Mathematics - Binomial Theorem Question with Solution | TestHub

$\begin{array}{rl}& {\mathrm{T}}_{\mathrm{r}+1}={}^{12}{\mathrm{C}}_{\mathrm{r}}{\left(\frac{3^{1/5}}{\mathrm{x}}\right)}^{12-\mathrm{r}}{\left(\frac{2\mathrm{x}}{5^{1/3}}\right)}^{\mathrm{r}}\\ & {\mathrm{T}}_{\mathrm{r}+1}=\frac{{}^{12}{\mathrm{C}}_{\mathrm{r}}(3{)}^{\frac{12-\mathrm{r}}{5}}(2{)}^{\mathrm{r}}(\mathrm{x}{)}^{2\mathrm{r}-12}}{(5{)}^{\mathrm{r}/3}}\\ & \mathrm{r}=6\\ & {\mathrm{T}}_7=\frac{{}^{12}{\mathrm{C}}_6(3{)}^{6/5}(2{)}^6}{5^2}=\left(\frac{9\times 11\times 7}{25}\right)2^8\cdot 3^{1/5}\\ & 25\alpha =693\end{array}$