If `(a,a^(2))` falls inside the angle made by the linear equations `y=x/2,x gtandy=3x,x gt0,` then 'a' belong to

Options

A. `(0,(1)/(2))`
B. `(3,oo)`
C. `((1)/(2),3)`
D. `(-3,-(1)/(2))`

Answer

C

Explanation

Clearly , point `(a,a^(2))` lies on the opposite sides of the two lines.
`therefore ((a)/(2)-a^(2))(3a-a^(2)) lt 0`
`implies a^(2)(1-2a)(3-a) lt 0`
`implies (2a-a)(a-3) lt 0 implies (1)/(2) lt a lt 3 implies a in (1//2,3)`