NIMCET 2017 Question Paper with solutions

Given equations of line are
x + (a - 1) y + 1 = 0 ... (i)
and 2x + ${\mathit{a}}^2\mathit{y}$ - 1 = 0 ... (ii)
Since, line (i) and line (ii) are perpendicular
∴ Slope of line 1 x
Slope of line 2 = -1
∴ Slope of line x + (a - 1) y + 1 = 0
${\mathit{m}}_1$ = $\frac{-1}{\mathit{a}-1}$
and slope of line 2x + ${\mathit{a}}^2\mathit{y}$ - 1 = 0
${\mathit{m}}_2$ = $\frac{-2}{{\mathit{a}}^2}$
${\mathit{m}}_1{\mathit{m}}_2$ = - 1
∴ $\frac{1}{\left(\mathit{a}-1\right)}\frac{2}{{\mathit{a}}^2}$ = - 1
⇒ 2 = - ${\mathit{a}}^2$ (a - 1)
⇒ 2 = $-{\mathit{a}}^3+{\mathit{a}}^2$
⇒ ${\mathit{a}}^3+{\mathit{a}}^2$ - 2 = 0 ... (iii)
On solving Eq. (in), we get
a = - 1