Online Test: Sets | Class 11 Mathematics

Question 1 of 10 medium

In a class of 50 students in a Bengaluru school, 30 study Kannada, 25 study Sanskrit, and 10 study both. How many students study neither Kannada nor Sanskrit?

5

10

15

0

Explanation: Let K be Kannada, S be Sanskrit. n(K ∪ S) = n(K) + n(S) − n(K ∩ S) = 30 + 25 − 10 = 45. Students studying neither = Total − n(K ∪ S) = 50 − 45 = 5.

Question 2 of 10 easy

If two sets A and B are mutually disjoint, how are they represented in a Venn Diagram?

Two concentric circles.

Two intersecting circles.

Two separate, non-overlapping circles.

One circle divided into two halves.

Explanation: Disjoint sets have no elements in common (A ∩ B = ∅). Therefore, they are drawn as circles that do not overlap or touch.

Question 3 of 10 easy

If A={1,2,3,4,5} and B={2,4,6}, then A∩B has how many elements?

1

2

3

4

Explanation: A∩B={2,4}.

Question 4 of 10 easy

If A is the set of all letters in the word 'TRIGONOMETRY', then the roster form of A is:

{T, R, I, G, O, N, M, E, Y}

{T, R, I, G, O, N, O, M, E, T, R, Y}

{T, R, I, G, O, N, M, E, T, Y}

{T, R, I, G, N, M, E, Y}

Explanation: In roster form, all elements of a set are listed, separated by commas, and elements are not repeated. 'TRIGONOMETRY' contains distinct letters T, R, I, G, O, N, M, E, Y.

Question 5 of 10 medium

Consider the set B = {x : x is an integer and −3 < x < 7}. The number of elements in B is:

9

10

8

11

Explanation: The integers strictly between −3 and 7 are −2, −1, 0, 1, 2, 3, 4, 5, 6. Counting these gives exactly 9 elements.

Question 6 of 10 medium

A shop records buyers of tea and coffee. 35 buy tea, 25 coffee and 10 both. Total buying at least one is:

50

60

70

40

Explanation: 35+25−10=50.

Question 7 of 10 medium

In a colony in Chennai, Set A represents households that read 'The Hindu', and Set B represents households that read 'The Indian Express'. What does A − B signify?

Households reading both newspapers.

Households reading at least one newspaper.

Households reading only 'The Hindu'.

Households reading neither newspaper.

Explanation: A − B consists of elements in A but not in B. Contextually, these are households that read 'The Hindu' but DO NOT read 'The Indian Express'. Thus, they read only 'The Hindu'.

Question 8 of 10 easy

If A and B are disjoint sets, then A ∩ B is equal to:

A

B

Universal Set

∅

Explanation: By definition, two sets are disjoint if they have no common elements. Therefore, their intersection is the empty set, ∅.

Question 9 of 10 medium

Which among the following represents the empty set?

{x : x is an even prime number}

{x : x is a real number and x² < 0}

{0}

{x : x² − 1 = 0 and x is an integer}

Explanation: The square of any real number is always non-negative (≥ 0). Thus, no real number satisfies x² < 0, making it an empty set. {0} is a singleton set.

Question 10 of 10 easy

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9} be the universal set and A = {1, 2, 3, 4}. The complement of set A, denoted as A', is:

{1, 2, 3, 4}

{5, 6, 7, 8}

{5, 6, 7, 8, 9}

∅

Explanation: The complement A' contains all elements in the universal set U that are not in A. Removing 1, 2, 3, 4 from U leaves {5, 6, 7, 8, 9}.

Online Test — Sets