Bunuel wrote:

If -1 < x < 1, and x ≠ 0, which of the following inequalities must be true?

I. x^3 < x^4

II. x^2 > x^4

III. x^3 > x^5

A. I only

B. I and II

C. II only

D. II and III

E. I, II, and III

Ans:-

Given :- -1<x<0 and 0<x<1 means all fractions in between .

Must be true.

I. if x = -1/2 (true) but if x =1/2 (false) eliminate it.

II. Generally irrespective of signs all even powers will be positive and if power is greater value also will be greater for integers but for fractions it is reverse.

ex:- test for x =1/2 or -2/3 and so on.

This option Holds goodIII. odd powers this statement is false for all positive numbers and true for all negatives.

for fractions if x= 1/2 (true) but for x=-1/2 (false) eliminate.

SO only II must be true . Ans is [b}

C[/b]