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General Term of Binomial Expansion

If the coeffi...

Question

If the coefficients of $r^{t h}$ term and $(r + 1)^{t h}$ term in the expansion of $(1 + x)^{20}$ are in the ration 1 : 2, then $r =$

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Solution

The correct option is C 7
The ratio of the coefficient of rth term and (r+1)th term 1 : 2
$\Rightarrow^{20} C_{r - 1} :^{20} C_{r} = 1 : 2$
$\Rightarrow \frac{r}{21 - r} = \frac{1}{2} \Rightarrow 2 r = 21 - r$
$\Rightarrow r = 7$

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