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Functions question

2023 · 1 Feb · Shift 1 · Q31

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PYQ Library
JEE Main
Mathematics
Functions
2023 · 1 Feb · Shift 1 · Q31

Functions question

2023 · 1 Feb · Shift 1 · Q31

JEE MainMathematicsFunctionsMCQ+4 / −1

Let

f(x) = \left| {\begin{matrix} {1 + {{\sin }^2}x} & {{{\cos }^2}x} & {\sin 2x} \\ {{{\sin }^2}x} & {1 + {{\cos }^2}x} & {\sin 2x} \\ {{{\sin }^2}x} & {{{\cos }^2}x} & {1 + \sin 2x} \\ \end{matrix} } \right|,\,x \in \left[ {{\pi \over 6},{\pi \over 3}} \right]

. If

\alpha

and

\beta

respectively are the maximum and the minimum values of

f

, then

A
${\alpha ^2} - {\beta ^2} = 4\sqrt 3$
B
${\beta ^2} - 2\sqrt \alpha = {{19} \over 4}$
C
${\beta ^2} + 2\sqrt \alpha = {{19} \over 4}$
D
${\alpha ^2} + {\beta ^2} = {9 \over 2}$

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