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x is a fraction (1/2 ..) condition 1 holds true....but I dont get any other number satisfying any of the other two condition...! or my brain has froze...

sst 1 holds true all fractions...
for numbers none of these hold true...
so if x is postive then x must be fraction..
so my pick is one... but what is OA

2x < 1/x when x < Sqrt(2)/2
x^2 < 1/x when x < 1
x^2 < 2x when x < 2

for x < Sqrt(2)/2 we have x^2 < 2x < 1/x
for sqrt(2)/2 < x < 1 we have x^2 < 1/x < 2x
for 1 < x < 2 we have 1/x < x^2 < 2x
for x > 2 we have 1/x < 2x < x^2

so 1. and 2. both work.

This is a good example of why you don't plug in numbers. You would need to pick a number between Sqrt(2)/2 and 1 to get the right answer.

2x < 1/x when x < Sqrt(2)/2 x^2 < 1/x when x < 1 x^2 < 2x when x < 2

for x < Sqrt(2)/2 we have x^2 < 2x < 1/x for sqrt(2)/2 < x < 1 we have x^2 < 1/x < 2x for 1 < x < 2 we have 1/x < x^2 < 2x for x > 2 we have 1/x < 2x < x^2

so 1. and 2. both work.

This is a good example of why you don't plug in numbers. You would need to pick a number between Sqrt(2)/2 and 1 to get the right answer.

Could you please explain how did you come up with values for various inequalities

Thanks Joey..!
Uphill climb ur suggestion will not work, u should remember any decimal is baiscally a fraction..the key is to choose the right intervals..!