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Q.

Let m and M be respectively the minimum and maximum values of $| \begin{array}{l} \cos^{2} x 1 + \sin^{2} x \sin 2 x \\ 1 + \cos^{2} x \sin^{2} x \sin 2 x \\ \cos^{2} x \sin^{2} x 1 + \sin 2 x \end{array} |$ Then the ordered pair (m, M) is equal to

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a

$(- 4, - 1)$

b

$(1, 3)$

c

$(- 3, 3)$

d

$(- 3, - 1)$

answer is B.

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Detailed Solution

$R_{2} \to R_{2} \to R_{1}, R_{3} \to R_{3} - R_{1}$

$| \begin{array}{l} \cos^{2} x 1 + \sin^{2} x \sin 2 x \\ 1 - 1 0 \\ 0 - 1 1 \end{array} | = - 2 - \sin 2 x = - 3, - 1$

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