2023 AISS AM S3 EOY Q11

In the expansion of \({\left( x^2 + \frac{1}{3x} \right)^n}\) in descending powers of \({x}\), the coefficients of the second and the third term are in the ratio of \({6:11}\).

1. Show that the value of \({n}\) is \({12}\).[6]
2. Find the middle term.[2]
3. Find the coefficient of \({x^6}\) in the expansion of \({\left(2 - x^3\right)\left(x^2 + \frac{1}{3x}\right)^{12}}\).[3]