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

Answer

N/a

Explanation

`T_(r+1)=^(11)C_(r)(2x^(2))^(11-r)(-(3)/(x))^(r)`
`=^(11)C_(r).2^(11-r).x^(22-2r).((-3)^(r))/(x^(r))`
`=^(11)C_(r).2^(11-r)(-3)^(r).x^(22-3r)`
Let 22-3r =6
`rArr" "3r=16`
`rArr " "r=(16)/(3)=5(1)/(3)`
But 'r' cannot be in fraction .
Therefore the term containing `x^(6)` is not existing in the expansion of `(2x^(2)-(3)/(x))^(11)`