NIMCET 2014 Question Paper with solutions

Let length of side of ΔABC be I.

i.e. AB = I Then,
cos 30° = $\frac{\mathit{A}\mathit{M}}{\mathit{A}\mathit{B}}$
AM = xcos 30°
AM = l $\frac{\sqrt{3}}{2}$
and $\frac{\mathit{B}\mathit{M}}{\mathit{A}\mathit{B}}$ = sin 30°
BM = $\frac{\mathit{l}}{2}$
∴ The coordinate of B are $\left(\mathit{l}\frac{\sqrt{3}}{2},\frac{\mathit{l}}{2}\right)$
B lies on the parabola ${\mathit{y}}^2$ = 4ax
∴ $\frac{{\mathit{l}}^2}{4}$ = 4 al $\frac{\sqrt{3}}{2}$
l = 8 $\mathit{a}\sqrt{3}$