Class 11th Maths – RD Sharma Chapter 1 : Sets – Multiple Choice Questions (MCQs) Solution
Mark the correct alternative in each of the following:
- For any set A, (A′)′ is equal to
(a) A′
(b) A
(c) ϕ
(d) none of these Watch Solution - Let A and B be two sets in the same universal set. Then, A − B =
(a) A ∩ B
(b) A′ ∩ B
(c) A ∩ B′
(d) none of these Watch Solution - The number of subsets of a set containing n elements is
(a) n
(b) 2ⁿ − 1
(c) n²
(d) 2ⁿ Watch Solution - For any two sets A and B, A ∩ (A ∪ B) =
(a) A
(b) B
(c) ϕ
(d) none of these Watch Solution - If A = {1, 3, 5, B} and B = {2, 4}, then
(a) 4 ∈ A
(b) {4} ⊂ A
(c) B ⊂ A
(d) none of these Watch Solution - The symmetric difference of A and B is not equal to
(a) (A − B) ∩ (B − A)
(b) (A − B) ∪ (B − A)
(c) (A ∪ B) − (A ∩ B)
(d) {(A ∪ B) − A} ∪ {(A ∪ B) − B} Watch Solution - The symmetric difference of A = {1, 2, 3} and B = {3, 4, 5} is
(a) {1, 2}
(b) {1, 2, 4, 5}
(c) {4, 3}
(d) {2, 5, 1, 4, 3} Watch Solution - For any two sets A and B, (A − B) ∪ (B − A) =
(a) (A − B) ∪ A
(b) (B − A) ∪ B
(c) (A ∪ B) − (A ∩ B)
(d) (A ∪ B) ∩ (A ∩ B) Watch Solution - Which of the following statement is false :
(a) A − B = A ∩ B′
(b) A − B = A − (A ∩ B)
(c) A − B = A − B′
(d) A − B = (A ∪ B) − B Watch Solution - For any three sets A, B and C
(a) A ∩ (B − C) = (A ∩ B) − (A ∩ C)
(b) A ∩ (B − C) = (A ∩ B) − C
(c) A ∪ (B − C) = (A ∪ B) ∩ (A ∪ C′)
(d) A ∪ (B − C) = (A ∪ B) − (A ∪ C). Watch Solution
- Let A = {x : x ∈ R, x > 4} and B = {x ∈ R : x < 5}. Then, A ∩ B =
(a) (4, 5] (b) (4, 5)
(c) [4, 5)
(d) [4, 5] Watch Solution - Let U be the universal set containing 700 elements. If A, B are sub-sets of U such that
n(A) = 200, n(B) = 300 and n(A ∩ B) = 100. Then, n(A′ ∩ B′) =
(a) 400
(b) 600
(c) 300
(d) none of these. Watch Solution - Let A and B be two sets such that n(A) = 16, n(B) = 14, n(A ∪ B) = 25. Then, n(A ∩ B) is equal to
(a) 30
(b) 50
(c) 5
(d) none of these Watch Solution - If A = {1, 2, 3, 4, 5}, then the number of proper subsets of A is
(a) 120
(b) 30
(c) 31
(d) 32 Watch Solution - In set-builder method the null set is represented by
(a) { }
(b) Φ
(c) {x : x ≠ x}
(d) {x : x = x} Watch Solution - If A and B are two disjoint sets, then n(A ∪ B) is equal to
(a) n(A) + n(B)
(b) n(A) + n(B) − n(A ∩ B)
(c) n(A) + n(B) + n(A ∩ B)
(d) n(A) n(B) Watch Solution - For two sets A ∪ B = A iff
(a) B ⊆ A
(b) A ⊆ B
(c) A ≠ B
(d) A = B Watch Solution - If A and B are two sets such that n(A) = 70, n(B) = 60, n(A ∪ B) = 110, then n(A ∩ B) is equal to
(a) 240
(b) 50
(c) 40
(d) 20 Watch Solution - If A and B are two given sets, then A ∩ (A ∩ B)ᶜ is equal to
(a) A
(b) B
(c) Φ
(d) A ∩ Bᶜ Watch Solution - If A = {x : x is a multiple of 3} and, B = {x : x is a multiple of 5}, then A − B is
(a) A ∩ B
(b) A ∩ B̅
(c) A̅ ∩ B̅
(d) A̅ ∩ B Watch Solution - In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, persons travelling by car or bus is
(a) 80%
(b) 40%
(c) 60%
(d) 70% Watch Solution - If A ∩ B = B, then
(a) A ⊆ B
(b) B ⊆ A
(c) A = Φ
(d) B = Φ Watch Solution - An investigator interviewed 100 students to determine the performance of three drinks: milk, coffee and tea. The investigator reported that 10 students take all three drinks milk, coffee and tea; 20 students take milk and coffee; 25 students take milk and tea; 20 students take coffee and tea; 12 students take milk only; 5 students take coffee only and 8 students take tea only. Then the number of students who did not take any of the three drinks is
(a) 10
(b) 20
(c) 25
(d) 30 Watch Solution - Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then, the values of m and n are:
(a) 7, 6
(b) 6, 3
(c) 6, 4
(d) 7, 4 Watch Solution - In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?
(a) 35
(b) 48
(c) 60
(d) 22 Watch Solution - Suppose A₁, A₂,….,A₃₀ are thirty sets each having 5 elements and B₁, B₂,….,Bₙ are n sets each with 3 elements, let
⋃₁³⁰ Aᵢ = ⋃₁ⁿ Bⱼ = S and each element of S belongs to exactly 10 of the Aᵢ’s and exactly 9 of the Bⱼ’s, then n is equal to
(a) 15
(b) 3
(c) 45
(d) 35 Watch Solution - Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of m and n are respectively
(a) 4, 7
(b) 7, 4
(c) 4, 4
(d) 7, 7 Watch Solution - For any two sets A and B, A ∩ (A ∪ B)′ is equal to
(a) A
(b) B
(c) ϕ
(d) A ∩ B Watch Solution - The set (A ∪ B′) ∪ (B ∩ C) is equal to
(a) A′ ∪ B ∪ C
(b) A′ ∪ B
(c) A′ ∪ C′
(d) A′ ∩ B Watch Solution - Let F₁ be the set of all parallelograms, F₂ the set of all rectangles, F₃ the set of all rhombuses, F₄ the set of all squares and F₅ the set of all trapeziums in a plane. Then F₁ may be equal to
(a) F₂ ∩ F₃
(b) F₃ ∩ F₄
(c) F₂ ∪ F₃
(d) F₂ ∪ F₃ ∪ F₄ ∪ F₁ Watch Solution - If X = {8ⁿ − 7n − 1 : n ∈ N} and Y = {49n − 49 : n ∈ N}. Then,
(a) X ⊂ Y
(b) Y ⊂ X
(c) X = Y
(d) X ∩ Y = ϕ Watch Solution - A survey shows that 63% of the people watch a News channel whereas 76% watch another channel. If x % of the people watch both channel, then
(a) x = 35
(b) x = 63
(c) 39 ≤ x ≤ 63
(d) x = 39 Watch Solution - If sets A and B are defined as
A = {(x, y) : y = 1/x, 0 ≠ x ∈ R},
B = {(x, y) : y = −x, x ∈ R}, then
(a) A ∩ B = A
(b) A ∩ B = B
(c) A ∩ B = ϕ
(d) A ∪ B = A Watch Solution - Each set Xᵣ contains 5 elements and each set Yᵣ contains 2 elements and
⋃₍ᵣ₌₁₎²⁰ Xᵣ = S = ⋃₍ᵣ₌₁₎ⁿ Yᵣ. If each element of S belongs to exactly 10 of the Xᵣ’s and to exactly 4 of the Yᵣ’s, then n is
(a) 10
(b) 20
(c) 100
(d) 50 Watch Solution - Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The value of m and n respectively are:
(a) 7, 6
(b) 5, 1
(c) 6, 3
(d) 8, 7 Watch Solution - The set (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ∪ C′ is equal to
(a) B ∩ C′
(b) A ∩ C
(c) B ∪ C′
(d) A ∩ C′ Watch Solution - If A and B are two sets, then A ∩ (A ∪ B) equals
(a) A
(b) B
(c) ϕ
(d) A ∩ B Watch Solution - Let S = {x : x is a positive multiple of 3 less than 100}, P = {x : x is a prime less than 20}. Then, n(S) + n(P) is
(a) 34
(b) 31
(c) 33
(d) 30 Watch Solution - In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 both. Then the number of persons who read neither is
(a) 210
(b) 290
(c) 180
(d) 260 Watch Solution - In a class of 60 students, 25 students play cricket and 20 students play tennis and 10 students play both the games. Then the number of students who play neither is
(a) 0
(b) 25
(c) 35
(d) 45 Watch Solution - Let S = the set of points inside the square, T = the set of points inside the triangle and C = the set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then,
(a) S ∩ T ∩ C = ϕ
(b) S ∪ T ∪ C = C
(c) S ∪ T ∪ C = S
(d) S ∪ T = S ∩ C Watch Solution
Chapter 1: Sets – R. D. Sharma Class 11th Maths
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Sets Exercise 1.1 Video Solution
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Sets Exercise 1.2 Video Solution
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Sets Exercise 1.3 Video Solution
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Sets Exercise 1.4 Video Solution
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Sets Exercise 1.5 Video Solution
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Sets Exercise 1.6 Video Solution
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Sets Exercise 1.7 Video Solution
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Sets Exercise 1.8 Video Solution
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Sets Multiple Choice Questions (MCQs) Video Solution Video Solution
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Sets Fill in the Blanks (FBQs) Video Solution
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Sets Very Short Answer Questions (VSAQs) Video Solution Video Solution