Question

If  [x] denotes the greatest integer ≤ x, then the system of linear equations [sin θ]x + [–cosθ]y = 0, [cot θ]x + y = 0

(1)  has a unique solution if θ ∈(π/2, 2π/3) and have infinitely many solutions if θ ∈(π, 7π/6)

(2)  have infinitely many solutions if θ ∈(π/2, 2π/3) and has a unique solution if θ ∈(π ,7π/6)

(3)  have infinitely many solutions if θ ∈(π/2, 2π/3) ∪ (π,7π/6)

(4)  has a unique solution if θ ∈(π/2, 2π/3) ∪ (π,7π/6)

Answer 1

Correct option (2)  have infinitely many solutions if θ ∈(π/2, 2π/3) and has a unique solution if θ ∈(π ,7π/6)

Explanation:

It will have unique solution is all cases x = 0, y = 0