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

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: 2x

^{2}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

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}

View Answer

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

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

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}

View Answer

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-a_{1})^{n1} / (x-a_{2})^{n2} / (x-a_{3})^{n3} …………… / (x-a_{k})^{nk} * (x-b_{1})^{m1} / (x-b_{2})^{m2} / (x-b_{3})^{m3} …….. /(x-b_{p})^{mp}

b) (x-a_{1})^{n1} + (x-a_{2})^{n2} +(x-a_{3})^{n3} …………… + (x-a_{k})^{nk} / (x-b_{1})^{m1} + (x-b_{2})^{m2} + (x-b_{3})^{m3} …….. + (x-b_{p})^{mp}

c) (x-a_{1})^{n1} (x-a_{2})^{n2} (x-a_{3})^{n3} …………… (x-a_{k})^{nk} / (x-b_{1})^{m1} (x-b_{2})^{m2} (x-b_{3})^{m3} …….. (x-b_{p})^{mp}

d) (x-a_{1})^{n1} – (x-a_{2})^{n2} – (x-a_{3})^{n3} …………… – (x-a_{k})^{nk} / (x-b_{1})^{m1} – (x-b_{2})^{m2} – (x-b_{3})^{m3} ……..- (x-b_{p})^{mp}

View Answer

Explanation: The method of intervals {or wavy curve} is used for solving inequalities of the form

f(x) = (x-a

_{1})

^{n1}(x-a

_{2})

^{n2}(x-a

_{3})

^{n3}…………… (x-a

_{k})

^{nk}/ (x-b

_{1})

^{m1}(x-b

_{2})

^{m2}(x-b

_{3})

^{m3}…….. (x-b

_{p})

^{mp}> 0 (< 0, ≤ 0, or ≥ 0)

where, n1, n2, ,n3, …….. nk and m1, m2, m3, …….. , mp are natural numbers .

a

_{1}, a

_{2}, a

_{3}, ……..a

_{k}and b

_{1}, b

_{2}, b

_{3}, …….. 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

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)/(x^{3} + 6x^{2} + 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

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, ∞).

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

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

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 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 natural number so x can be positive only. x

^{2}-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 x

^{2}-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

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

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

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 X^{2}+3X+2=0 in roster form?

a) {-1, 2}

b) {-1, -2}

c) {1, -2}

d) {1, 2}

View Answer

Explanation: Solving the equation:

X

^{2}+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 x^{3}<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

Explanation: 0 is not a positive integer moreover

3

^{3}<50 and 4

^{3}>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

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

**More MCQs on Class 11 Maths Chapter 1:**

- Chapter 1 – Sets MCQ (Set 2) – Sets and their Representations
- Chapter 1 – Sets MCQ (Set 3) – Empty Set
- Chapter 1 – Sets MCQ (Set 4) – Finite and Infinite Sets
- Chapter 1 – Sets MCQ (Set 5) – Equal Sets
- Chapter 1 – Sets MCQ (Set 6) – Subsets – 1
- Chapter 1 – Sets MCQ (Set 7) – Subsets – 2
- Chapter 1 – Sets MCQ (Set 8) – Power Sets
- Chapter 1 – Sets MCQ (Set 9) – Universal Set
- Chapter 1 – Sets MCQ (Set 10) – Venn Diagrams
- Chapter 1 – Sets MCQ (Set 11) – Operation on Sets-1
- Chapter 1 – Sets MCQ (Set 12) – Operation on Sets-2
- Chapter 1 – Sets MCQ (Set 13) – Complement of a Set
- Chapter 1 – Sets MCQ (Set 14) – Practical Problems

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