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JEE Main 2019 Mathematics question

MathematicsDeterminantsJEE Main 2019

The number of values of θ ∈ (0, π) for which the system of linear equations x + 3y + 7z = 0, −x + 4y + 7z = 0, (sin 3θ)x + (cos 2θ)y + 2z = 0 has a non-trivial solution, is:

Answer: (A)

Solution

Δ = 14(1 − cos 2θ) − 7 sin 3θ = 0 ⇒ sin θ(4sinθ + 4 sin θ − 3) = 0 ⇒ sin θ = 1/2: θ = π/6, 5π/6.

Question ID VK-010638