JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A = \left[ {\begin{array}{*{20}{c}}
1&{\sin \,\theta }&1\\
{ - \,\sin \,\theta }&1&{\sin \,\theta }\\
{ - 1}&{ - \,\sin \,\theta }&1
\end{array}} \right];\) then for all \(\theta \, \in \,\left( {\frac{{3\pi }}{4},\frac{{5\pi }}{4}} \right),\) det \((A)\) lies in the interval
- A \(\left( {1,\left. {\frac{5}{2}} \right]} \right.\)
- B \(\left[ {\frac{5}{2},\left. 4 \right)} \right.\)
- C \(\left( {\left. {0,\frac{3}{2}} \right]} \right.\)
- D \(\left( {\frac{3}{2},\left. 3 \right]} \right.\)
Answer & Solution
Correct Answer
(D) \(\left( {\frac{3}{2},\left. 3 \right]} \right.\)
Step-by-step Solution
Detailed explanation
\(\left| A \right| = \left| {\begin{array}{*{20}{c}} 1&{\sin \theta }&1\\ { - \sin \theta }&1&{\sin \theta }\\ { - 1}&{ - \sin \theta }&1 \end{array}} \right|\) \( = 2\left( {1 + {{\sin }^2}\theta } \right)\)…
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