Given, \(x^7-x^5<0\)
Or, \(x^5(x^2-1)<0\)
Or, \(x^5(x+1)(x-1)<0\)

Using wavy curve method to find the interval of 'x':-

a) Let f(x)= \(x^5(x+1)(x-1)<0\)
Finding out the critical points of f(x)=0, we have x=0,-1,1

b) Arranging the critical points in ascending order: -1,0,1

c) We observed that all the indices of the critical points are odd. (When the power of is odd number cross the number-line otherwise repeat in the same direction)

d) Let' draw the diagram. (Enclosed for reference)

e) We have to consider those set of values which are below the number line as the inequality sign is <.

So, \(x: \:\left(-\infty \:,\:-1\right)\cup \left(0,\:1\right)\)

Ans. (C)

_________________

Regards,

PKN

Rise above the storm, you will find the sunshine