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NCERT Solutions Class 11 Maths Chapter 1 Set – Here are all the NCERT solutions for Class 11 Maths Chapter 1. This solution contains questions, answers, images, explanations of the complete chapter 1 titled Of Set taught in Class 11. If you are a student of Class 11 who is using NCERT Textbook to study Maths, then you must come across chapter 1 Set After you have studied lesson, you must be looking for answers of its questions. Here you can get complete NCERT Solutions for Class 11 Maths Chapter 1 Set in one place.

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NCERT Solutions Class 11 Maths Chapter 1 SET

Here on AglaSem Schools, you can access to NCERT Book Solutions in free pdf for Maths for Class 11 so that you can refer them as and when required. The NCERT Solutions to the questions after every unit of NCERT textbooks aimed at helping students solving difficult questions.

For a better understanding of this chapter, you should also see summary of Chapter 1 SET , Maths, Class 11.

Class 11
Subject Maths
Book Mathematics
Chapter Number 1
Chapter Name

SET

NCERT Solutions Class 11 Maths chapter 1 SET

Class 11, Maths chapter 1, SET solutions are given below in PDF format. You can view them online or download PDF file for future use.

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NCERT Solutions for Class 11 Maths Chapter 1 Sets

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Question & Answer

Q.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 batsmen 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 this Chapter.
(ix) A collection of most dangerous animals of the world.

Ans : (i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects because one can definitely identify a month that belongs to this collection. Hence, this collection is a set. 
(ii) The collection of ten most talented writers of India is not a well-defined collection because the criteria for determining a writer's talent may vary from person to person. Hence, this collection is not a set, 
(iii) A tearn of eleven best cricket batsmen of the world is not a well-defined collection because the criteria for determining a batsrnan's talent may varv from person to person. Hence, this collection is not a set. 
(iv) The collection of all boys in your class is a well-defined collection because you can definitely identify a boy who belongs to this collection. Hence, this collection is a set, 
(v) The collection of all natural numbers less than 100 is a well-defined collection because one can definitely identify a number that belongs to this collection. Hence, this collection is a set. 
(vi) A collection of novels written by the writer Munshi Prenn Chand is a well-defined collection because one can definitely identify a book that belongs to this collection.
Hence, this collection is a set. 
(vii) The collection of all even integers is a well-defined collection because one can definitely identify an even integer that belongs to this collection. Hence, this collection is a Set. 
(viii) The collection of questions in this chapter is a well-defined collection because one can definitely identify a question that belongs to this chapter. Hence, this collection is a set. 
(ix) The collection of most dangerous mimals of the world is not a well-defined collection because the criteria for determining the dangerousness of an animal can vary from person to person. Hence, this collection is not a set. 
Q.2: Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank
Spaces: 
(i) 5. . .A       (ii) 8 . . . A   (iii) 0. . .A 
(iv) 4. . . A     (v) 2. . .A       (vi) 10. . .A

Ans : \(\begin{array}{l}{\text { (i) } 5 \in \mathrm{A}} \\ {\text { (ii) } 8 \notin \mathrm{A}} \\ {\text { (iii) } 0 \notin \mathrm{A}}\end{array}\)
\(\begin{array}{l}{\text { (iv) } 4 \in \mathrm{A}} \\ {\text { (v) } 2 \in \mathrm{A}} \\ {\text { (vi) } 10 \notin \mathrm{A}}\end{array}\) 
Q.3: Write the following sets in roster form:  
\(\begin{aligned}\text { (i) } A=\{x : x \text { is an integer and }-3 \leq x<7\} \\ \text { (ii) }  B=\{x : x \text { is a natural number less than } 6\} \end{aligned}\)
\(\begin{array}{l}{\mathrm(iii)\ {C}=\{x : x \text { is a two-digit natural number such that the sum of its digits is } 8\}} \\ {\text { (iv) } \mathrm{D}=\{x : x \text { is a prime number which is divisor of } 60\}}\end{array}\)
\(\begin{array}{l}{\text { (v) } \mathrm{E}=\text { The set of all letters in the word TRIGONOMETRY }} \\ {\text { (vi) } \mathrm{F}=\text { The set of all letters in the word BETTER }}\end{array}\)

Ans : \(\begin{array}{l}{\text { (i) } A=\{x : x \text { is an integer and }-3< x < 7\}} \\ {\text { The elements of this set are }-2,-1,0,1,2,3,4,5, \text { and } 6 \text { only. }} \\ {\text { Therefore, the given set can be written in roster form as }} \\ {A=\{-2,-1,0,1,2,3,4,5,6\}} \\ {\text { (ii) } B=\{x : x \text { is a natural number less than } 6\}} \\ {\text { The elements of this set can be written in roster form as }} \\ {\text { B }=\{1,2,3,4,5\}}\end{array}\)
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
The elements of this set are 17, 26, 35, 44, 53, 62, 71, and 80 only.
Therefore, this set can be written in roster form as
C = {17, 26, 35, 44, 53, 62, 71, 80}


(iv) D = {x: x is a prime number which is a divisor of 60}
  
∴60 = 2 × 2 × 3 × 5
The elements of this set are 2, 3, and 5 only.
Therefore, this set can be written in roster form as D = {2, 3, 5}.
(v) E = The set of all letters in the word TRIGONOMETRY
There are 12 letters in the word TRIGONOMETRY, out of which letters T, R, and O are repeated.
Therefore, this set can be written in roster form as
E = {T, R, I, G, O, N, M, E, Y}
(vi) F = The set of all letters in the word BETTER 
There are 6 letters in the word BETTER, out of which letters E and T are repeated.
Therefore, this set can be written in roster form as  
F = {B, E, T, R} 
Q.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) {3, 6, 9, 12} = {x: x = 3n, n∈ N and 1 ≤ n ≤ 4}
(ii) {2, 4, 8, 16, 32}
It can be seen that 2 = 21, 4 = 22, 8 = 23, 16 = 24, and 32 = 25.
∴ {2, 4, 8, 16, 32} = {x: x = 2n, n∈ N and 1 ≤ n ≤ 5}
(iii) {5, 25, 125, 625}
It can be seen that 5 = 51, 25 = 52, 125 = 53, and 625 = 54.
∴ {5, 25, 125, 625} = {x: x = 5n, n∈N and 1 ≤ n ≤ 4}
(iv) {2, 4, 6 …}
It is a set of all even natural numbers.
∴ {2, 4, 6 …} = {x: x is an even natural number}
(v) {1, 4, 9 … 100}
It can be seen that 1 = 12, 4 = 22, 9 = 32 …100 = 102.
∴ {1, 4, 9… 100} = {x: x = n2, n∈N and 1 ≤ n ≤ 10} 
Q.5: List all the elements of the following sets :
(i) A = {x : x is an odd natural number}
(ii) B {x: x is an integer,  -1/2 < x <9/2}
(iii) C = {x : x is an integer, \(x^{2} \leq 4 \}\)
(iv) D = {x : x is a letter in the word “LOYAL”}
(v) E = {x : x is a month of a year not having 31 days}
(vi) F = {x : x is a consonant in the English alphabet which precedes k }.

Ans : (i) A = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …}
  


(iii) C = {x: x is an integer;}
It can be seen that
(–1)2 = 1 ≤ 4; (–2)2 = 4 ≤ 4; (–3)2 = 9 > 4
02 = 0 ≤ 4
12 = 1 ≤ 4
22 = 4 ≤ 4
32 = 9 > 4
∴C = {–2, –1, 0, 1, 2}


(iv) D = (x: x is a letter in the word “LOYAL”) = {L, O, Y, A}
(v) E = {x: x is a month of a year not having 31 days}
= {February, April, June, September, November}
(vi) F = {x: x is a consonant in the English alphabet which precedes k}
= {b, c, d, f, g, h, j}

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