This set of Class 11 Maths Chapter 1 Multiple Choice Questions & Answers (MCQs) focuses on “Sets and their Representations – 2”.

1. Which of the following set is not possible?

a) Honest persons

b) Prime numbers up to 100

c) Even numbers up to 100

d) Letters forming the word SCHOOL

View Answer

Explanation: A set is a collection of well defined objects but honesty has no precise definition.

Prime number is a number which can be divisible only by 1 and itself.

Even number is a number which can be divisible by 2.

Set of letters forming the word SCHOOL {S,C,H,O,L}.

2. Write solution set of equation x^{2}-3x+2=0 in roster form.

a) {1,3}

b) {2,4}

c) {1,4}

d) {1,2}

View Answer

Explanation: x

^{2}-3x+2=0

=>x

^{2}-x-2x-2=0=>x(x-1)-2(x-1)=0

=>(x-1)(x-2)=0=>x=1,2

so, the solution set of equation x

^{2}-3x+2=0 in roster form is {1,2}.

3. Write the set \({\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}}\) in set builder form.

a) {x: \(x=\frac{n}{n+1}\) where n is a natural number less than 6}

b) {x: \(x=\frac{n+1}{n+2}\) where n is a natural number less than 6}

c) {x: \(x=\frac{n+1}{n}\) where n is a natural number less than 6}

d) {x: \(x=\frac{n}{n+1}\) where n is a natural number less than 5}

View Answer

Explanation: Since denominator is one more than numerator and only 5 terms are present. So, the above set can be written as {x : \(x=\frac{n}{n+1}\) where n is a natural number less than 6}.

4. Write the set {x : x is an integer and x^{2}-9=0} in roster form.

a) {3}

b) {-3}

c) {3,-3}

d) {9,3}

View Answer

Explanation: Since x is given as integer so x can be positive as well as negative.

x

^{2}-9=0 => (x-3)(x+3)=0 => x=3,-3.

So, the set {x : x is an integer and x

^{2}-9=0} can be written as {3,-3}.

5. What is the interval of f(x) = (x – 1)(x – 2)(x – 3)/(x^{3} + 6x^{2} + 11x+ 6) where f(x) is negative?

a) (-∞, -3) ∪ (3, ∞)

b) (3, -2) ∪ (1, 1) ∪ (2, 3)

c) (-∞, -3) ∪ (2, -1) ∪ (1, 2) ∪ (3, ∞)

d) (-∞, ∞)

View Answer

Explanation: f(x) = (x – 1)(x – 2)(x – 3)/(x

^{3}+ 6x

^{2}+ 11x+ 6)

After solving the cubic equation (x

^{3}+ 6x

^{2}+ 11x+ 6) we get (x+1)(x+2)(x+3)

Now, we can see that this implies f(x) = (x – 1)(x – 2)(x – 3)/(x + 1)(x + 2)(x + 3)

So, the critical points of x are, x = 1, 2, 3, -1, -2, -3

So, for f(x) < 0 ᵾ x € (3, -2) ∪ (1, 1) ∪ (2, 3).

6. What is the set of all x for which 1/(x – 1)(3 – x) ≤ 1?

a) (-∞, 1) ∪ (3, ∞)

b) (-∞, 1) ∪ (3, ∞) ∪ {2}

c) (-∞, 1) ∪ {2}

d) (3, ∞) ∪ {2}

View Answer

Explanation: 1/(x – 1)(3 – x) ≤ 1

Now, on solving the equation further we get,

1/(x – 1)(3 – x) -1 ≤ 0

This also implies,

1- 1/(x – 1)(3 – x) ≥ 0

(x – 1)(3 – x) – 1/(x – 1)(3 – x) ≥ 0

So, (x – 2)

^{2}/(x – 1)(3 – x) ≥ 0.

This implies, (-∞, 1) ∪ (3, ∞) ∪ {2}.

7. Which one of the following is the correct representation of set A = {2,4,8,16….} in set builder form?

a) {x: x = 2n where n ∈ N}

b) {x: x = 2^{n} where n ∈ N}

c) {x: x = 4n where n ∈ N}

d) {x: x = 2n+4 where n ∈ N}

View Answer

Explanation: The sequence is a geometric progression with base 2 hence 2

^{n}is the correct answer.

8. Let A={1,2,3,4,5}. Insert appropriate symbol in 2 ________ A.

a) =

b) <

c) ∈

d) ∉

View Answer

Explanation: Here, 2 is an element of set A.

So, 2 belong to set A. 2∈A.

9. Which one of the following is the correct representation of set A = {1,3,5,7….} in set builder form?

a) {x: x = 2n where n ∈ N}

b) {x: x = n^{2}-1 where n ∈ N}

c) {x: x = 2n+1 where n ∈ N}

d) {x: x = 2n-1 where n ∈ N}

View Answer

Explanation: The given sequence is an odd number sequence of the format 2n+1 or 2n-1, but since n is given as a natural number so 2n+1 is not valid as 0 is not a natural number hence 2n-1 is the correct answer.

10. Which of the following is true for set A = {1,2,3,5,7,10}?

a) 0 ∈ A

b) 2 ∈ A

c) 3 ∉ A

d) 5 ∉ A

View Answer

Explanation: Here 2 is given in the set A therefore 2 ∈ A.

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