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QJEEM20Ma60af: JEE Main 2020 Mathematics - Class 12 JEEM20Ma60af Solution: The area (in sq. units) of the largest rectangle ABCD whose…

The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the parabola, y = x2–1 below the x-axis, is :

Multiple Choice Options

  • A 133{1 \over {3\sqrt 3 }}
  • B 233{2 \over {3\sqrt 3 }}
  • C 433{4 \over {3\sqrt 3 }}
  • D 43{4 \over 3}

Step-by-Step Verified Solution

JEE Main 2020 (Online) 4th September Evening Slot Mathematics - Application of Derivatives Question 125 English Explanation

Area (A) = 2t. (1 −- t2)

(0 < t < 1)

A = 2t −- 2t3

dAdt=2−6t2{{dA} \over {dt}} = 2 - 6{t^2} = 0

⇒\Rightarrow t=t = ±\pm 13{1 \over {\sqrt 3 }}

∴\therefore Amax⁡=∣23(1−13)∣=433{A_{\max }} = |{2 \over {\sqrt 3 }}\left( {1 - {1 \over 3}} \right)| = {4 \over {3\sqrt 3 }}

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