If f(θ) = | array ccc 1 & 1 & -1 1 & e^ i & 1 1 & -1 & -e^ -i array | then

Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants

If f(θ) = \[\left|\begin{array}{ccc} 1 & 1 & -1 \\ 1 & e^{i \theta} & 1 \\ 1 & -1 & -e^{-i \theta} \end{array}\right|\] then

\[\int_{-\pi / 2}^{\pi / 2} f(\theta) d \theta=2 \int_{0}^{\pi / 2} f(\theta) d \theta\]
f(θ) is purely real
f(π/2) = 2
None of these

Answer

(A) _ - / 2 ^ / 2 f( ) d =2 _ 0 ^ / 2 f( ) d, (B) f( θ ) is purely real, (C) f( π /2) = 2

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