Question

System of equations
$x+2y+z=0,2x+3y-z=0$ and $\left(tan\theta \right)x+y-3z=0$ has non-trivial solution then number of value(s) of $\theta ϵ(-\pi ,\pi )$ is equal to?

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is C 2

For non-trivial solutions
$\left|\begin{array}{ccc}1& 2& 1\\ 2& 3& -1\\ tan\theta & 1& -3\end{array}\right|=0$
$\Rightarrow 6-5\tan \theta =0$
$\Rightarrow \tan \theta =\frac{6}{5}$
Hence, the number of solutions in $(-\pi ,\pi )$ is 2
Hence, option 'C' is correct.