The greatest terms of the expansion $(2x+5y)^{13}$ when $x=10$, $y=2$ is?

Calculate $\mathrm{m}=\frac{\mathrm{n}+1}{1+\left|\frac{\mathrm{a}}{\mathrm{b}}\right|}$ as in $(\mathrm{a}+\mathrm{b})^{\mathrm{n}}$

$\mathrm{m}=\frac{13+1}{1+\left|\frac{2 x}{5 y}\right|}=\frac{14}{1+2}=\frac{14}{3}$

$\mathrm{m}$ is not integer so greatest term is $\mathrm{T}_{[\mathrm{m}]+1}$

$\begin{array}{l} \Rightarrow \mathrm{T}_{5}={ }^{13} \mathrm{C}_{4}(2 \mathrm{x})^{9} \cdot(5 \mathrm{y})^{4} \\ ={ }^{13} \mathrm{C}_{4} \cdot \quad 20^{9} \cdot \quad 10^{4} \quad[\because \mathrm{x}=10, \mathrm{y}=2] \end{array}$