KVPY SX SB Exam 2015 Question Paper

Question : 11 of 120

Marks: +1, -0

Among all sectors of a fixed perimeter, choose the one with maximum area. Then the angle at the center of this sector (i.e., the angle between the bounding radii) is -

$π/3$
$3/2$
$√3$
2

Validate

Solution:

Given that

2r + rθ = P

r=P/{2+θ}

area =

1/2r^2θ=1/2θ(P/{2+θ})^2

=1/2{P^2θ}/(2+θ)^2

{dA}/{dθ}=0

θ=2^C

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