State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of 5
(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0, 0)

Solution:

(i) The set of lines which are parallel to the x-axis is an infinite set because lines parallel to the x-axis are infinite (cannot be counted).

(ii) The set of letters in the English alphabet is a finite set because it has finite number(26) of elements.

(iii) The set of numbers that are multiples of 5 is an infinite set because there are infinite number of multiples of 5 such as 5, 10, 15, ...,

(iv) The set of animals living on the earth is a finite set because the number of animals living on the earth is finite (though it is quite a large number, they can be counted).

(v) The set of circles passing through the origin (0, 0) is an infinite set because an infinite number of circles can pass through the origin

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.2 Question 3

State whether each of the following set is finite or infinite: (i) The set of lines which are parallel to the x-axis (ii) The set of letters in the English alphabet (iii) The set of numbers which are multiple of 5 (iv) The set of animals living on the earth (v) The set of circles passing through the origin (0, 0)

Summary:

We are asked to state whether each of the following set is finite or infinite. We found that 
(i) The set of lines which are parallel to the x-axis is infinite.
(ii) The set of letters in the English alphabet is finite.
(iii) The set of numbers which are multiple of 5 is infinite.
(iv) The set of animals living on the earth is finite.
(v) The set of circles passing through the origin (0, 0) is infinite.