Numerically greatest term, in the expansion of $(8 - 5 x)^{18}$ (where x = $2 / 5$ ) is :

1623 \times 2^{24}

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1623 \times 2^{22}

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1623 \times 2^{23}

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none of these

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Solution

The correct option is D none of these
The general term in $(8 - 5 x)^{18}$ is $^{18} C_{r} (8)^{18 - r} (- 5 x)^{r}$
Given $x = 2 / 5$
$⟹$ $^{18} C_{r} (8)^{18 - r} (- 5 x)^{r} =^{18} C_{r} (2)^{54 - 3 r} (- 2)^{r} = (- 1)^{r} (2)^{54 - 2 r}^{18} C_{r}$
Which will be maximum when $r = 9$
SO the numerically greatest term is $48620 \times 2^{36}$

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