ) is T
(c) ~ (∨ q ∨ q ∨ r ) ≡ ~ p ∧ ~ q ∧ ~ r
(d) The truth value of p ∧ ~ (p ∨ q) is always T

Question. The negation of the statement
“If become a teacher, then I will open a school”, is 
(a) I will become a teacher and I will not open a school
(b) Either I will not become a teacher or I will not open a school
(c) Neither I will become a teacher nor I will open a school
(d) I will not become a teacher or I will open a school

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

Question. Which of the following statement is a contradiction?
(a) (~ p ∨ ~ q) ∨ (p ∨ ~ q)
(b) (p → q) ∨ (p ∧ ~ q)
(c) (~ p ∧ q) ∧ (~ q)
(d) (~ p ∧ q) ∨ (~ q)

Question. If (q ∧ – r) ⇒(q ∨ r) is false, then p is 
(a) True
(b) False
(c) May be true and false
(d) None of these

Question. If p, q and r are simple proposition, then(~ p ∨ q)⇒r is true, when p, q and r are, respectively
(a) T, F, T 
(b) T, T, T
(c) T, F, F
(d) F, F, F

Question. If ~ ( p ∧ q) is false, then corresponding values of pand q are, respectively
(a) T, T
(b) T, F
(c) F, T
(d) None of these

Question. Which of the following is wrong?
(a) p ∨ ~ p is a tautology
(b) ~ (~ p) ↔ p is a tautology
(c) p ∧ ~ p is a contradiction
(d) (p ∧ q) → q) → p is a tautology

Question. If p, q and r are simple propositions, then ( p ∧ q) ∧ (q ∧ r) is true, then
(a) p, q and r are true
(b) p, q are true and r is false
(c) p is true and q, r are false
(d) p, q and r are false

Question. Let p be the statement ‘x is an irrational number’, q be the statement ‘y is a transcendental number’ and r be the statement ‘x is a rational number iff y is a transcendental number’.
Statement I r is equivalent to either q or p.
Statement II r is equivalent to ~ ( p↔~ p).

Question. If p and q are simple proposition, then (~ p ∧ q) ∨ (~ q ∧ p) is false when p and q are respectively
(a) T, T
(b) T, F
(c) F, F
(d) F, T 

Question. The statement p →(q → p) is equivalent to
(a) p → (p ↔ q)
(b) p → (p → q)
(c) p → (p ∨ q)
(d) p → (p ∧ q)

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

Question. The propositions ( p⇒~ p) ∧ (~ p⇒ p) is
(a) Tautology and contradiction
(b) Neither tautology nor contradiction
(c) Contradiction
(d) Tautology

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

Question. The proposition S : ( p⇒ q) ⇔(~ p ∨ q) is
(a) a tautology
(b) a contradiction
(c) either (a) or (b)
(d) neither (a) nor (b)

Question. Let p and q be two statements. Then,(~ p ∨ q) ∧ (~ p ∧~ q) is a
(a) tautology
(b) contradiction
(c) neither tautology nor contradiction
(d) both tautology and contradiction

Question. Consider the statement∼ “For an integer n, if n3 – 1 is even, then n is odd.” The contrapositive statement of this statement is∼ 
(a) For an integer n, if n is even, then n3 – 1 is odd.
(b) For an intetger n, if n3 – 1 is not even, then n is not odd.
(c) For an integer n, if n is even, then n3 – 1 is even.
(d) For an integer n, if n is odd, then n3 – 1 is even.

Question. The statement ( p→(q→ p))→( p→( p ∨ q)) is ∼
[Sep. 05, 2020 (II)]
(a) equivalent to ( p ∧ q)∨ (~ q)
(b) a contradiction
(c) equivalent to ( p ∨ q) ∧ (~ p)
(d) a tautology

Question. Contrapositive of the statement ∼
‘If a function f is differentiable at a, then it is also continuous at a’, is ∼ 
(a) If a function f is continuous at a, then it is not differentiable at a.
(b) If a function f is not continuous at a, then it is not differentiable at a.
(c) If a function f is not continuous at a, then it is differentiable at a
(d) If a function f is continuous at a, then it is differentiable at a.

Question. The contrapositive of the statement “If I reach the station in time, then I will catch the train” is ∼ 
(a) If I do not reach the station in time, then I will catch the train.
(b) If I do not reach the station in time, then I will not catch the train.
(c) If I will catch the train, then I reach the station in time.
(d) If I will not catch the train, then I do not reach the station in time.

Question. The contrapositive of the statement “If you are born in India, then you are a citi en of India”, is :
(a) If you are not a citi en of India, then you are not born in India.
(b) If you are a citi en of India, then you are born in India.
(c) If you are born in India, then you are not a citi en of India.
(d) If you are not born in India, then you are not a citi en of India.

Question. Contrapositive of the statement “If two numbers are not equal, then their squares are not equal”. is :
(a) If the squares of two numbers are not equal, then the numbers are equal.
(b) If the squares of two numbers are equal, then the numbers are not equal.
(c) If the squares of two numbers are equal, then the numbers are equal.
(d) If the squares of two numbers are not equal, then the numbers are not equal.

Question. Contrapositive of the statement
‘If two numbers are not equal, then their squares are not equal’, is : 
(a) If the squares of two numbers are equal, then the numbers are equal.
(b) If the squares of two numbers are equal, then the numbers are not equal.
(c) If the squares of two numbers are not equal, then the numbers are not equal.
(d) If the squares of two numbers are not equal, then the numbers are equal.

Question. The contrapositive of the following statement,
“If the side of a square doubles, then its area increases four times”, is : [Online April 10, 2016]
(a) If the area of a square increases four times, then its side is not doubled.
(b) If the area of a square increases four times, then its side is doubled.
(c) If the area of a square does not increases four times, then its side is not doubled.
(d) If the side of a square is not doubled, then its area does not increase four times.

Question. Consider the following two statements :
P : If 7 is an odd number, then 7 is divisible by 2.
Q : If 7 is a prime number, then 7 is an odd number.
If V1 is the truth value of the contrapositive of P and V2 is the truth value of contrapositive of Q, then the ordered pair (V1, V2) equals:
(a) (F, F)
(b) (F, T)
(c) (T, F)
(d) (T, T)

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 equivalently expressed as :
(a) ~ Q « ~ P ∨ R
(b) ~ Q « ~ P ∧ R
(c) ~ Q « P ∨ ~ R
(d) ~ Q « P ∧ ~ R

Question. The contrapositive of the statement “If it is raining, then I will not come”, is :
(a) If I will not come, then it is raining.
(b) If I will not come, then it is not raining.
(c) If I will come, then it is raining.
(d) If I will come, then it is not raining.

Question. The contrapositive of the statement “if I am not feeling well, then I will go to the doctor” is
(a) If I am feeling well, then I will not go to the doctor
(b) If I will go to the doctor, then I am feeling well
(c) If I will not go to the doctor, then I am feeling well
(d) If I will go to the doctor, then I am not feeling well.

Question. Let p and q denote the following statements
p : The sun is shining
q: I shall play tennis in the afternoon
The negation of the statement “If the sun is shining then I shall play tennis in the afternoon”, is
(a) q ⇒: p
(b) q ∧ : p
(c) p ∧ : q
(d) : q ⇒: p

Question. If p and q are two statements, then statement p⇒ q ∧ ~ q is
(a) tautology
(b) contradiction
(c) neither tautology nor contradiction
(d) None of the above

Question. Let p and q be two statements, then ( p ∨ q) ∨ ~ p is
(a) tautology
(b) contradiction
(c) Both (a) and (b)
(d) None of these

Question. The statement p ∨~ pis
(a) tautology
(b) contradiction
(c) neither a tautology nor a contradiction
(d) None of the above

Question. The statement ( p⇒ q) ⇔(~ p ∧ q) is a
(a) tautology
(b) contradiction
(c) neither (a) nor (b)
(d) None of these

Question. The proposition ~ ( p⇒ q) ⇒(~ p ∨ ~ q) is
(a) a Tautology
(b) a Contradiction
(c) either (a) or (b)
(d) neither (a) nor (b)

Question. The negation of the compound proposition is p ∨ (~ p ∨ q)
(a) (p ∧ ~ q) ∧ ~ p
(b) (p ∨ ~ q) ∨ ~ p
(c) (p ∧ ~ q) ∨ ~ p
(d) None of the above

Question. If p and q are two statements, then ~( p ∧ q) ∨~ (q⇔ p) is
(a) tautology
(b) contradiction
(c) neither tautology nor contradiction
(d) either tautology or contradiction

Question. The proposition ( p⇒~ p) ∧ (~ p ⇒ p) is
(a) contigency
(b) neither Tautology nor Contradiction
(c) contradiction
(d) tautology

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

Directions (Q. Nos. 12-21) Each of these questions contans two statements : statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternatite choice, only one of which is the correct answer.You has to select one of the codes (a), (b), (c), (d) given below.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I true, Statement II is false.
(d) Statement I is false, Statement II is true.

Question. Statement I The statement [ p ∧ ( p→ q)]→ q is a tautology.   
Statement II If all truth values of a statement is true, then the statement is a tautology.

Question. Let p: Ice is cold and q : blood is green be two statements, then     
Statement I p ∨ q : Ice is cold or blood is green.
Statement II p ∧ q : Ice is not cold or blood is green.

Question. Let S :~ ( p⇔ q) ∨ ~ (q⇔ p)       
Statement I The statement S is logically equivalent to ( p⇔q) 
Statement II The logically equivalent proposition of pÛ q is ( p⇔ q) ∧ (q⇔p)

Question. If p→ q be any conditional statement,      
Statement I The converse of p→ q is the statement q→ p.
Statement II The inverse of p→ q is the statement ~ q→~ p.

Question. Suppose p, q and r be any three statements.    
Statement I The statement p→(q→ r) is a tautology.
Statement II ( p ∧ q) → r and p→(q→ r) are identical.

Question. Let p be the statement, “Mr A passed the examination”, qbe the statement, “Mr A is sad” and r be the statement “It is not true that Mr A passed therefore he is sad.”
Statement I r ≡ p⇔ q   
Statement II The logical equivalent of p⇔ qis~ p ∨ q.    

Question. Statement I ~ ( p ↔ ~ q) is equivalent to p ↔ q     
Statement II ~ ( p ↔ ~ q) is a tautology

Question. Statement I ~ (A ⇔ ~ b) is equivalent to A ⇔ B.    
Statement II A ∨ (~ (A ∧ ~ B)) a tautology.

Question. Consider       
Statement I ( p∧~ q) ∧(~ p∧ q) is a fallacy.
Statement II ( p→ q) ↔(~ q→~ p) is a tautology.

Question. Which of the following is wrong?
(a) p ∨ ~ p is a tautology
(b) ~ (~ p) ↔ p is a tautology
(c) p ∧ ~ p is a contradiction
(d) (p ∧ q) → q) → p is a tautology

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