For (1/3) < x < y < 2, which of the following statements is/are always correct?<br/>I. x + (1/x) < y + (1/y)<br/>II. (√(1 + y^2)/y) < (√(1 + x^2)/x)<br/>Select the answer using the code given below.<br/>

I. Let f(t)=t+1/t for t>0. Then f'(t)=1-1/t^2, so f decreases on (0,1) and increases on (1,∞). Hence it is not always increasing on (1/3,2). Counterexample: x=1/2, y=3/4 gives f(x)=2.5 and f(y)=2.083..., so I is false.
II. Let g(t)=sqrt(1+t^2)/t = sqrt(1+1/t^2) for t>0. As t increases, 1/t^2 decreases, so g(t) decreases. Since x<y, g(y)<g(x). So II is always true.
Therefore, only II is always correct.