I know any fraction would suffice condition 1, but just not able to get number which would fit in to condition 2.
(I) x^2 < 2x < 1/x implies x^2 < 2x or x < 2 and 2x < 1/x or x < 1/√2. Both these condition can be true. So, I holds true.
(II) x^2 < 1/x < 2x implies x^2 < 1/x or x^3 < 1 or x < 1. Also, 1/x < 2x implies x > 1/√2. Hence the condition holds true if 1/√2 < x < 1
If x = 4/5, then 1/√2 = 0.7, x = 0.8 and hence the condition holds true.
(III) will not hold true for any positive value of x.
[spoiler]The correct answer is (D).[/spoiler]
