JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The number of \(\theta \in(0,4 \pi)\) for which the system of linear equations \(3(\sin 3 \theta) x-y+z=2\), \(3(\cos 2 \theta) x+4 y+3 z=3\), \(6 x+7 y+7 z=9\) has no solution is.
- A \(6\)
- B \(7\)
- C \(8\)
- D \(9\)
Answer & Solution
Correct Answer
(B) \(7\)
Step-by-step Solution
Detailed explanation
The system of equation has no solution. \(D=\left|\begin{array}{ccc}3 \sin 3 \theta & -1 & 1 \\3 \cos 2 \theta & 4 & 3 \\6 & 7 & 7\end{array}\right|=0\)\(21 \sin 3 \theta+42 \cos 2 \theta-42=0\)\(\sin 3 \theta+2 \cos 2 \theta-2=0\) Number of solution is \(7\) in \((0,4 \pi)\)
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