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Sets Class 11 MCQs Questions with Answers
Students are advised to solve the Sets Multiple Choice Questions of Class 11 Maths to know different concepts. Practicing the MCQ Questions on Sets Class 11 with answers will boost your confidence thereby helping you score well in the exam.
Explore numerous MCQ Questions of Sets Class 11 with answers provided with detailed solutions by looking below.
Question 1.
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)
Answer
Answer: (a) 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)
Question 2.
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
Answer
Answer: (a) {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}
Question 3.
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}
Answer
Answer: (a) {(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}
Question 4.
Empty set is a?
(a) Finite Set
(b) Invalid Set
(c) None of the above
(d) Infinite Set
Answer
Answer: (a) 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.
Question 5.
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
Answer
Answer: (a) 6, 3
Let A and B be two sets having m and n numbers of elements respectively
Number of subsets of A = 2m
Number of subsets of B = 2n
Now, according to question
2m – 2n = 56
⇒ 2n( 2m-n – 1) = 2³(2³ – 1)
So, n = 3
and m – n = 3
⇒ m – 3 = 3
⇒ m = 3 + 3
⇒ m = 6
Question 6.
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
Answer
Answer: (d) 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
Question 7.
Every set is a ___________ of itself
(a) None of the above
(b) Improper subset
(c) Compliment
(d) Proper subset
Answer
Answer: (b) 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.
Question 8.
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
Answer
Answer: (d) 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
Question 9.
In 3rd Quadrant?
(a) X < 0, Y < 0 (b) X > 0, Y < 0
(c) X < 0, Y > 0
(d) X < 0, Y > 0
Answer
Answer: (a) X < 0, Y < 0
In the 3rd quadrant,
X < 0, Y < 0
Question 10.
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
Answer
Answer: (d) B = C
If A ∪ B = A ∪ C and A ∩ B = A ∩ C
Then B = C
Question 11.
A set is known by its _______.
(a) Elements
(b) Values
(c) Members
(d) Letters
Answer
Answer: (a) Elements
A set is known by its elements.
Question 12.
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
Answer
Answer: (a) pq
Given the set A has p elements, B has q elements.
then number of elements in A × B = pq
Question 13.
Which from the following set has closure property w.r.t multiplication?
(a) {0, -1}
(b) {1, -1}
(c) {-1}
(d) {-1,-1}
Answer
Answer: (b) {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.
Question 14.
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
Answer
Answer: (a) 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)
Question 15.
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) 2m + n
(b) 2m / n
(c) 2m – n
(d) 2mn
Answer
Answer: (d) 2mn
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 = 2mn
Question 16.
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}
Answer
Answer: (d) {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}
Question 17.
In 2nd quadrant?
(a) X < 0, Y < 0
(b) X < 0, Y > 0
(c) X > 0, Y > 0
(d) X > 0, Y < 0
Answer
Answer: (b) X < 0, Y > 0
In the second quadrant,
X < 0, Y > 0
Question 18.
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.
Answer
Answer: (a) 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
Question 19.
Which from the following set has closure property w.r.t addition?
(a) {0}
(b) {1}
(c) {1, 1}
(d) {1, -1}
Answer
Answer: (a) {0}
A set is closed under addition if, when we add any two elements, we always get another element in the set.
(a) Closed under addition. The only possible way to add two numbers in the set is 0 + 0 = 0, which is in the set.
(b) Not closed under addition. For example, 1 + 1 = 2, which is not in the set.
(c) Not closed under addition. For example, 1 + 1 = 2, which is not in the set.
(d) Not closed under addition. For example, 1 + (-1) = 0, which is not in the set.
Question 20.
A’ will contain how many elements from the orginal set A
(a) 0
(b) All elements in A
(c) 1
(d) Infinite
Answer
Answer: (a) 0
A’ will contain zero many elements from the original set A.
Let A = {1, 2, 3, 4}, then |A| = 4
Now A’ = {}, then |A| = 0
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