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MCQMediumJEE Main 2023 · 1 February, Shift 1Properties of Determinants

Mathematics Question from JEE Main 2023 · 1 February, Shift 1

Let f(x)=[1+sin⁡2xcos⁡2xsin⁡2xsin⁡2x1+cos⁡2xsin⁡2xsin⁡2xcos⁡2x1+sin⁡2x]f(x) = \begin{bmatrix} 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{bmatrix} where x∈[π6,π3]x \in \left[ \frac{\pi}{6}, \frac{\pi}{3} \right]. If α,β\alpha, \beta are respectively the maximum and the minimum values of ff, then

  • A

    β2−2α=194\beta^2 - 2\sqrt{\alpha} = \frac{19}{4}

  • B

    β2+2α=194\beta^2 + 2\sqrt{\alpha} = \frac{19}{4}

  • C

    α2−β2=43\alpha^2 - \beta^2 = 4\sqrt{3}

  • D

    α2+β2=92\alpha^2 + \beta^2 = \frac{9}{2}

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