NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.2

NCERT Solutions are best way to check your understanding of the chapter. Here you will find Chapter 1 Sets Exercise 1.2 Class 11 Maths NCERT Solutions that will be useful for building your basics and prepare going for advance level books. It will increase your efficient and develop your mind to achieve more marks in the exams. This is very important if you want to crack any entrance exams such as JEE or NEET. These NCERT Solutions for Class 11 Maths will introduce to important formulas that you need to keep in mind before appearing for any competitive exams.

1. Which of the following are examples of the null set: 
(i) Set of odd natural numbers divisible by 2. 
(ii) Set of even prime numbers. 
(iii) {x: x is a natural numbers, x < 5 and x > 7} 
(iv) {y: y is a point common to any two parallel lines}

Answer

(i) Set of odd natural numbers divisible by 2 is a null set, because no odd natural number is divisible by 2. 
(ii) We know that 2 is the only even prime number. Therefore, set of even prime numbers is not a null set.
(iii) {x: x ε N, x < 5 and x > 7}is a null set, because there is no natural number which is less than 5 and greater than 7 simultaneously. 
(iv) {y: y is a point common to any two parallel lines} is a null set, because there is no point common to any two parallel lines.

2. Which of the following sets are finite or infinite:
(i) The set of months of a year 
(ii) {1, 2, 3,...} 
(iii) {1, 2, 3,..., 99, 100} 
(iv) The set of positive integers greater than 100. 
(v) The set of prime numbers less than 99.

Answer

(i) Finite 
(ii) Infinite 
(iii) Finite 
(iv) Infinite 
(v) Finite.

3. State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis. 
(ii) The set of letters in the English alphabet. 
(iii) The set of numbers which are multiple of 5. 
(iv) The set of animals living on the earth. 
(v) The set of circles passing through the origin (0, 0).

Answer

(i) Infinite 
(ii) Finite 
(iii) Infinite 
(iv) Finite 
(v) Infinite

4. In the following, state whether A = B or not:
(i) A = {a, b, c, d} B = {d, c, b, a} 
(ii) A = {4, 8, 12, 16} B = {8, 4, 16, 18} 
(iii) A = {2, 4, 6, 8, 10} B = {x: x is positive even integer and x ≤ 10} 
(iv) A = {x: x is a multiple of 10} B = {10, 15, 20, 25, 30,...}

Answer

(i) Yes, A = B 
(ii) No, A ≠ B 
(iii) Yes, A = B 
(iv) No, A ≠ B.

5. Are the following pairs of sets equal? Gives reasons.
(i) A = {2, 3}, B = {x: x is solution of x2 + 5x + 6 = 0} 
A = {x: x is a letter in the word 'FOLLOW'} 
(ii) B = {y: y is a letter in the word ‘WOLF’}

Answer

(i) No, A = {2, 3} 
But solution of x + 5x + 6 = 0 
⇒ x2 + 3x + 2x + 6 = 0
⇒ x (x + 3) + 2(x + 3) = 0
⇒ (x + 3) (x + 2) = 0 
⇒ x + 3 = 0 or x + 2 = 0 
⇒ x = –3 or x = – 2 
⇒ B = {–2, – 3} 
Hence, A ≠ B 

(ii) Yes, A = {F, O, L, W} 
and B = {W, O, L, F} 
Hence, A = B

6. From the sets given below, select equal sets:
A = {2, 4, 8, 12}, 
B = {1, 2, 3, 4}, 
C = {4, 8, 12, 14}, 
D = {3, 1, 4, 2},
E = {–1, 1}, 
F = {0, a}, 
G = {1, –1}, 
H = {0, 1}

Answer

(i) B = D, (ii) E = G
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