Analyse the first option:

Case I:
x^3 (1 - x^2) <0>1
i.e. x^2-1>0 ...................... this condition is not supplied in the question

Case II:
x^3 = -ve, then (1-x^2) must be +ve
The necessary and sufficient condition for (1-x^2) to be +ve, is
x^2<1
i.e x^2-1<0 .......... Which is the conditon supplied in statement 2

thus c should be the answer

Case I:
for, x^3 (1 - x^2) <0>1[/b]
i.e. x^2-1>0 ...................... this condition is not supplied in the question

musicdaemon wrote:Case I:
for, x^3 (1 - x^2) <0>1[/b]
i.e. x^2-1>0 ...................... this condition is not supplied in the question

MODS,
There is some problem in formatting of this part, not able to paste it properly.

anyway case 2 suffices my explanation

musicdaemon wrote:

musicdaemon wrote:Case I:
for, x^3 (1 - x^2) <0>1[/b]
i.e. x^2-1>0 ...................... this condition is not supplied in the question

MODS,
There is some problem in formatting of this part, not able to paste it properly.

anyway case 2 suffices my explanation

HTML is the devil!

HTML uses < > for its tags, so if you have HTML turned on you'll often have formatting issues on inequality questions.

If you click the "Disable HTML in this post" box, your problems will disappear. You can either do so for particular posts or you can change the setting permanently in your profile - change "Always allow HTML" from "yes" to "no" (that's what I've done, since BBCode accomplishes the same thing as HTML and doesn't cause the same issues to arise).

Yup, whatever Stuart said..