Inequalities

[grkmurthy]

Given that 0 < x < 1, which of the following inequalities must be valid?

I. x^3 > x^5.
II. x^4 + x^ 5 < x^3 + x^2
III. x^2 – x^3 > x^4 – x^5

(1) I only.
(2) II only
(3) None
(4) I, II & III
(5) I & II only

[ksvickram]

All the three are valid.

Let x = 1 / 2 =>

Stmt I 1 / 8 > 1 / 32 which is TRUE
Stmt II 1 / 16 < 1 / 4 which is TRUE
Stmt III 1 / 4 > 1 / 16 which is also TRUE.