Question

If $(a,a^2)$ falls inside the angle made by the lines $y=\frac{x}{2}$ and $y=3x$ in first quadrant, then $a$ belongs to

• A. $(0,\frac{1}{2})$
• B. $(3,\infty )$
• C. $\left(\frac{1}{2},3\right)$
• D. $(-3,-\frac{1}{2})$

Answer 1

The correct option is C $\left(\frac{1}{2},3\right)$

Given that $(a,a^2)$ falls inside the angle made by the lines
$y=\frac{x}{2},x>0$ and $y=3x,x>0$
$\Rightarrow a^2-3a<0$ and $a^2-\frac{a}{2}>0\Rightarrow \frac{1}{2}<a<3$