NIMCET 2017 Question Paper with solutions

Given equations of line are
x + (a - 1) y + 1 = 0 ... (i)
and 2x + a2y - 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
m1 =

−1

a−1

and slope of line 2x + a2y - 1 = 0
m2 =

−2

a2

m1m2 = - 1
∴

1

(a−1)

2

a2

= - 1
⇒ 2 = - a2 (a - 1)
⇒ 2 = −a3+a2
⇒ a3+a2 - 2 = 0 ... (iii)
On solving Eq. (in), we get
a = - 1