# If the minimum and the maximum values of the function :, R 4 2 f é ù p p ê ú ® ë û , defined by 2 2 2 2 sin 1 sin 1 ( ) cos 1 cos 1 12 10 2 f – q — q q= – q — q – are m and M respectively, then the ordered pair (m, M) is equal to :

Question:

If the minimum and the maximum values of the function

$f:\left[\frac{\pi}{4}, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$, 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 :

1. $(0,2 \sqrt{2})$

2. $(-4,0)$

3. $(-4,4)$

4. $(0,4)$

Correct Option: 2

JEE Main Previous Year 1 Question of JEE Main from Mathematics Matrices and Determinants chapter.
JEE Main Previous Year Sep. 05, 2020 (I)

Solution:

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