JEE MAIN - Mathematics (2006 - No. 26)
If $$\left( {a,{a^2}} \right)$$ falls inside the angle made by the lines $$y = {x \over 2},$$ $$x > 0$$ and $$y = 3x,$$ $$x > 0,$$ then a belong to :
$$\left( {0,{1 \over 2}} \right)$$
$$\left( {3,\infty } \right)$$
$$\left( {{1 \over 2},3} \right)$$
$$\left( {-3,-{1 \over 2}} \right)$$
Explanation
Clearly for point $$P,$$
$${a^2} - 3a < 0$$ and $${a^2} - {a \over 2} > 0 \Rightarrow {1 \over 2} < a < 3$$
$${a^2} - 3a < 0$$ and $${a^2} - {a \over 2} > 0 \Rightarrow {1 \over 2} < a < 3$$
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