If $(a,a^2)$ falls inside the angle made by the lines $y=x/2,x>0$ and $y=3x,x>0$, then $a$ belongs to:

For the point $(a,a^2)$ to be within the angle:It must be above $y=x/2$: $a^2>a/2⟹a(a-1/2)>0$.Since $x>0$ for the lines, $a>0$, so $a>1/2$.It must be below $y=3x$: $a^2<3a⟹a(a-3)<0$.Since $a>0$, this implies $a<3$.Combining both conditions: $1/2<a<3$.So $a\in (1/2,3)$.