JEE Main 2013 Mathematics question
Statement-1: The system of linear equations
x + (α)y + (α)z = 0
x + (α)y + (α)z = 0
x - (α)y - (α)z = 0
has a non-trivial solution for only one value of α lying in the interval . Statement-2: The equation in α
= 0
has only one solution lying in the interval
Answer: (1)
Solution
Statement 1: the coefficient determinant is (s = sin α, c = cos α), which vanishes in (0, π/2) only at α = π/4 — true. Statement 2: expanding, $ - - s(-2sc) + c(-1) = -
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