GATE 2025 ST – Question 12

Calculus · Sequences and Series · 1 mark · Multiple choice

1. The union over n≥0 of {Σᵢ₌₀ⁿ10ⁱa_i:a_i∈{1,2}} is uncountable.
2. The set {Σₙ₌₁∞a_n/10ⁿ:a_n∈{1,2}}⊂(0,1) is uncountable.
3. An uncountable family of pairwise disjoint open intervals in ℝ exists.
4. All intervals with rational endpoints form an uncountable set.

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