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NCERT Solutions for Class 11 Maths Chapter 1
Sets Class 11
Chapter 1 Sets Exercise 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, miscellaneous Solutions
Exercise 1.1 : Solutions of Questions on Page Number : 4
Q1 :
Which of the following are sets? Justify our answer.
(i) The collection of all 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.
Answer :
(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 team of eleven best cricket batsmen of the world is not a well-defined collection because the criteria for
determining a batsman's talent may vary 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 Prem Chand is a well-defined collection because one can
definitely identify a book that belongs to this collection.
Hence, this collection is a set.
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(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 animals 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.
Q2 :
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
Answer :
(i) 5 A
(ii) 8 A
(iii) 0 A (iv) 4 A
(v) 2 A (vi)
10 A
Q3 :
Write the following sets in roster form:
(i) A = {x: x is an integer and -3 < x < 7}.
(ii) B = {x: x is a natural number less than 6}.
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8} (iv) D = {x: x 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.
Answer :
(i) A = {x: x is an integer and –3 < x < 7}
The elements of this set are –2, –1, 0, 1, 2, 3, 4, 5, and 6 only.
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Therefore, the given set can be written in roster form as
A = {–2, –1, 0, 1, 2, 3, 4, 5, 6} (ii) B = {x:
x is a natural number less than 6}
The elements of this set are 1, 2, 3, 4, and 5 only.
Therefore, the given set can be written in roster form as
B = {1, 2, 3, 4, 5}
(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}
2 60
2 30
3 15
5
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}
Q4 :
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 …}
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(v) {1, 4, 9 … 100}
Answer :
(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}
Q5 :
List all the elements of the following sets:
(i) A = {x: x is an odd natural number}
(ii) B = {x: x is an integer,}
(iii) C = {x: x is an } integer,
(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 proceeds k}.
Answer :
(i) A = {x:x is an odd natural number} = {1, 3, 5, 7, 9 …}
(ii) B = {x:x } is an integer;
It can be seen and that
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NCERT Solutions for Class 11 Maths Chapter 1
Sets Class 11
Chapter 1 Sets Exercise 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, miscellaneous Solutions
Exercise 1.1 : Solutions of Questions on Page Number : 4
Q1 :
Which of the following are sets? Justify our answer.
(i) The collection of all 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.
Answer :
(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 team of eleven best cricket batsmen of the world is not a well-defined collection because the criteria for
determining a batsman's talent may vary 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 Prem Chand is a well-defined collection because one can
definitely identify a book that belongs to this collection.
Hence, this collection is a set.
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(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 animals 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.
Q2 :
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
Answer :
(i) 5 A
(ii) 8 A
(iii) 0 A (iv) 4 A
(v) 2 A (vi)
10 A
Q3 :
Write the following sets in roster form:
(i) A = {x: x is an integer and -3 < x < 7}.
(ii) B = {x: x is a natural number less than 6}.
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8} (iv) D = {x: x 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.
Answer :
(i) A = {x: x is an integer and –3 < x < 7}
The elements of this set are –2, –1, 0, 1, 2, 3, 4, 5, and 6 only.
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Therefore, the given set can be written in roster form as
A = {–2, –1, 0, 1, 2, 3, 4, 5, 6} (ii) B = {x:
x is a natural number less than 6}
The elements of this set are 1, 2, 3, 4, and 5 only.
Therefore, the given set can be written in roster form as
B = {1, 2, 3, 4, 5}
(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}
2 60
2 30
3 15
5
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}
Q4 :
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 …}
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(v) {1, 4, 9 … 100}
Answer :
(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}
Q5 :
List all the elements of the following sets:
(i) A = {x: x is an odd natural number}
(ii) B = {x: x is an integer,}
(iii) C = {x: x is an } integer,
(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 proceeds k}.
Answer :
(i) A = {x:x is an odd natural number} = {1, 3, 5, 7, 9 …}
(ii) B = {x:x } is an integer;
It can be seen and that
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