If `(a,a^(2))` falls inside the angle made by the lines `y=(x)/(2), x gt 0 and y=3x, x gt 0`, then a belongs to the interval

Options

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

Answer

B

Explanation

The graph of equations x-2y = 0 and 3x -y =0 as shown in the figure. , given point `(a,a^(2))` lies in the shaded region.

` a^(2) -a/2 gt 0 and a^(2) -3a lt 0`
a in (-oo,0 ) cup (1/2, oo)`
` and a in (0,3) Rightarrow a in (1/2 , 3)`