29 verified questions · ~44 minutes · answer key checked against the official NTA final key across multiple sources. Text-only questions (diagram-based excluded until they can be shown properly).
Consider the system of linear equations x + y + z = 5, x + 2y + λ²z = 9, x + 3y + λz = μ, where λ, μ ∈ ℝ. Then, which of the following statement is NOT correct?
For α, β ∈ (0, π/2), let 3 sin(α + β) = 2 sin(α − β) and a real number k be such that tan α = k tan β. Then the value of k is equal to:
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