Mathematics Questions and Answers – Sets and their Representations – 1

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Sets and their Representations – 1”.

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

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. Which of the following is not a set of letters of word PRINCIPAL?
a) {P,R,I,N,C,A,L}
b) {C,A,P,I,N,R,L}
c) {P,R,I,N,C,I,P,A,L}
d) {L,N,I,P,C,A,R}

Explanation: A set has all unique elements. So the set which contain all the elements of word PRINCIPAL and no letter is repeated. Hence, {P,R,I,N,C,I,P,A,L} cannot be a set.

3. Write solution set of equation x2-3x+2=0 in roster form.
a) {1,3}
b) {2,4}
c) {1,4}
d) {1,2}

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}.

4. 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}

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}.

5. 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}

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}.

6. Write the set {x : x is a natural number and x2-9=0} in roster form.
a) {3}
b) {-3}
c) {3,-3}
d) {9,3}

Explanation: Since x is given as natural number so x can be positive only. x2-9=0 => (x-3)(x+3)=0 => x=3,-3.
Here, -3 is not a natural number so, the set {x : x is a natural number and x2-9=0} can be written as {3}.

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

Explanation: Here, 2 is an element of set A.
So, 2 belong to set A. 2∈A.

8. Let X={1,2,3,4,5,6}. Insert appropriate symbol in 9 ________ X.
a) =
b) <
c) ∈
d) ∉

Explanation: Here, 9 is not an element of set X.
So, 9 does not belongs to set A. 9∉X.

9. Which of the following does not belong to set {x : x is a vowel in English alphabet}?
a) e
b) b
c) i
d) o

Explanation: There are five vowels in English Alphabet a, e, i, o, u. So, set can be written in roster form as {a, e, i, o, u}. ‘b’ does not belongs to given set.

10. The number of elements in set {x : x is a letter of word TRIGONOMETRY} is __________
a) 8
b) 7
c) 9
d) 10

Explanation: The above set can be represented as {T,R,I,G,O,N,M,E,Y}. So, the number of elements in the set is 9.

11. What is the solution set of the equation X2+3X+2=0 in roster form?
a) {-1, 2}
b) {-1, -2}
c) {1, -2}
d) {1, 2}

Explanation: Solving the equation:
X2+2X+X+2=0
(x+2) (X+1) = 0
X= -2 and X = -1

12. Which one of the following is the correct representation for the set {x: x is a positive integer and x3<50} in roster form?
a) {0,1,2,3,4,5}
b) {-1,1,2,3}
c) {1,2,3}
d) {0,1,2,3}

Explanation: 0 is not a positive integer moreover
33<50 and 43>50

13. 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}

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.

14. 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

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

15. Which one of the following is not a set?
a) The collection of all whole numbers less than 200
b) The collection of all boys in your class
c) The collection of talented actors in Hollywood
d) The collection of all books written by Chetan Bhagat