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Trigonometry — Hard JEE math MCQ

Consider all rectangles lying in the region \[ \left\{(x, y) \in \mathbb{R} \times \mathbb{R}: 0 \leq x \leq \frac{\pi}{2} \text { and } 0 \leq y \leq 2 \sin (2 x)\right\} \] and having one side on the $x$-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is
  1. A. $\frac{3 \pi}{2}$
  2. B. $\pi$
  3. C. $\frac{\pi}{2 \sqrt{3}}$
  4. D. $\frac{\pi \sqrt{3}}{2}$

Solution

The correct option is **C**.

MATH

hard • PYQ Reworded
Question
Read carefully, then pick the best option.
Consider all rectangles lying in the region {(x,y)∈R×R:0≤x≤π2 and 0≤y≤2sin⁡(2x)} \left\{(x, y) \in \mathbb{R} \times \mathbb{R}: 0 \leq x \leq \frac{\pi}{2} \text { and } 0 \leq y \leq 2 \sin (2 x)\right\} and having one side on the xx-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is
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