GATE 2022 ST – Question 40
The line y=αx,α≥√2,divides R={(x,y):0≤x≤√y,0≤y≤2} into equal areas. Find α.
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Correct answer: (A) 3/√2
Explanation
The total area is ∫₀²√y dy=4√2/3. Since α≥√2,the line x=y/α lies inside each horizontal slice. The area on its left is ∫₀²y/α dy=2/α. Equal division requires 2/α=2√2/3,so **α=3/√2, A**.