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 `