# Class 11 Maths MCQ – Sets

This set of Class 11 Maths Chapter 1 Multiple Choice Questions & Answers (MCQs) focuses on “Sets”. These MCQs are created based on the latest CBSE syllabus and the NCERT curriculum, offering valuable assistance for exam preparation.

1. How to define a set?
a) A collection of well-defined objects or element
b) A collection of unordered objects or element
c) Any random elements
d) A collection of special characters

Explanation: Generally, a set is defined as a collection of well defined objects or elements.
Each element in a set is unique.
Say for example, if S a set it is represented as,
S = {x: 2x2 ᵾ x< 5 and x € N}
Then the elements present in the set will be
S = {2, 8, 18, 32}.

2. How is a set denoted?
a) ()
b) {}
c) []
d) **

Explanation: A set is represented by {}.
Usually, but not necessarily a set is denoted by a capital letter e.g. A, B……. V, W, X, Y, Z.
The elements are enclosed between { } denoted by small letters a, b, ……., y, z.

3. How will you define a set of all real numbers?
a) {x: -1 < x < 1}
b) {x: 0 < x < ∞}
c) {x: -∞ < x < ∞}
d) {x: -Z < x < +Z}

Explanation: All the numbers whether it is an integer or rational number or irrational number is defined as Real Number. The range of the real number lies between in the range (-∞, +∞).

4. How will you define Union of two sets A and B?
a) {x: x € A or x € B}
b) {x: x € A or x € B (or both)}
c) {x: x € A and B}
d) {x: x € A – B}

Explanation: Union of two or more sets is the set of all elements that belongs to any of these sets.
The symbol used for this union of sets is ‘∪‘.
If A = {1, 2, 3, 4} and B = {2, 4, 5, 6} and C = {1, 2, 6, 8}
Then, A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}.

5. How will you define the difference of two sets B-A?
a) {x: x € A and x Ɇ B}
b) {x: x Ɇ A and x € B}
c) {x: x € A and x € B}
d) {x: x Ɇ A and x Ɇ B}

Explanation: The difference of a set A and B is denoted as A-B. A-B is a set of those elements that are in the set A but not in the set B. Similarly, the difference of a set B and A is denoted as B-A. It is a set of those elements that are in the set B but not in the set A.

6. What will be the set of the interval (a, b]?
a) {x: a < x < b}
b) {x: a ≤ x ≤ b}
c) {x: a < x ≤ b}
d) {x: a ≤ x < b}

Explanation: The symbol ( ) implies that the value will always be less than or greater than the x value i.e. end points are not included.
{ } implies that all the values that does not satisfy a given interval are included inside {}.
[ ] implies that the value will always be less than equal to or greater than equal to the x value i.e. end points are included. This is possible only when both a and b are finite.

7. How to define Wavy Curve Method f(x)?
a) (x-a1)n1 / (x-a2)n2 / (x-a3)n3 …………… / (x-ak)nk * (x-b1)m1 / (x-b2)m2 / (x-b3)m3 …….. /(x-bp)mp
b) (x-a1)n1 + (x-a2)n2 +(x-a3)n3 …………… + (x-ak)nk / (x-b1)m1 + (x-b2)m2 + (x-b3)m3 …….. + (x-bp)mp
c) (x-a1)n1 (x-a2)n2 (x-a3)n3 …………… (x-ak)nk / (x-b1)m1 (x-b2)m2 (x-b3)m3 …….. (x-bp)mp
d) (x-a1)n1 – (x-a2)n2 – (x-a3)n3 …………… – (x-ak)nk / (x-b1)m1 – (x-b2)m2 – (x-b3)m3 ……..- (x-bp)mp

Explanation: The method of intervals {or wavy curve} is used for solving inequalities of the form
f(x) = (x-a1)n1 (x-a2)n2 (x-a3)n3 …………… (x-ak)nk / (x-b1)m1 (x-b2)m2 (x-b3)m3 …….. (x-bp)mp > 0 (< 0, ≤ 0, or ≥ 0)
where, n1, n2, ,n3, …….. nk and m1, m2, m3, …….. , mp are natural numbers .
a1, a2, a3, ……..ak and b1, b2, b3, …….. bp are any real numbers such that ai ≠ bj where i = 1, 2, 3, ……. , k and j = 1, 2, 3, ….. , p.

8. How to solve for x, if |x-1| ≥ 3?
a) (-∞, -2) ∪ (4, ∞)
b) (-∞, -2] ∪ [4, ∞)
c) (0, -2] ∪ (4, 0)
d) (-∞, ∞) – {-2, 4}

Explanation: Given, |x-1| ≥ 3
= x-1 < -3 or x – 1 ≥ 3
= x ≤ -2 or x ≥ 4
Hence, x c (-∞, -2] ∪ [4, ∞).

9. What is the interval of f(x) = (x – 1)(x – 2)(x – 3)/(x3 + 6x2 + 11x + 6) where f(x) is positive?
a) (-∞, -3) ∪ (3, ∞)
b) (3, -2) ∪ (1, 1) ∪ (2, 3)
c) (-∞, -3) ∪ (2, -1) ∪ (1, 2) ∪ (3, ∞)
d) (-∞, ∞)

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, ∞).

10. 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.

11. A set can be a collection but a collection cannot be a set.
a) True
b) False

Explanation: A collection becomes a set when it is well defined for example a collection of good football players is not a set since the phrase “good football players” is vague and not defined.

12. 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}.

13. 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.

14. 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.

15. 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.

16. 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

17. 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

18. 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

Explanation: The collection of actors is not a set as there is no specific criterion to determine whether an actor is talented or not.

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