MCQ Questions for Class 11 Maths Chapter 1 Sets with Answers

Sets Class 11 Maths MCQs Questions with Answers

Check the below NCERT MCQ Questions for Class 11 Maths Chapter 1 Sets with Answers Pdf free download. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. We have Provided Sets Class 11 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 11 Maths Chapter 1 Quiz

Class 11 Maths Chapter 1 MCQ Online Test

You can refer to NCERT Solutions for Class 11 Maths Chapter 1 Sets to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

Sets Class 11 Maths MCQ online test

Q1.	If f(x) = log [(1 + x)/(1 – x), then f(2x )/(1 + x²) is equal to
	A.2f(x)
	B.{f(x)}²
	C.{f(x)}³
	D.3f(x)

Ans: 2f(x)
Given f(x) = Log [(1 + x)/(1-x)]
Now, f{(2x )/(1 + x²)} = Log [{(1 + (2x )/(1 + x²))}/{(1 – (2x )/(1 + x²))}]
⇒ f{(2x )/(1 + x²)} = Log [{(1 + x² + 2x )/(1 + x²))}/{(1 + x² – 2x )/(1 + x²))}]
⇒ f{(2x )/(1 + x²)} = Log [(1 + x² + 2x )/{(1 + x² – 2x )]
⇒ f{(2x )/(1 + x²)} = Log [(1 + x)2 /{(1 – x)2]
⇒ f{(2x )/(1 + x²)} = Log [(1 + x)/{(1 – x)]2
⇒ f{(2x )/(1 + x²)} = 2 × Log [(1 + x)/{(1 – x)]
⇒ f{(2x )/(1 + x²)} = 2 f(x)

Q2.	The smallest set a such that A ∪ {1, 2} = {1, 2, 3, 5, 9} is
	A.{3, 5, 9}
	B.{2, 3, 5}
	C.{1, 2, 5, 9}
	D.None of these

Ans: {3, 5, 9}
Given, a set A such that A ∪ {1, 2} = {1, 2, 3, 5, 9}
Now, smallest set A = {3, 5, 9}
So, A ∪ {1, 2} = {1, 2, 3, 5, 9}

Q3.	Let R= {(x, y) : x, y belong to N, 2x + y = 41}. The range is of the relation R is
	A.{(2n – 1) : n belongs to N, 1 ≤ n ≤ 20}
	B.{(2n + 2) : n belongs to N, 1 < n < 20}
	C.{2n : n belongs to N, 1< n< 20}
	D.{(2n + 1) : n belongs to N , 1 ≤ n ≤ 20}

Ans: {(2n – 1) : n belongs to N, 1 ≤ n ≤ 20}
Given,
2x + y = 41
⇒ y = 41 – 2x
x : 1 2 3 ………………20
y : 39 37 35 ……………..1
So, range is
{(2n – 1) : n belongs to N, 1 ≤ n ≤ 20}

Q4.	Empty set is a?
	A.Finite Set
	B.Invalid Set
	C.None of the above
	D.Infinite Set

Ans: Finite Set
In mathematics, and more specifically set theory, the empty set is the unique set having no elements and its size or cardinality (count of elements in a set) is zero.
So, an empty set is a finite set.

Q5.	Two finite sets have M and N elements. The total number of subsets of the first set is 56 morethan the total number of subsets of the second set. The values of M and N are respectively.
	A.6, 3
	B.8, 5
	C.none of these
	D.4, 1

Ans: 6, 3
Let A and B be two sets having m and n numbers of elements respectively
Number of subsets of A = 2^m
Number of subsets of B = 2ⁿ
Now, according to question
2^m – 2ⁿ = 56
⇒ 2ⁿ( 2^m-n – 1) = 2³(2³ – 1)
So, n = 3
and m – n = 3
⇒ m – 3 = 3
⇒ m = 3 + 3
⇒ m = 6

Q6.	If the number of elements in a set S are 5. Then the number of elements of the power set P(S) are?
	A.5
	B.6
	C.16
	D.32

Ans: 32
Given, the number of elements in a set S are 5
Then the number of elements of the power set P(S) = 2⁵ = 32

Q7.	Every set is a ___________ of itself
	A.None of the above
	B.Improper subset
	C.Compliment
	D.Proper subset

Ans: Improper subset
An improper subset is a subset containing every element of the original set.
A proper subset contains some but not all of the elements of the original set.
Ex: Let a set {1, 2, 3, 4, 5, 6}. Then {1, 2, 4} and {1} are the proper subset while {1, 2, 3, 4, 5} is an improper subset.
So, every set is an improper subset of itself.

Q8.	If x ≠ 1, and f(x) = x + 1 / x – 1 is a real function, then f(f(f(2))) is
	A.2
	B.1
	C.4
	D.3

Ans: 3
Given f(x) = (x + 1)/(x – 1)
Now, f(2) = (2 + 1)/(2 – 1) = 3
Now since f(2) is independent of x
So, f(f(f(2))) = 3

Q9.	In 3rd Quadrant?
	A.X < 0, Y < 0 (b) X > 0, Y < 0
	B. X > 0, Y < 0
	C.X < 0, Y > 0
	D.X < 0, Y > 0

Ans: X < 0, Y < 0
MCQ Questions for Class 11 Maths Chapter 1 Sets with Answers 1

In the 3rd quadrant,
X < 0, Y < 0

Q10.	IF A ∪ B = A ∪ C and A ∩ B = A ∩ C, THEN
	A.none of these
	B.B = C only when A I C
	C.B = C only when A ? B
	D.B = C

Ans: B = C
If A ∪ B = A ∪ C and A ∩ B = A ∩ C
Then B = C

Q11.	A set is known by its _______.
	A.Elements
	B.Values
	C.Members
	D.Letters

Ans: 1Q 12.12341Q 13.12342Q 14.12341Q 15.

Q12.	If the set has P elements, B has q elememts then number of elements in A × B is
	A.pq
	B.p + q
	C.p + q + 1
	D.p²

Ans: pq
Given the set A has p elements, B has q elements.
then number of elements in A × B = pq

Q13.	Which from the following set has closure property w.r.t multiplication?
	A.{0, -1}
	B.{1, -1}
	C.{-1}
	D.{-1,-1}

Ans: {1, -1}
The set {1, -1} has closure property w.r.t multiplication.
This is because -1 × 1 = -1 which is an element in the given set.

Q14.	Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of containing all determinants with value 1. Let C be the subset of containing all determinants with value -1 then
	A.B has many elements as C
	B.A = B ∪ C
	C.B has twice as many elements as C.
	D.C is empty

Ans: B has many elements as C
The matrix C is not empty because
|1 0 0|
|1 0 1| = -1
|1 1 0|
Let Δ ∈ B
So, Δ = 1
Again let Δ₁ be the determinant obtained by interchanging any two rows and columns of Δ
So, Δ₁ = -1 ⇒ n(B) ≥ n(C)
Similarly, we can show that n(C) ≥ n(B)
So, n(B) = n(C)

Q15.	If A and B are two sets containing respectively M and N distinct elements. How many different relations can be defined for A and B?
	A.2^{m + n}
	B.2^{m / n}
	C.2^{m – n}
	D.2^mn

Ans: 2^mn
Given A and B are two sets containing respectively m and n distinct elements.
Then number of different relations can be defined for A and B = 2^mn

Q16.	Let R be a relation N define by x + 2y = 8. The domain of R is
	A.{2, 4, 6, 8}
	B.{1, 2, 3, 4}
	C.{2, 4, 8}
	D.{2, 4, 6}

Ans: {2, 4, 6}
Given R be a relation N define by x + 2y = 8
⇒ 2y = 8 – x
⇒ y = 8/4 – x/2
⇒ y = 4 – x/2
Now, the pair of x any satisfying the above equation is:
(2, 3), (4, 2),(6, 1)
So R = {(2, 3), (4, 2),(6, 1)}
Now, Dom(R) = {2, 4, 6}

Q17.	In 2nd quadrant?
	A.X < 0, Y < 0
	B.X < 0, Y > 0
	C.X > 0, Y > 0
	D.X > 0, Y < 0

Ans: X < 0, Y < 0
MCQ Questions for Class 11 Maths Chapter 1 Sets with Answers 1

In the second quadrant,
X < 0, Y > 0

Q18.	A survey shows that 63% of the americans like cheese whereas 76% like apples. If X% of the americans like both cheese and apples, then we have
	A.39 ≤ x ≤ 63
	B.x ≤ 63
	C.x ≤ 39
	D.none of these.

Ans: 39 ≤ x ≤ 63
Given,
Number of americans who like cheese n(C) = 63
Number of americans who like apple n(A) = 76
Total number of person = 100 (since 100%)
Number of americans who like both n(A ∩ B) = x
Now, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
⇒ 100 = 63 + 76 – x
⇒ 100 = 139 – x
⇒ x = 139 – 100
⇒ x = 39
This is the minimum value of x
Now, let us look for the highest value of x, the intersection or the common portion
between A and C, it would be larger when one set takes in more of the other.
Thus, when the smaller set gets completely absorbed into the larger and in that situation then x = 63
So 39 ≤ x ≤ 63

Q19.	Which from the following set has closure property w.r.t addition?
	A.{0}
	B.{1}
	C.{1, 1}
	D.{1, -1}

Ans: {0}
A set is closed under addition if, when we add any two elements, we always get another element in the set.
Closed under addition. The only possible way to add two numbers in the set is 0 + 0 = 0, which is in the set.
Not closed under addition. For example, 1 + 1 = 2, which is not in the set.
Not closed under addition. For example, 1 + 1 = 2, which is not in the set.
Not closed under addition. For example, 1 + (-1) = 0, which is not in the set.