GATE Real Analysis: Metric Spaces and Continuity – Previous Year Questions
8 GATE previous year questions on Metric Spaces and Continuity (Real Analysis, Mathematics) with answers and explanations, from every paper.
- GATE 2021 MA Q20 – Let f:(−π/2,π/2)→ℝ be f(x)=π/2+x−arctan x. P: f(x)−f(y) < x−y for all x,y in the domain. Q:f has a fixed point. Choose truth values.
- GATE 2021 MA Q21 – On (0,1): P:d₁(x,y)= log(x/y) is a metric. Q:d₂(x,y)= x + y for x≠y and zero for x=y is a metric. Choose truth values.
- GATE 2022 MA Q41 – In ℚ with usual distance, E=p∈ℚ:2<p²<3. Which holds?
- GATE 2023 MA Q20 – In C[0,1] with supremum metric let X=f:‖f‖∞≥1/2. Set f₁(x)=x and f₂(x)=1−x. P:f₁ lies in int X. Q:f₂ lies in int X. Choose truth values.
- GATE 2023 MA Q21 – Let ρ₁ be usual distance and ρ₂ the discrete metric on ℝ. X=n∈ℕ:n≥3,Y=n+1/n:n∈ℕ. Define f=2 on X and f=3 on Y. P:f:(X∪Y,ρ₁)→(ℝ,ρ₁) is uniformly…
- GATE 2023 MA Q53 – In C[0,1] with supremum metric, let f n(x)=xⁿ and P=f n:n∈ℕ. Which hold?
- GATE 2025 MA Q65 – On ℝ² let d₁ be Manhattan distance and d₂=d₁/(1+d₁). The d₁-open ball centered at zero with radius 1/7 equals the d₂-open ball with radius 1/α. Find α…
- GATE 2026 MA Q20 – Let d₁,d₂,d₃ be metrics on a set X with at least two elements. Which formula does NOT define a metric?