# NCERT Solutions For Class 11 Maths Chapter 1 Sets Ex 1.1

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 1 |

Exercise | Class 11 Maths Chapter 1 Sets Exercise 1.1 |

Number of Questions Solved | 6 |

## NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1

**NCERT TEXTBOOK EXERCISES**

**Ex 1.1 Class 11 Maths Question 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 world.

**Solution.**

**(i)** The collection of all months of a year beginning with J is {J anuary, 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 batsmen of the world is not well defined because opinions 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, 4,…………, 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 of all even integers is {…………..,-4, -2, 0, 2, 4,……….. } 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 opinions about ‘most dangerous animals’ vary from person to person and hence it does not form a set.

**Ex 1.1 Class 11 Maths 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

**Solution.**

**(i) **Since 5 is the element of A. ∴ 5 ∉ A.**(ii) **As 8 is not the element of A. ∴ 8 ∉ A**(iii) **As 0 is not the element of A ∴ 0 ∈ A.**(iv) **4 is the element of A ∴ 4 ∈ A.**(v) **2 is the element of A ∴ 2 ∈ A.**(vi) **10 is not the element of A ∴ 10 ∉ A.

**Ex 1.1 Class 11 Maths Question 3. 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}**(v)** E = The set of all letters in the word TRIGONOMETRY**(vi)** F = The set of all letters in the word

**Solution.**

**(i)** Integers lying between -3 and 7 are -2, -1, 0, 1, 2, ……….. , 6

∴ A = {-2,-1, 6}.

**(ii)** Natural numbers less than 6 are 1, 2, 3, 4, 5.

∴ B = 11, 2, 3, 4, 5}

**(iii)** Two digit natural numbers such that the sum of its digits is 8 are 17, 26, 35, 44, 53, 62, 71, 80.

∴ C= (17, 26, 35, 44, 53, 62, 71,80}

**(iv)** Prime number divisors of 60 are 2, 3, 5.

∴ D = (2, 3, 5}

**(v)** Word TRIGONOMETRY is formed by using the letters T, R, I, G, O, N, M, E, Y.

∴ E = (T, R, I, G, N, O, M, E, Y}

**(vi)** Word BETTER is formed by using the letters B, E, T, R

∴ F = (B, E, T, R}

**Ex 1.1 Class 11 Maths 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}

**Solution.**

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

All elements of the set are natural numbers that are multiples of 3.

∴ A = (x : x = 3n, n∈N and 1 ≤ n ≤4}

**(ii)** Let B = (2, 4, 8, 16, 32} = (2^{1}, 2^{2}, 2^{3}, 2^{4}, 2^{5}}

∴ B = {x : x = 2^{n}, n ∈ N and 1 ≤ n ≤ 5}

**(iii)** Let C = (5, 25, 125, 625} = (5^{1}, 5^{2}, 5^{3}, 5^{4}}

∴ C = {x : x = 5^{n}, n ∈ N and 1 ≤ n ≤ 4}

**(iv)** Let D = (2, 4, 6,……………..}

All elements of the set are even natural numbers.

∴ D = (x: x is an even natural number)

**(v)** Let E = {1,4,9,……….,100}

All elements of the set are perfect squares.

∴ E = {x: x = n^{2}, n ∈ N and 1 ≤ n ≤ 10}

**Ex 1.1 Class 11 Maths 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, −1/2 < x < 9/2}**(iii)** C = {x: x is an integer, x^{2} ≤ 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}.

**Solution.**

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

∴ A = {1, 3, 5, 7,……………}

**(ii)** B = {x: x is an integer, −1/2 < x < 9/2}

∴ B = { 0, 1, 2, 3, 4}

**(iii)** C = {x: x is an integer, x^{2} ≤ 4}

x^{2} ≤ 4⇒ -2 ≤ x ≤ 2

∴ C = {-2, -1, 0, 1, 2}

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

∴ D = {L, O, Y, A}

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

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

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

∴ F = {b, c, d, f, g, h, j}

**Ex 1.1 Class 11 Maths 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}.

**Solution.**

**(i)** → (c),**(ii)** → (a),**(iii)** → (d),**(iv)** → (b).

**The sets which are in set-builder form can be written in roster form as follows:(a)** {x : x is a prime number and a divisor of 6} = {2, 3}

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

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

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

## NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.1 PDF

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