NIMCET 2017 — Mathematics PYQ

Concept:
The lines a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0 are perpendicular then product of slope is -1.
⇒ a_1 a_2 + b_1 b_2 = 0
Calculations:
Given, the lines x + (a - 1)y + 1 = 0 and 2x + a^2y - 1 = 0 are perpendicular.
⇒ 1 × 2 + (a - 1) × a^2 = 0
⇒ a^3 - a^2 + 2 = 0
⇒ a^3 + a^2 - 2a^2 - 2a + 2a + 2 = 0
⇒ a^2(a + 1) - 2a(a + 1) + 2(a + 1) = 0
⇒ (a + 1)(a^2 - 2a + 2) = 0
⇒ (a + 1) = 0
⇒ a = -1