The number of values of $x$ in the interval $[0,5\pi ]$ satisfying the equation $3{\sin }^{2}x-7\sin x+2=0$ is

The correct option is B $6$

$\text{Given}:3{\sin }^{2}x-7\sin x+2=0$
$\Rightarrow (\sin x-2)(3\sin x-1)=0$
$\Rightarrow \sin x=\frac{1}{3}\text{or}\sin x=2$
$\sin x=2$ is not possible
$\therefore \text{only possible}\sin x=\frac{1}{3}$

There exists two values in$(0,\pi ),(2\pi ,3\pi )\text{and}(4\pi ,5\pi ).$
Hence there are six solutions
Thus, option C is correct.