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CUET · MATHS · PYQ PAPER 2023

Let \(A=\left[\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right]\),where \(0 \leq \theta \leq 2 \pi\).
Then \(\operatorname{det}(A)\) lies in the interval :

  1. A \([2,3]\)
  2. B \([3,4]\)
  3. C \([2,4]\)
  4. D \((2,4)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \([2,4]\)

Step-by-step Solution

Detailed explanation

\(\operatorname{det}(A) = 1(1 - (-\sin^2 \theta)) - \sin \theta(-\sin \theta - (-\sin \theta)) + 1(\sin^2 \theta - (-1))\) \(\operatorname{det}(A) = 1(1 + \sin^2 \theta) - \sin \theta(0) + 1(\sin^2 \theta + 1)\) \(\operatorname{det}(A) = 1 + \sin^2 \theta + \sin^2 \theta + 1\)…