Class 11 Maths MCQ – Sets

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1. Which of the following is not a set?

a) The collection of all boys in a class
b) The collection of all tall students in a school
c) The collection of all natural numbers less than 100
d) The collection of all interesting numbers

Answer:

d) The collection of all interesting numbers

Explanation:

"Interesting numbers" is a subjective term and not well-defined, so it's not a set.

2. A set with no elements is called:

a) Finite set
b) Singleton set
c) Null set
d) Infinite set

Answer:

c) Null set

Explanation:

A set with no elements is called a null set or empty set.

3. If A = {x: x is an even number less than 10}, then A is:

a) {2, 4, 6, 8}
b) {2, 4, 6, 8, 10}
c) {1, 3, 5, 7, 9}
d) {0, 2, 4, 6, 8}

Answer:

a) {2, 4, 6, 8}

Explanation:

The set A contains even numbers less than 10.

4. The set of all letters in the word "LETTER" is:

a) {L, E, T, T, E, R}
b) {L, E, T, R}
c) {L, E, T}
d) {L, T, R}

Answer:

b) {L, E, T, R}

Explanation:

In set theory, repetitive elements are counted once.

5. The number of subsets of the set {1, 2, 3} is:

a) 6
b) 3
c) 8
d) 7

Answer:

c) 8

Explanation:

The subsets are {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}.

6. The universal set is denoted by:

a) U
b) A
c) N
d) X

Answer:

a) U

Explanation:

The universal set, which often contains all the elements under consideration, is denoted by U.

7. If A = {1, 2, 3} and B = {3, 4, 5}, A ∩ B is:

a) {1, 2, 3, 4, 5}
b) {3}
c) {1, 2}
d) {4, 5}

Answer:

b) {3}

Explanation:

A ∩ B represents the intersection of sets A and B, which is the set of common elements.

8. The set {x: x is a prime number less than 10} is:

a) {2, 3, 5, 7}
b) {2, 3, 4, 5, 6, 7, 8, 9}
c) {1, 2, 3}
d) {2, 3, 5}

Answer:

a) {2, 3, 5, 7}

Explanation:

Prime numbers less than 10 are 2, 3, 5, and 7.

9. Two sets with no common elements are called:

a) Universal sets
b) Finite sets
c) Disjoint sets
d) Equal sets

Answer:

c) Disjoint sets

Explanation:

Sets with no common elements are termed as disjoint sets.

10. If A = {1, 2} and B = {3, 4}, the Cartesian product A x B is:

a) {(1,3), (1,4), (2,3), (2,4)}
b) {(3,1), (4,1), (3,2), (4,2)}
c) {(1,2), (3,4)}
d) {(1,1), (2,2), (3,3), (4,4)}

Answer:

a) {(1,3), (1,4), (2,3), (2,4)}

Explanation:

The Cartesian product A x B is the set of all ordered pairs (a,b) where a is in A and b is in B.

11. A set that contains an infinite number of elements is called:

a) Finite set
b) Infinite set
c) Null set
d) Singleton set

Answer:

b) Infinite set

Explanation:

An infinite set has an endless number of elements.

12. If A = {x: x is a natural number less than 5}, then A is:

a) {1, 2, 3, 4}
b) {0, 1, 2, 3, 4}
c) {5}
d) {1, 2, 3, 4, 5}

Answer:

a) {1, 2, 3, 4}

Explanation:

The set A contains natural numbers less than 5.

13. The complement of set A with respect to the universal set U is denoted by:

a) A'
b) U'
c) A-U
d) U-A

Answer:

a) A'

Explanation:

The complement of set A with respect to U is the set of all elements in U that are not in A.

14. The set of all real numbers between 1 and 10 is represented by:

a) {x: 1 < x < 10}
b) {x: 1 ≤ x ≤ 10}
c) {x: x < 1 or x > 10}
d) {x: 1 > x > 10}

Answer:

a) {x: 1 < x < 10}

Explanation:

This represents all real numbers greater than 1 and less than 10.

15. If A = {a, b, c} and B = {b, c, d}, A ∪ B is:

a) {a, b, c, d}
b) {a, b, c}
c) {b, c, d}
d) {a, d}

Answer:

a) {a, b, c, d}

Explanation:

A ∪ B represents the union of sets A and B, which includes all unique elements from both sets.

16. If N is the set of natural numbers, then the set {x: x ∈ N, x^2 < 30} is:

a) {1, 2, 3, 4, 5}
b) {1, 2, 3, 4}
c) {1, 2, 3}
d) {5, 6}

Answer:

b) {1, 2, 3, 4}

Explanation:

The numbers 1^2, 2^2, 3^2, and 4^2 are all less than 30, but 5^2 is 25 which is less than 30, however, 6^2 is 36 which is greater than 30.

17. Two sets that contain exactly the same elements are called:

a) Equivalent sets
b) Equal sets
c) Subset and superset
d) Disjoint sets

Answer:

b) Equal sets

Explanation:

Sets that have the same elements are termed as equal sets.

18. The set {x: x is a vowel in the word "APPLICATION"} is:

a) {A, I, O}
b) {A, E, I, O, U}
c) {A, E, I}
d) {A, I}

Answer:

d) {A, I}

Explanation:

The vowels in the word "APPLICATION" are A and I.

19. If A ⊆ B, it implies:

a) A is the subset of B
b) B is the subset of A
c) A and B are disjoint sets
d) A and B are equal sets

Answer:

a) A is the subset of B

Explanation:

A ⊆ B denotes that every element of set A is also an element of set B.

20. If A = {1, 2, 3} and B = {4, 5}, the number of elements in the Cartesian product A x B is:

a) 5
b) 15
c) 6
d) 3

Answer:

c) 6

Explanation:

The Cartesian product A x B will have 3×2 = 6 ordered pairs.

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