Question

Let a and b be two positive real numbers such that a + 2b ≤ 1. Let A₁ and A₂ be respectively the areas of circles with radii ab³ and b². Then, the maximum possible value of A₁/A₂ is

(a) 1/16

(b) 1/64

(c) 1/16√2

(d) 1/32

Answer 1

Answer is : (b) 1/64

Given, a + 2b ≤ 1 a, b are positive real number.

Radius of circle C₁ = ab³

Radius of circle C₂ = b²

∴ Area of circle C₁ = A₁ = πa²b⁶

and area of circle C₂ = A₂ = πb⁴

∴ Maximium value of A₁/A₂ = 1/64