**Class 11 Maths Chapter 1 Sets**

**NCERT Solutions For Class 11 Maths Chapter 1 Sets, (Maths) exam are Students are taught thru NCERT books in some of state board and CBSE Schools. As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation. Students need to clear up those exercises very well because the questions withinside the very last asked from those. **

**Sometimes, students get stuck withinside the exercises and are not able to clear up all of the questions. To assist students solve all of the questions and maintain their studies with out a doubt, we have provided step by step NCERT Solutions for the students for all classes. These answers will similarly help students in scoring better marks with the assist of properly illustrated solutions as a way to similarly assist the students and answering the questions right.**

**NCERT Solutions For Class 11 Maths Chapter 1 Sets**

**Class 11 Maths Chapter 1 Sets**

**Exercise 1.1**

**1. Which of the following are sets? Justify your answer.**

**(i) The collection of all the months of a year beginning with the letter J.**

**(ii) The collection of ten most talented writers of India.**

**(iii) A team of eleven best-Cricket batmen of the world.**

**(iv) The collection of all boys in your class.**

**(v) The collection of all natural numbers less than 100.**

**(vi) A collection of novels written by the writer Munshi Prem Chand.**

**(vii) The collection of all even integers.**

**(viii) The collection of questions in the chapter.**

**(ix) A collection of most dangerous animals of the world.**

**Ans. (i) **The collection of all months of a year beginning with J is {January, June, July}, which is well defined and hence it forms a set.

**(ii) **The collection of most talented writers of India is not well defined because opinions about ‘most talented writers’ vary from person to person and hence it does not form a set.

**(iii) **A team of eleven best-cricket batmen of the world us not well defined because opinion about ‘best-cricket batsmen’ vary from person to person and hence it does not form a set.

**(iv) **The collection of all boys in your class is well defined and hence it forms a set.

**(v) **The collection of all natural numbers less than 100 is {1, 2, 3, ……., 99} which is well defined and hence it forms a set.

**(vi) **A collection of novels written by the writer Munshi Prem Chand is well defined and hence it forms a set.

**(vii) **The collection al all even integers is which is well defined and hence it forms a set.

**(viii) **The collection of questions in this chapter is well defined and hence it forms a set.

**(ix) **A collection of most dangerous animals of the world is not well defined because opinion about ‘most dangerous animals’ vary from person to person and hence it does not form a set.

**2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol or on the blank space:**

**(i) 5 _______ A**

**(ii) 8 _______ A**

**(iii) 0 _______ A**

**(iv) 4 _______ A**

**(v) 2 _______ A**

**(vi) 10 _______ A**

**Ans. **Given: A = {1, 2, 3, 4, 5, 6}

**(i) **5 is an element of set A

5 A

**(ii) **8 is not an element of set A

8 A

**(iii) **0 is not an element of set A

0 A

**(iv) **4 is an element of set A

4 A

**(v) **2 is an element of set A

2 A

**(vi) **10 is not an element of set A

10 A

**3. Write the following sets in roster form:**

**(i) A = { is an integer and }**

**(ii) B = { is a natural number less than 6}**

**(iii) C = { is a two-digit natural number such that the sum of its digits is 8}**

**(iv) D = { is a prime number which is divisor of 60}**

**(v) E = The set of all letters in the word TRIGONOMETRY**

**(vi) F = The set of all letters in the word BETTER**

**Ans. (i) **A = { is an integer and } A =

**(ii) **B = { is a natural number less than 6} B = {1, 2, 3, 4 5}

**(iii) **C = { is a two-digit natural number such that the sum of its digits is 8}

C = {17, 26, 35, 44, 53, 62, 71, 80}

**(iv) **D = { is a prime number which is divisor of 60}

D = {2, 3, 5}

**(v) **E = The set of all letters in the word TRIGONOMETRY

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

**(vi) **F = The set of all letters in the word BETTER

F = {B, E, T, R}

**4. Write the following sets in the set-builder form:**

**(i) {3, 6, 9, 12}**

**(ii) {2, 4, 8, 16, 32}**

**(iii) {5, 25, 125, 625}**

**(iv) {2, 4, 6, ……}**

**(v) {1, 4, 9, ………, 100}**

**Ans. (i) **Let A = {3, 6, 9, 12}.

Here all objects of the set are natural numbers that are multiples of 3.

A =

**(ii) **Let B = {2, 4, 8, 16, 32}

Here all objects of the set are natural numbers that are power of 2.

B =

**(iii) **Let C = {5, 25, 125, 625}

Here all objects of the set are natural numbers that are power of 5.

C =

**(iv) **Let D = {2, 4, 6, ……}

Here all objects of the set are even natural numbers.

D =

**(v) **Let E = {1, 4, 9, ………, 100}

Here all objects of the set are perfect square.

D =

**5. List all the elements of the following sets:**

**(i) A = { is an odd natural number}**

**(ii) B = { is an integer, }**

**(iii) C = { is an integer, }**

**(iv) D = { is a letter in the word “LOYAL”}**

**(v) E = { is a month of a year not having 31 days}**

**(vi) F = { is a consonant in the English alphabet which precedes K}**

**Ans. (i) **A = { is an odd natural number}

A = {1, 3, 5, 7, ……..}

**(ii) **B = { is an integer, }

B = {0, 1, 2, 3, 4}

**(iii) **C = { is an integer, }

C =

**(iv) **D = { is a letter in the word “LOYAL”}

D = {L, O, Y, A}

**(v) **E = { is a month of a year not having 31 days}

E = {February, April, June, September, November}

**(vi) **F = { is a consonant in the English alphabet which precedes K}

F = {B, C, D, F, G, H, J}

**6. Match each of the set on the left in the roster form with the same set on the right described in the set-builder form:**

**(i) {1, 2, 3, 6}**

**(a) { is a prime number and a divisor of 6}**

**(ii) {2, 3}**

**(b) { is an odd natural number less than 10}**

**(iii) {M, A, T, H, E, I, C, S}**

**(c) { is a natural number and divisor of 6}**

**(iv) {!, 3, 5, 7, 9}**

**(d) { is a letter of word “MATHEMATICS”}**

**Ans. **The sets which are in set-builder form can be written as

**(a) **{ is a prime number and a divisor of 6} = {2, 3}

**(b) **{ is an odd natural number less than 10} = {1, 3, 5, 7, 9}

**(c) **{ is a natural number and divisor of 6} = {1, 2, 3, 6}

**(d) **{ is a letter of word “MATHEMATICS”} = {M, A, T, H, E, I, C, S}

Hence the correct matching is:

**(i) ** (c)

**(ii)** (a)

**(iii) **(d)

**(iv) **(b)

**NCERT solutions for class 11 Maths Chapter 1 Sets Exercise 1.2, (Maths) exam are Students are taught thru NCERT books in some of state board and CBSE Schools. As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation. Students need to clear up those exercises very well because the questions withinside the very last asked from those. **

**Sometimes, students get stuck withinside the exercises and are not able to clear up all of the questions. To assist students solve all of the questions and maintain their studies with out a doubt, we have provided step by step NCERT Solutions for the students for all classes. These answers will similarly help students in scoring better marks with the assist of properly illustrated solutions as a way to similarly assist the students and answering the questions right.**

**NCERT Solutions For Class 11 Maths**

**Chapter 1 : Sets **

**Exercise 1.2**

**1. Which of the following are examples of the null set:**

**(i) Set of odd natural numbers divisible by 2.**

**(ii) Set of even prime numbers.**

**(iii) { is a natural number, and }**

**(iv) { is a point common to any two parallel lines}**

**Ans. (i) **Set of odd natural numbers divisible by 2 is an empty set because odd natural numbers are not divisible by 2.

**(ii) **Set of even prime numbers is {2} which is not empty set.

**(iii) **{ is a natural number, and } is an empty set because there is no natural number which satisfies simultaneously and .

**(iv) **{ is a point common to any two parallel lines} is an empty set because two parallel lines do not have a common point.

**2. Which of the following sets are finite or infinite:**

**(i) The set of months of a year.**

**(ii) {1, 2, 3, ………..}**

**(iii) {1, 2, 3, ………….., 99, 100}**

**(iv) The set of positive integers greater than 100.**

**(v) The set of prime numbers less than 99.**

**Ans. (i) **The set of months of a year is finite set because there are 12 months in a year.

**(ii) **{1, 2, 3, ………..} is an infinite set because there are infinite elements in the set.

**(iii) **{1, 2, 3, ………….., 99, 100} is a finite set because the set contains finite number of elements.

**(iv) **The set of positive integers greater than 100 is an infinite set because there are infinite number of positive integers greater than 100.

**(v) **The set of prime numbers less than 99 is a finite set because the set contains finite number of elements.

**3. State whether each of the following sets is finite or infinite:**

**(i) The set of lines which are parallel to the 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).**

**Ans. (i) **The set of lines which are parallel to the axis is an infinite set because we can draw infinite number of lines parallel to axis.

**(ii) **The set of letters in the English alphabet is a finite set because there are 26 letters in the English alphabet.

**(iii) **The set of numbers which are multiple of 5 is an infinite set because there are infinite multiples of 5.

**(iv) **The set of animals living on the earth is a finite set because the number of animals living on the earth is every large but finite.

**(v) **The set of circles passing through the origin (0, 0) is an infinite set because we can draw infinite number of circles through origin in different radii.

**4. In the following, state whether A = B or not:**

**(i) A = B = **

**(ii) A = {4, 8, 12, 16} B = {8, 4, 16, 18}**

**(iii) A = {2, 4, 6, 8, 10} B = { is a positive even integer and }**

**(iv) A = { is a multiple of 10} B = {10, 15, 20, 25, 30, ….}**

**Ans. (i) **A = and B = are equal sets because order of elements does not change a set. Therefore, A = B =

**(ii) **A = {4, 8, 12, 16} and B = {8, 4, 16, 18} are not equal sets because 12 A, 12 B and 18 B, 19 A

**(iii) **A = {2, 4, 6, 8, 10} and B = { is a positive even integer and } which can be written in roster form as B = {2, 4, 6, 8, 10} are equal sets.

**(iv) **A = { is a multiple of 10} can be written in roster form as A = {10, 20, 30, 40, …..} and B = {10, 15, 20, 25, 30, ….} are not equal sets because 15 B, 15 A.

**5. Are the following pairs of sets equal? Give reason.**

**(i) A = {2, 3} and B = { is a solution of }**

**(ii) A = : is a letter in the word FOLLOW}**

**B = { is a letter in the word WOLF}**

**Ans. (i) **A = {2, 3} and B

= { is a solution of }

Here

B =

Therefore, A and B are not equal sets.

**(ii) **A = : is a letter in the word FOLLOW} = {F, O, L, W}

B = { is a letter in the word WOLF} = {W, O, L, F}

Therefore, A = B = {F, O, L, W}

**6. From the sets given below, select equal sets:**

**A = {2, 4, 8, 12}**

**B = {1, 2, 3, 4}**

**C = {4, 8, 12, 14}**

**D = {3, 1, 4, 2}**

**E = **

**F = **

**G = **

**H = {0, 1}**

**Ans. **From the given sets, Set B and D have same elements and also sets E and G have same element.

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