Question

" there is no term involving $x^6$ in the expansion of ${(2x^2-\frac{3}{x})}^{11}$ where $x\ne 0$. " that statement is____

• A. True
• B. False

Answer 1

The correct option is A True

$x^{6}in{(2x^2-\frac{3}{x})}^{11}$

$T_{r+1}={}^{11}Cr{\left(2x^2\right)}^r{\left(\frac{-3}{x}\right)}^{11-r}$

To find term containing $x^6$

$2r-11+r=6$

$3r=17$

$r=\frac{17}{3}$ which is not an integer.

So there is no term containing $x^6$