$\left(1-x^{2}+3 x^{3}\right)\left(\frac{5}{2} x^{3}-\frac{1}{5 x^{2}}\right)^{11}$
General term of $\left(\frac{5}{2} x^{3}-\frac{1}{5 x^{2}}\right)^{11}$ is
${ }^{11} C_{r}\left(\frac{5}{2} x^{3}\right)^{11-r}\left(-\frac{1}{5 x^{2}}\right)^{r}$
General term is ${ }^{11} C _{ r }\left(\frac{5}{2}\right)^{11- r }\left(-\frac{1}{5}\right)^{ r } x ^{33-5 r }$
Now, term independent of $x$
$1 \times$ coefficient of $x^{0}$ in $\left(\frac{5}{2} x^{3}-\frac{1}{5 x^{2}}\right)^{11}$
$-1 \times$ coefficient of $x^{-2}$ in $\left(\frac{5}{2} x^{3}-\frac{1}{5 x^{2}}\right)^{11}+$
$3 \times$ coefficient of $x^{-3}$ in $\left(\frac{5}{2} x^{3}-\frac{1}{5 x^{2}}\right)^{11}$
for coefficient of $x ^{0} 33-5 r =0$ not possible
for coefficient of $x^{-2} 33-5 r=-2$
$ 35=5 r \Rightarrow r=7 $
for coefficient of $ x ^{-3} 33-5 r=-3$
$36=5 r$ not possible
So term independent of $x$ is
$(-1)^{11} C _{7}\left(\frac{5}{2}\right)^{4}\left(-\frac{1}{5}\right)^{7}=\frac{33}{200}$