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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 the interval

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0,12

(3,∞)

12,3

−3,−12

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detailed solution

Correct option is C

Clearly , point a,a2 lies on the opposite sides of the two lines .∴ a2−a23a−a2<0⇒ a2(1−2a)(3−a)<0⇒ (2a−1)(a−3)<0⇒12

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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 the interval

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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 the interval