CBSE NCERT Solutions For Class 11th Maths Chapter 1 : Set. NCERT Solutins For Class 11 Mathematics. Exercise 1.1, Exercise 1.2, Exercise 1.3, Exercise 1.4, Exercise 1.5, Exercise 1.6, (Miscellaneous Excercise) many more solutions

**Exercise 1.1**

**Question 1:**

Which of the following are sets? Justify our answer.

- The collection of all months of a year beginning with the letter J.
- The collection of ten most talented writers of India.
- A team of eleven best-cricket batsmen of the world.
- The collection of all boys in your class.
- The collection of all natural numbers less than 100.
- A collection of novels written by the writer Munshi Prem Chand.
- The collection of all even integers.
- The collection of questions in this Chapter.
- A collection of most dangerous animals of the world.

Answer

- 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.

- 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.
- 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.
- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

**Question 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

Answer

- 5 ∈ A
- 8 ∉ A
- 0 ∉ A
- 4 ∈ A
- 2 ∈ A
- 10 ∉ A

**Question 3:**

Write the following sets in roster form:

- A = {
*x*:*x*is an integer and –3 <*x*< 7}. - B = {
*x*:*x*is a natural number less than 6}. - C = {
*x*:*x*is a two-digit natural number such that the sum of its digits is 8} - D = {
*x*:*x*is a prime number which is divisor of 60}. - E = The set of all letters in the word TRIGONOMETRY.
- 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.

Therefore, the given set can be written in roster form as

A = {–2, –1, 0, 1, 2, 3, 4, 5, 6}

- 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}

- 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}

- 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}

**Question 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}** **Answer

- {3, 6, 9, 12} = {
*x*:*x*= 3*n*,*n*∈ N and 1 ≤*n*≤ 4} - {2, 4, 8, 16, 32}

It can be seen that 2 = 2^{1}, 4 = 2^{2}, 8 = 2^{3}, 16 = 2^{4}, and 32 = 2^{5}. ∴ {2, 4, 8, 16, 32} = {*x*: *x* = 2* ^{n}*,

*n*∈ N and 1 ≤

*n*≤ 5}

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

It can be seen that 5 = 5^{1}, 25 = 5^{2}, 125 = 5^{3}, and 625 = 5^{4}. ∴ {5, 25, 125, 625} = {*x*: *x* = 5* ^{n}*,

*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 = 1^{2}, 4 = 2^{2}, 9 = 3^{2} …100 = 10^{2}. ∴ {1, 4, 9… 100} = {*x*: *x* = *n*^{2}, *n*∈N and 1 ≤ *n* ≤ 10}

**Question 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, }

- C = {
*x*:*x*is an integer, } - D = {
*x*:*x*is a letter in the word “LOYAL”} - 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 that and

∴ B

**(iii) **C = {*x*:** ***x*** **is an integer; } It can be seen that

(–1)^{2} = 1 ≤ 4; (–2)^{2} = 4 ≤ 4; (–3)^{2} = 9 > 4 0^{2} = 0 ≤ 4 1^{2} = 1 ≤ 4 2^{2} = 4 ≤ 4 3^{2} = 9 > 4

∴C = {–2, –1, 0, 1, 2}

**(iv) **D = (*x*:** ***x*** **is a letter in the word “LOYAL”) = {L, O, Y, A}

- E = {
*x*:*x*is a month of a year not having 31 days} = {February, April, June, September, November} - F = {
*x*:*x*is a consonant in the English alphabet which precedes*k*} = {*b, c, d, f, g, h, j*}

**Question 6:**

Match each of the set on the left in the roster form with the same set on the right

described in set-builder form: | ||

(i) {1, 2, 3, 6} | (a) {x: x is a prime number and a divisor of 6} | |

(ii) {2, 3} | (b) {x: x is an odd natural number less than 10} | |

(iii) {M, A,T, H, E, I,C, S} | (c) {x: x is natural number and divisor of 6} | |

(iv) {1, 3, 5, 7, 9} | (d) {x: x is a letter of the word MATHEMATICS} | |

Answer |

- All the elements of this set are natural numbers as well as the divisors of 6. Therefore,
**(i)**matches with**(c)**. - It can be seen that 2 and 3 are prime numbers. They are also the divisors of 6. Therefore,
**(ii)**matches with**(a)**.- All the elements of this set are letters of the word MATHEMATICS. Therefore,
**(iii)**

- All the elements of this set are letters of the word MATHEMATICS. Therefore,

matches with **(d)**.

**(iv) **All the elements of this set are odd natural numbers less than 10. Therefore,** (iv)**

matches with **(b)**.

### NCERT Solutions for Class XI Maths: Chapter 1 – Set

**Exercise 1.1 Solutions****Exercise 1.2 Solutions****Exercise 1.3 Solutions****Exercise 1.4 Solutions****Exercise 1.5 Solutions****Exercise 1.6 Solutions****Miscellaneous Solutions**