# Class 11 Maths MCQ – Sets and their Representations – 2

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

Answer: a
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 x2-3x+2=0 in roster form.
a) {1,3}
b) {2,4}
c) {1,4}
d) {1,2}
View Answer

Answer: d
Explanation: x2-3x+2=0
=>x2-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 x2-3x+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

Answer: a
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}.
advertisement
advertisement

4. Write the set {x : x is an integer and x2-9=0} in roster form.
a) {3}
b) {-3}
c) {3,-3}
d) {9,3}
View Answer

Answer: c
Explanation: Since x is given as integer so x can be positive as well as negative.
x2-9=0 => (x-3)(x+3)=0 => x=3,-3.
So, the set {x : x is an integer and x2-9=0} can be written as {3,-3}.

5. What is the interval of f(x) = (x – 1)(x – 2)(x – 3)/(x3 + 6x2 + 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

Answer: b
Explanation: f(x) = (x – 1)(x – 2)(x – 3)/(x3 + 6x2 + 11x+ 6)
After solving the cubic equation (x3 + 6x2 + 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).
Note: Join free Sanfoundry classes at Telegram or Youtube

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

Answer: b
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 = 2n where n ∈ N}
c) {x: x = 4n where n ∈ N}
d) {x: x = 2n+4 where n ∈ N}
View Answer

Answer: b
Explanation: The sequence is a geometric progression with base 2 hence 2n is the correct answer.
advertisement

8. Let A={1,2,3,4,5}. Insert appropriate symbol in 2 ________ A.
a) =
b) <
c) ∈
d) ∉
View Answer

Answer: c
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 = n2-1 where n ∈ N}
c) {x: x = 2n+1 where n ∈ N}
d) {x: x = 2n-1 where n ∈ N}
View Answer

Answer: d
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.
advertisement

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

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

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

To practice all chapters and topics of class 11 Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]

advertisement
advertisement
Subscribe to our Newsletters (Subject-wise). Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

Youtube | Telegram | LinkedIn | Instagram | Facebook | Twitter | Pinterest
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

Subscribe to his free Masterclasses at Youtube & discussions at Telegram SanfoundryClasses.