HardMathematics
+4 / -1
Let A₁, A₂, A₃, ..., A₁₀₀ be 100 sets such that n(Aᵢ) = i + 1 and A₁ ⊂ A₂ ⊂ A₃ ⊂ ⋯ A₁₀₀, then ⋃ᵢ₌₁⁶⁰ Aᵢ contains total number of elements as
A
61
B
100
C
101
D
60
Explanation
As we know that, ⋃ᵢ₌₁ⁿ Aᵢ = A₁ ∪ A₂ ∪ A₃ ∪ A₄ .....∪ Aₙ. As per the question, A₁ ⊂ A₂ ⊂ A₃ ⊂ ⋯ A₁₀₀. Thus, ⋃ᵢ₌₁⁶⁰ Aᵢ = A₁ ∪ A₂ ∪ A₃ ∪ A₄ .....∪ A₆₀ = A₆₀. Since, n(A₆₀) = 60 + 1 = 61. Hence, ⋃ᵢ₌₁⁶⁰ Aᵢ = 61. --
More from Sets
Hard
If A₁ ⊂ A₂ ⊂ A₃ ⊂ ⋯ ⊂ A₅₀, and n(Aᵢ) = i – 1, then n(⋂ᵢ₌₁₁⁵⁰ Aᵢ) is equal to:
HardIf A = {(x, y): x² + y² ≤ 1, x,y ∈ R} and B = {(x, y): x² + y² ≤ 4, x,y ∈ R}, then
MediumTwo finite sets have m and n elements respectively. The total number of subsets of first set is 56 m
MediumWhich option is representing the given Venn diagram?
EasyIf A and B are two sets, then (A – B)∩(B – A)∩(A ∩ B) equals to:
MediumIn a town of 10,000 families, it was found that 40% family buy newspaper A, 20% buy newspaper B and
Practice Mathematics Exams
Full-length mock tests with detailed analytics, rank, and percentile.
Browse Exams