JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the minimum and the maximum values of the function \(f :\left[\frac{\pi}{4}, \frac{\pi}{2}\right] \rightarrow R ,\) defined by : \(f (\theta)=\left|\begin{array}{ccc}-\sin ^{2} \theta & -1-\sin ^{2} \theta & 1 \\ -\cos ^{2} \theta & -1-\cos ^{2} \theta & 1 \\ 12 & 10 & -2\end{array}\right|\) are \(m\) and \(M\) respectively, then the ordered pair \(( m , M )\) is equal to
- A \((0,4)\)
- B \((-4,4)\)
- C \((0,2 \sqrt{2})\)
- D \((-4,0)\)
Answer & Solution
Correct Answer
(D) \((-4,0)\)
Step-by-step Solution
Detailed explanation
\(C _{3} \rightarrow C _{3}-\left( C _{1}- C _{2}\right)\) \(f(\theta)=\left|\begin{array}{ccc}-\sin ^{2} \theta & -1-\sin ^{2} \theta & 0 \\ -\cos ^{2} \theta & -1-\cos ^{2} \theta & 0 \\ 12 & 10 & -4\end{array}\right|\)…
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