NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1

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

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

NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1 are the part of NCERT Solutions for Class 11 Maths. Here you can find the NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1.

### Ex 1.1 Class 11 Maths Question 1.

(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 {January, June, July}, which is well-defined and hence it is a set.
(ii) The collection of most talented writers of India is not well-defined because opinions about ‘most talented writers’ may vary from person to person and hence it is not a set.
(iii) A team of eleven best-cricket batsmen of the world is not well-defined because opinions about ‘best-cricket batsmen’ may vary from person to person and hence it is not a set.
(iv) The collection of all boys in your class is well-defined and hence it is 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 is a set.
(vi) A collection of novels written by the writer Munshi Prem Chand is well-defined and hence it is a set.
(vii) The collection of all even integers is {…………..,-4, -2, 0, 2, 4,……….. } which is well-defined and hence it is a set.
(viii) The collection of questions in this chapter is well-defined and hence it is a set.
(ix) A collection of most dangerous animals of the world is not well-defined because opinions about ‘most dangerous animals’ may vary from person to person and hence it is not 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 set A. 5 A.
(ii) Since 8 is not the element of set A.
8 A
(iii) Since 0 is not the element of set A
0 A.
(iv) Since 4 is the element of set A.
4 A.
(v) Since 2 is the element of set A.
2 A.
(vi) Since 10 is not the element of set 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}
(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

Solution.
(i) A = {x: x is an integer and -3 < x < 7}
Since integers lying between -3 and 7 are -2, -1, 0, 1, 2, 3, 4, 5, 6.
A = {-2, -1, 0, 1, 2, 3, 4, 5, 6}.

(ii) B = {x: x is a natural number less than 6}
Since natural numbers less than 6 are 1, 2, 3, 4, 5.
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}
Since 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) D = {x: x is a prime number which is divisor of 60}
Since prime numbers which are divisors of 60 are 2, 3, 5.
D = {2, 3, 5}

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

Since the letters in the word TRIGONOMETRY are T, R, I, G, O, N, M, E, Y.
E = (T, R, I, G, O, N, M, E, Y}

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

The 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} = (21, 22, 23, 24, 25}
B = {x: x = 2n, n N and 1 ≤ n ≤ 5}

(iii) Let C = (5, 25, 125, 625} = (51, 52, 53, 54}
C = {x: x = 5n, 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 = n2, 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, x2 ≤ 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, x2 ≤ 4}
x2 ≤ 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).

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