Question
If $$\left( {a,\,{a^2}} \right)$$ falls inside the angle made by the lines $$y = \frac{x}{2},\,x > 0$$ and $$y = 3x,\,x > 0$$ then $$a$$ belong to-
A.
$$\left( {0,\,\frac{1}{2}} \right)$$
B.
$$\left( {3,\,\infty } \right)$$
C.
$$\left( {\frac{1}{2},\,3} \right)$$
D.
$$\left( { - 3,\, - \frac{1}{2}} \right)$$
Answer :
$$\left( {\frac{1}{2},\,3} \right)$$
Solution :
Clearly for point $$P,$$
$${a^2} - 3a < 0\,{\text{ and }}{a^2} - \frac{a}{2} > 0\,\, \Rightarrow \frac{1}{2} < a < 3$$
Clearly for point $$P,$$
$${a^2} - 3a < 0\,{\text{ and }}{a^2} - \frac{a}{2} > 0\,\, \Rightarrow \frac{1}{2} < a < 3$$