If $2\mathrm{a}+2\mathrm{b}+3\mathrm{c}=\frac{1}{5}$ and $\mathrm{a},\mathrm{b},\mathrm{c}>0,$ then maximum value of term independent of x in the expansion of ${\left({\mathrm{abx}}^{1/2}+{\mathrm{cx}}^{-1/3}\right)}^{25}$ is

$\begin{array}{l}{\mathrm{T}}_{\mathrm{r}+1}{=}^{25}{\mathrm{C}}_{\mathrm{r}}(\mathrm{ab}{)}^{(25-\mathrm{r})}\cdot {\mathrm{x}}^{\left(\frac{25-\mathrm{r}}{2}\right)}\cdot {\mathrm{c}}^{\mathrm{r}}\cdot {\mathrm{x}}^{\left(-\frac{\mathrm{r}}{3}\right)}\Rightarrow \mathrm{r}=15{=}^{25}{\mathrm{C}}_{15}{\mathrm{a}}^{10}\cdot {\mathrm{b}}^{10}\cdot {\mathrm{c}}^{15}\\ 10\mathrm{a}+10\mathrm{b}+15\mathrm{c}=1\\ \frac{(\mathrm{a}+\mathrm{a}+\dots \dots +\mathrm{a})+(\mathrm{b}+\mathrm{b}+\dots ..+\mathrm{b})+(\mathrm{c}+\mathrm{c}+\dots .+\mathrm{c})}{35}\ge {\left({\mathrm{a}}^{10}{\mathrm{b}}^{10}{\mathrm{c}}^{15}\right)}^{\frac{1}{35}}\\ {\left(\frac{1}{35}\right)}^{35}\ge {\mathrm{a}}^{10}{\mathrm{b}}^{10}{\mathrm{c}}^{15}\end{array}$