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Provide Important Class 11 Maths MCQ Questions of Sets with Answers?

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Practicing the category 11 Maths MCQ Questions of Sets with Answers will boost your confidence thereby helping you to attain well within the exam. Students are advised to unravel the MCQ Questions of Sets Class 11 with answers to understand different concepts. Students can access the MCQ Questions for class 11 Maths Sets with Answers. It aids in your exam preparation and you'll get an honest hold of the chapter.

Class 11 MCQ Questions with Answers from here and test their problem-solving skills. Clear all the basics and prepare thoroughly for the exam taking help from Class 11 Maths Sets Objective Questions. you'll ask the stepwise solutions of all the important questions of this chapter here along-side the practice MCQ Questions at the bottom which are given the new guidelines of CBSE and cover all the concepts of the NCERT curriculum.

Practice MCQ Questions for class 11 Maths Chapter-Wise

1. If A, B and C are three sets, then A - (B - C) equals to 

(a) A − (B ∩ C)
(b) (A − B) ∪ C
(c) (A − B) ∪ (A ∩ C)
(d) (A - B) ∪ (A -C)

2. A – B is read as?

(a) Difference of A and B of B and A
(b) None of the above
(c) Difference of B and A
(d) Both a and b

3. If A,B and C are any three sets, then A∩(B△C) =

(a) (A∩B) Δ (A∩C)
(b) (A∩B) Δ (A-C)
(c) (A+B) Δ (A∩C)
(d) Both a and b

4. IF A = [5, 6, 7] and B = [7, 8, 9] then A ∪ B is equal to

(a) [5, 6, 7, 8, 9]
(b) [5, 6, 7]
(c) [7, 8, 9]
(d) None of these

5. If R = {(1,−1),(2,−2),(3,−1)} is relation, then find the range of R.

(a) {−1,−2,−1}.
(b) {1,−2,−1}.
(c) {−1, 2,−1}.
(d) None of these

6. The members of the set S = {x | x is the square of an integer and x < 100} is

(a) {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
(b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
(c) {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
(d) {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}

7. In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is?

(a) 102
(b) 42
(c) 1
(d) 38

8. Two finite sets have N and M elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second test. Then the value of M and N are

(a) 7, 6
(b) 6, 4
(c) 7, 4
(d) 6, 3

9. If A,B and C are three sets such that A∩B = A∩C and A∪B = A∪C, then

(a) A=B
(b) A=C
(c) B=C
(d) A∩B=ϕ

10. How many rational and irrational numbers are possible between 0 and 1?

(a) 0
(b) Finite
(c) Infinite
(d) 1

11. Empty set is a?

(a) Finite Set
(b) Invalid Set
(c) None of the above
(d) Infinite Set

12. Which of the following two sets are equal?

(a) A={1,2} and B={1}
(b) A={1,2} and B={1,2,3}
(c) A={1,2,3} and B={2,1,3}
(d) A={1,2,4} and B={1,2,3}

13. In a class of 50 students 35 opted for Mathematics and 37 opted for Biology How may have opted for only Mathematics? ( Assume that each student has to opt for at least one of the subjects)

(a) 15
(b) 17
(c) 13
(d) 19

14. If n(A)=3 and n(B)=6 and A⊆B, then the number of elements in  A∩B  is equal to

(a) 3
(b) 9
(c) 6
(d) none of these

15. Let U = {1,2,3,4,5,6,7,8,9,10}, A= {1,2,5}, B= {6,7} then A∩B′ is

(a) B'
(b) A
(c) A'
(d) B

16. If (x – 1, y + 1) = (5, 6), then the value of x and y is given by

(a) x = 5, y = 5
(b) x = 6, y = 5
(c) x = 5, y = 6
(d) x = 0, y = 0

17. What is the Cardinality of the Power set of the set {0,1,2}?

(a) 8
(b) 6 
(c) 7
(d) 9

18. If A = {x, y} then the power set of A is :

(a) {xx,yy}
(b) {ϕ,x,y}  
(c)  {ϕ,{x},{2y}}
(d) {ϕ,{x},{y},{x,y}}

19. Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then

(a) A  is always a subset of the complement of B
(b) B is always a subset of A
(c) A and B are always disjoint
(d) A  and the complement of B are always non disjoint

20. If A and B are finite sets, then which one of the following is the correct equation?  

(a) n (A - B) = n (A) - n (B)
(b) n (A - B) = n (B - A)
(c) n (A - B) = n (A) - n (A ∩ B)
(d) n (A - B) = n (B) - n (A ∩ B)

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Answer:

1. Answer: (c) (A − B) ∪ (A ∩ C)

Explanation: Venn diagram, shaded area shows A - (B - C)

In the above Venn diagram, horizontal lines mean

( A − B ) and vertical lines mean ( A ∩ C )

Total shaded portion = (A − B) ∪ (A ∩ C) 

∴ ( A - B) ∪ (A ∩ C) = A - (B - C)

2. Answer: (a) Difference of A and B of B and A

Explanation: A – B will read as difference of A and B of B and A .Ex: Let A = {1, 2, 3, 4, 5} and B = {1, 3, 5, 7} Now, A – B = {2, 4}.

3. Answer: (a) (A∩B) Δ (A∩C)

Explanation: A∩(BΔC) = A∩[(B∪C)−(B∩C)]

⇒ A∩(B∪C) − A∩(B∩C)

⇒ (A∩B) ∪ (A∩C) − (A∩B)∩(A∩C) (using distributive low)

= (A∩B) Δ (A∩C)

4. Answer: (a) [5, 6, 7, 8, 9]

Explanation: Union of two sets has all the elements of both the sets.

So, A∪B = {5,6,7,8,9}

Thus the total number of elements in the above set is 5

5. Answer: (a) {−1,−2,−1}.

Explanation: Range :- Set of y-coordinates

From given R={(1,−1),(2,−2),(3,−1)}

∴ Range ={−1,−2,−1}.

6. Answer: (b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

Explanation: The set S consists of the square of an integer less than 100. So, S = {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

7. Answer: (d) 38

Explanation: Let n(A)= number of students opted Mathematics = 70,

n(B)= number of students opted Physics =46,

n(C)= number of students opted Chemistry =28,

n(A∩B)=23,

n(B∩C)=9,

n(A∩C)=14,

n(A∩B∩C)=4,

Now n(A∪B∪C)

=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C)

=70+46+28−23−9−14+4

=102

Si number of students not opted for any course = Total −n(A∩B∩C)

=140−102

= 38

8. Answer: (b) 6, 4

Explanation: Let A and B be two sets having m and n numbers of elements respectively

Number of subsets of A = 2m

Number of subsets of B = 2n

Now, according to question

2m – 2n = 48

⇒ 2n(2m – n – 1) 

= 24(22 – 1)

So, n = 4 and m – n = 2

⇒ m – 4 = 2

⇒ m = 2 + 4

⇒ m = 6

9. Answer: (c) B=C

Explanation: A∪B=A∪C

⇒n(A∪B)=n(A∪C)

⇒n(A)+n(B)−n(A∩B)=n(A)+n(C)−n(A∩C)

⇒n(B)=n(C) since A∩C=A∩B

⇒B=C

10. Answer: (c) Infinite

Explanation: There are infinite many rational and irrational numbers are possible between 0 and 1
This is because between any two numbers, there are infinite numbers.

11. Answer: (a) Finite Set

Explanation: In mathematics, and more specifically set theory, the empty set is the unique set having no elements and its size or cardinality (count of elements in a set) is zero.
So, an empty set is a finite set.

12. Answer: (c) A={1,2,3} and B={2,1,3}

Explanation: A={1,2,3}

B={2,1,3} A=B(Both set A and B contain same element )

13. Answer: (c) 13

Explanation: Here n(M∪B) =50, n(M)=35, n(B)=37

∴n(M∩B)=n(M)+n(B)−n(M∪B)

=35+37−50

=22

⇒ 22 student have opted for both Mathematics and Biology. 

Now the number of students who have opted for Mathematics only

=n(M)−n(M∩B)

=35−22

=13

14. Answer: (a) 3

Explanation: Since A ⊆B

∴A∩B =A∴n(A∩B)

n(A) =3

15. Answer: (b) A

Explanation: B′={1,2,3,4,5,8,9,10}

∴A∩B 

={1,2,5}∩{1,2,3,4,5,8,9,10}

{1,2,5} =A

16. Answer: (b) x = 6, y = 5

Explanation: Given, 

(x−1,y+1) =(5,6)

Hence, x−1=5 

x = 6 and

y+1=6

y = 5   

⇒ x =6; y =5

17. Answer: (a) 8

Explanation: Power set P({0,1,2}) is the set of all subsets of {0,1,2}. Hence, P({0,1,2})={null,{0},{1},{2},{0,1},{0,2},{1,2},{0,1,2}}.

18. Answer: (d) {ϕ,{x},{y},{x,y}}

Explanation:  Let A={x,y}

Power set = Set of all possible subsets of A

∴P(A)={ϕ,{x},{y},{x,y}}

19. Answer: (d) A  and the complement of B are always non disjoint

Explanation: Since, A is not a subset of B.

∴ Some elements of A will not be elements of B. Hence, A and complement of B are always non-disjoint.

20. Answer: (c) n (A - B) = n (A) - n (A ∩ B)

Explanation: If A and B are finite sets, then

From the Venn diagram

⇒n(A−B) = n(A)−n(A∩B)

Click here to practice MCQ Questions for Sets class 11

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