JEE Main 2024 Mathematics question

Consider the system of linear equation x + y + z = 4μ, x + 2y + 2λz = 10μ, x + 3y + 4λ²z = μ² + 15, where λ, μ ∈ ℝ. Which one of the following statements is NOT correct?

(A)The system has infinite number of solutions if λ = 1/2 and μ = 15
(B)The system is consistent if λ ≠ 1/2
(C)The system is inconsistent if λ = 1/2 and μ ≠ 1Correct
(D)The system has unique solution if λ ≠ 1/2 and μ ≠ 1, 15

Answer: (C)

Solution

The coefficient determinant is Δ = (2λ − 1)². If λ ≠ 1/2 the system is consistent with a unique solution. If λ = 1/2, eliminating gives y = 6μ and the third equation reduces to (μ − 1)(μ − 15) = 0, so the

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Question ID VK-017086