This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Finite and Infinite Sets”.

1. Which of the following set is finite?

a) {1,2,3,4,……………………….}

b) {4,7,9}

c) {1,4,9,16,…………………….}

d) {1,8,27,……………………….}

View Answer

Explanation: {4,7,9} is finite set because it contains finite (countable) number of elements. Rest all are infinite sets. {1,2,3,4,…………..} is a set of natural numbers. {1,4,9,……………} is a set of square of natural numbers. {1,8,27,………………………} is a set of cube of natural numbers.

2. The finite set can have ________________ number of elements.

a) only zero

b) only one

c) at least one

d) zero or more but not infinite

View Answer

Explanation: A finite set can have any number of elements except infinity i.e. a finite set can have zero or more number of elements but not infinite.

3. The set is infinite if it has _______________ number of elements.

a) zero

b) one

c) finite

d) infinite

View Answer

Explanation: The set is infinite if it has infinite number of elements. Set having zero elements is empty set, set having one element is singleton set, set having finite number of elements is finite set.

4. Which of the following is infinite set?

a) Set of days of week

b) Set of points on a line

c) Set of months in a year

d) Set of prime numbers less than 99

View Answer

Explanation: There are infinite number of points on a line. So, the set of points on a line is infinite. Rest all sets contain finite number of elements.

Set of days of week has 7 elements and set of months in a year has 12 elements. Set of prime number less than 99 {2,3,5,7,11,……….,97}.

5. Set of letters of English alphabet is__________________

a) empty set

b) singleton set

c) finite set

d) infinite set

View Answer

Explanation: Set of letters of English alphabet has 26 elements so it is a finite set.

It is not a singleton, empty or infinite set. Empty set has no element, singleton set has one element, infinite set has infinite number of elements.

6. Which of the following is a finite set?

a) Set of natural numbers

b) Set of whole numbers

c) Set of even numbers

d) Set of even prime number

View Answer

Explanation: Set of even prime number {2} is a finite set as it contain one element. Rest all have infinite number of elements.

Set of natural numbers is {1,2,3,4,…………..}

Set of whole numbers is {0,1,2,3,4,………….}

Set of even numbers is {2,4,6,………………….}

7. Which of the set is singleton set?

a) Set of odd prime numbers

b) Set of even prime numbers

c) Set of odd numbers

d) Set of prime numbers

View Answer

Explanation: Set of even prime number {2} has one element so it is a singleton set.

Set of odd prime numbers {3,5,7,11,…………..}, set of odd numbers {1,3,5,7,……………}, set of prime numbers {2,3,5,…………} has infinite number of elements. So, they cannot form a singleton set.

8. Set {x : x is a natural number and 2x+1=0} is a finite set?

a) True

b) False

View Answer

Explanation: 2x+1=0 => x= -1/2 which is not a natural number so it is an empty set. Empty set is also a finite set as finite set have zero or more number of elements but not infinite.

9. Set of solutions of a quadratic equation is finite set.

a) True

b) False

View Answer

Explanation: A quadratic equation can have maximum two roots. So, the set can have 0 to 2 number of elements so it must be a finite set.

10. Finite set ______________ empty set.

a) is same as

b) is an

c) is not

d) may or may not

View Answer

Explanation: A finite set can have zero or more number of elements but not infinite so, finite set may or may not be empty set. Empty set is a set with no element in it.

11. Which of the following is an infinite set?

a) A set of girls in a college

b) A set of players in a cricket team

c) A set of points in a Line

d) A set of edges in a square

View Answer

Explanation: Since girls in a college, players in a team and number of edges in a square are all fixed quantities they come under finite set and points on a line are infinite hence they come under infinite set.

12. Which of the following is true?

a) A finite set has an infinite number of elements

b) An empty set is a finite set

c) An empty set is neither finite nor infinite

d) An infinite set has a countable number of elements

View Answer

Explanation: An empty has 0 elements hence it is countable and finite, Therefore, we say that empty set is a finite set. An infinite set has an uncountable number of elements.

13. Which of the following is a finite set?

a) Set of points in a line

b) Set of natural numbers

c) Set of mothers in a family

d) Set of prime numbers

View Answer

Explanation: Set of points in a line, set of prime numbers and natural numbers are uncountable hence belong to an infinite set. Here the number of mothers in a family can be counted.

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