The numerically greatest term in the expansion of $(3 x + 5 y)^{24}$ , when x=4 and y=2 is:

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Solution

The correct option is D

Let $T_{r + 1}$ be the numerically greatest term. Then
r= $[\frac{(n + 1)}{(1 + | \frac{x}{y} |)}]$

r= $[\frac{24 + 1}{(1 + \frac{3 x}{5 y})}]$

r= $[\frac{24 + 1}{(1 + \frac{3 \times 4}{5 \times 2})}]$

r= $[\frac{25}{(1 + \frac{12}{10})}]$

r= $[\frac{25}{1 + 1.2}]$

r=11
$\Rightarrow T_{12}$ is the numerically greatest term

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