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CUET · MATHS · PYQ PAPER 2023

Number of solutions of the equation \(\left|\begin{array}{ccc}-1 & 0 & \sin \theta \\ \sin \theta & -1 & 0 \\ 0 & \sin \theta & -1\end{array}\right|=0\) in \((0, \pi)\) is:

  1. A exactly one
  2. B exactly zero
  3. C exactly two
  4. D infinitely many
Verified Solution

Answer & Solution

Correct Answer

(A) exactly one

Step-by-step Solution

Detailed explanation

\( (-1)((-1)(-1) - 0) - 0 + \sin \theta ((\sin \theta)(\sin \theta) - 0) = 0 \) \( -1(1) + \sin \theta (\sin^2 \theta) = 0 \) \( -1 + \sin^3 \theta = 0 \) \( \sin^3 \theta = 1 \) \( \sin \theta = 1 \) \( \theta = \frac{\pi}{2} \) for \( \theta \in (0, \pi) \) Number of…