Question

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

• A. ${ }^{13} C _5 \cdot 20^8 \cdot 10^5$
• B. ${ }^{13} C _6 \cdot 20^7 \cdot 10^4$
• C. ${ }^{13} C _4 \cdot 20^9 \cdot 10^4$
• D. none of these

Answer 1

Answer: (C)

$\frac{ T _{ r +1}}{ T _{ r }}=\frac{14- r }{ r } \cdot \frac{5 y }{2 n }=\frac{14- r }{ r } \cdot \frac{1}{2}>1 \Rightarrow r <4 \frac{2}{3}$
$\Rightarrow \text { 5th term is greatest } \left.\Rightarrow T _5={ }^{13} C _4(2 x )^9(5 y )^4\right]$