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Matrices and Determinants question

2019 · 12 Jan · Shift 2 · Q38
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  5. /2019 · 12 Jan · Shift 2 · Q38

Matrices and Determinants question

2019 · 12 Jan · Shift 2 · Q38

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1
If A = [1sin⁡θ1−sin⁡θ1sin⁡θ−1−sin⁡θ1]\left[ {\begin{matrix} 1 & {\sin \theta } & 1 \\ { - \sin \theta } & 1 & {\sin \theta } \\ { - 1} & { - \sin \theta } & 1 \\ \end{matrix} } \right]​1−sinθ−1​sinθ1−sinθ​1sinθ1​​; then for all θ∈\theta \inθ∈ (3π4,5π4)\left( {{{3\pi } \over 4},{{5\pi } \over 4}} \right)(43π​,45π​), det (A) lies in the interval :
  1. A
    (32,3]\left( {{3 \over 2},3} \right](23​,3]
  2. B
    (0,32]\left( {0,{3 \over 2}} \right](0,23​]
  3. C
    [52,4)\left[ {{5 \over 2},4} \right)[25​,4)
  4. D
    (1,52]\left( {1,{5 \over 2}} \right](1,25​]
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