The term independent of x in the expansion of $\left(1-{\mathrm{x}}^2+3{\mathrm{x}}^3\right){\left(\frac{5}{2}{\mathrm{x}}^3-\frac{1}{5{\mathrm{x}}^2}\right)}^{11},\mathrm{x}\ne 0$ is :

General term of ${\left(\frac{5}{2}{\mathrm{x}}^3-\frac{1}{5{\mathrm{x}}^2}\right)}^{11} \mathrm{is}$ =${ }^{11}{\mathrm{C}}_{\mathrm{r}}{\left(\frac{5}{2}{\mathrm{x}}^3\right)}^{11-\mathrm{r}}{\left(-\frac{1}{5{\mathrm{x}}^2}\right)}^{\mathrm{r}}$

General term is ${ }^{11}{\mathrm{C}}_{\mathrm{r}}{\left(\frac{5}{2}\right)}^{11-\mathrm{r}}{\left(-\frac{1}{5}\right)}^{\mathrm{r}}{\mathrm{x}}^{33-5\mathrm{r}}$

Now, term independent of x

$=1\times \text{ coefficient of }{\mathrm{x}}^0\text{ in }{\left(\frac{5}{2}{\mathrm{x}}^3-\frac{1}{5{\mathrm{x}}^2}\right)}^{11}$

$$\begin{gathered} -1\times \text{ coefficient of }{\mathrm{x}}^{-2}\text{ in }{\left(\frac{5}{2}{\mathrm{x}}^3-\frac{1}{5{\mathrm{x}}^2}\right)}^{11} \\ + 3\times \text{ coefficient of }{\mathrm{x}}^{-3}\text{ in }{\left(\frac{5}{2}{\mathrm{x}}^3-\frac{1}{5{\mathrm{x}}^2}\right)}^{11} \end{gathered}$$

for coefficient of ${\mathrm{x}}^0, 33-5\mathrm{r}=0\text{ not possible, since r is non negative integer}$

for coefficient of ${\mathrm{x}}^{-2} 33-5\mathrm{r}=-2$

                                       $35=5\mathrm{r}\Rightarrow \mathrm{r}=7$

for coefficient of ${\mathrm{x}}^{-3} 33-5\mathrm{r}=-3$

                                       36 = 5r not possible

So term independent of x is

$(-1{)}^{11}{\mathrm{C}}_7{\left(\frac{5}{2}\right)}^4{\left(-\frac{1}{5}\right)}^7=\frac{33}{200}$