If $0<2 x<1$, which of the following is smallest?

$x^2$

The correct answer is Option (2) → $x^2$

$0 < 2x < 1 \Rightarrow 0 < x < \frac{1}{2}$

$\text{For } 0 < x < 1,\ x^2 < x$

$\text{Also, } \frac{1}{x} > 1 \text{ and } \frac{1}{x^2} > \frac{1}{x}$

$\text{ therefore }x^2 < x < \frac{1}{x} < \frac{1}{x^2}$

$\text{Smallest value is } x^2$