Question

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 1

Answer: (B)

The system of equation has no solution.
$ D = \begin{vmatrix}3 \sin 3 \theta & -1 & 1 \\3 \cos 2 \theta & 4 & 3 \\6 & 7 & 7\end{vmatrix}=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 $(0,4 \pi)$