If (a,a2) falls inside the angle made by the lines y=x2 , x>0 and y=3x , x>0 then a belongs to

3x−y=0−(1) x−2y=0−(2) L11L22<0⇒3a−a2a−2a2<O ⇒a2−3a2a2−a<0 ⇒a−32a−1<0 ⇒a∈(12,3)

If (a,a2) falls inside the angle made by the lines y=x2 , x>0 and y=3x , x>0 then a belongs to

3x−y=0−(1) x−2y=0−(2) L11L22<0⇒3a−a2a−2a2<O ⇒a2−3a2a2−a<0 ⇒a−32a−1<0 ⇒a∈(12,3)

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

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$(0, \frac{1}{2})$

$(- 3, \frac{- 1}{2})$

$(\frac{1}{2}, 3)$

$(3, \infty)$

answer is C.

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Detailed Solution

$3 x - y = 0 - (1) x - 2 y = 0 - (2) \frac{L_{11}}{L_{22}} < 0 \Rightarrow \frac{3 a - a^{2}}{a - 2 a^{2}} < O \Rightarrow \frac{a^{2} - 3 a}{2 a^{2} - a} < 0 \Rightarrow \frac{a - 3}{2 a - 1} < 0 \Rightarrow a \in (\frac{1}{2}, 3)$

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If (a,a2) falls inside the angle made by the lines y=x2 , x>0 and y=3x , x>0 then a belongs to

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