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IPMAT Indore 2023 - QA (SA) Q10 Explanation
December 9, 2024
Explanation:
(14)
Equation of circle is 𝑥^2 + 𝑦^2 = 4
∴ Coordinate of the centre is (0, 0) and radius is 2.
Consider a right angle ∆ AQB,
Area = 1/2 × AB × QT
= 1/2 ×4 × y = 2y
2y should be an integer. (given)
If is only possible when,
y = 1/2 or 1 or 3/2 or 2 Since, y ≤ 2 (given)
So, in each quadrant we will get 3 ∆s, with altitude 1/1, 1 and 3/2 units.
∴ 3 × 4 = 12 ∆s.
And with y = 2, we have only 2 ∆s, with vertex at M & N.
∴ Total ∆s = 12+2 = 14. Ans.