JEE Mains Model Paper 4

We have cos−1α + cos−1β + cos−1γ = 3π
We know that 0 ≤ cos−1x ≤ π
⇒ cos−1α + cos−1β + cos−1γ = 3π is possible if and only if
cos−1α + cos−1β + cos−1γ = π⇒ α = β = γ = -1
∴ α (β + γ) + β (γ + α) + γ (α + β)
= -1(-1 -1) -1(-1 -1) -1(-1 -1) = 6