Class 11 Maths Chapter 1 Sets MCQ

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
View Answer

Answer: a
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) **
View Answer

Answer: b
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: -∞ < x < ∞]
c) {x: -∞ < x < ∞}
d) {x: -Z < x < +Z}
View Answer

Answer: c
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}
View Answer

Answer: 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}
View Answer

Answer: 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.

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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}
View Answer

Answer: c
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-a_k)^nk * (x-b₁)^m1 / (x-b₂)^m2 / (x-b₃)^m3 …….. /(x-b_p)^mp
b) (x-a₁)ⁿ¹ + (x-a₂)ⁿ² +(x-a₃)ⁿ³ …………… + (x-a_k)^nk / (x-b₁)^m1 + (x-b₂)^m2 + (x-b₃)^m3 …….. + (x-b_p)^mp
c) (x-a₁)ⁿ¹ (x-a₂)ⁿ² (x-a₃)ⁿ³ …………… (x-a_k)^nk / (x-b₁)^m1 (x-b₂)^m2 (x-b₃)^m3 …….. (x-b_p)^mp
d) (x-a₁)ⁿ¹ – (x-a₂)ⁿ² – (x-a₃)ⁿ³ …………… – (x-a_k)^nk / (x-b₁)^m1 – (x-b₂)^m2 – (x-b₃)^m3 ……..- (x-b_p)^mp
View Answer

Answer: c
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-a_k)^nk / (x-b₁)^m1 (x-b₂)^m2 (x-b₃)^m3 …….. (x-b_p)^mp > 0 (< 0, ≤ 0, or ≥ 0)
where, n1, n2, ,n3, …….. nk and m1, m2, m3, …….. , mp are natural numbers .
a₁, a₂, a₃, ……..a_k and b₁, b₂, b₃, …….. b_p are any real numbers such that a_i ≠ b_j 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}
View Answer

Answer: b
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) (-∞, ∞)
View Answer

Answer: c
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}
View Answer

Answer: c
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
View Answer

Answer: a
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}
View Answer

Answer: a
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) ∉
View Answer

Answer: 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
View Answer

Answer: b
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
View Answer

Answer: c
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}
View Answer

Answer: b
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}
View Answer

Answer: c
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
View Answer

Answer: c
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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