Q.

Consider all rectangles lying in the region (x,y)∈ℝ×ℝ:0≤x≤π2 and 0≤y≤2sin⁡(2x)and having one side on the x-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is

see full answer

Want to Fund your own JEE / NEET / Foundation preparation ??

Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*
An Intiative by Sri Chaitanya

a

3π2

b

π

c

π23

d

π32

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Perimeter =2(2α+2cos⁡2α)     since if x=π4+α⇒y=2 sin2π4+α=2 cos 2αP=4(α+cos⁡2α)dPdα=4(1−2sin⁡2α)=0sin⁡2α=122α=π6,5π6d2Pdα2=−16cos⁡2α for maximum α=π12  if 2α=π6⇒d2Pdα2=−16cos⁡π6=-83<0 Area =(2α)(2cos⁡2α)=π6×2×32=π23
Watch 3-min video & get full concept clarity
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon