Home › Previous year questions › GATE 2025 MA › Question 65GATE 2025 MA – Question 65 Real Analysis · Metric Spaces and Continuity · 2 marks · Numerical answer
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 (integer).
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Show answer and explanation Correct answer: 8 to 8
Explanation The increasing map t→t/(1+t) sends threshold 1/7 to $(1/7)/(1+1/7)=1/8$. Hence the same set has d₂ radius 1/8, so **α=8**.
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