Correct Answer – c
Given , ` ” ” 3sin ^(2) x – 7 sin x + 2 = 0 `
` rArr 3 sin ^(2) x – 6sin x – sin x + 2 = 0`
` rArr 3 sin x (sinx – 2 ) – 1 ( sinx – 2 ) = 0 `
` rArr ” ” (3sin x – 1 )(sinx – 2 ) = 0 `
` rArr ” ” sinx = (1)/(3)” “[because sin x = 2 ` is rejected `]`
` rArr ” ” x = n pi + (-1) ^(n) sin ^(-1) “”(1)/(3) , n in I `
For ` ” ” 0 le n le5, x in [0, 5pi]`
There are six values of ` x in [0, 5 pi]` which satisfy the equation ` 3 sin ^(2) x – 7 sin x + 2 = 0 `

`3sin^2x-7sinx+2=0`
`3sin^2x-6sinx-sinxx+2=0`
`3sinx(sinx-2)-1(sinx-2)=0`
`(sinx-2)(3sinx-1)=0`
`sinx=2`
No solution
`sinx=1/3`
Number of x=6
Option C is correct.