Prove that there is no term involving `x^6` in the expansion of `(2x^2-3/x)^(11)` , where `!=0.`

Explanation

General term in the given expression can be given as,

`T_(r+1) = C(11,r)(2x^2)^(11-r)(-3/x)^r`

So, terms involving `x` will be `x^(22-2r)*x^(-r)`.

`:.` For the term involving `x^6`,

`22-2r-r = 6`

`=>r = 16/3`

But, `r` can not be a fraction.

It means the expansion does not involve `x^6`.