Suppose A and B are the coefficients of $30^{ ext {th }}$ and $12^{ ext {th }}$ terms respectively in the binomial expansion of $(1+x)^{2 \mathrm{n}-1}$. If $2 \mathrm{~A}=5 \mathrm{~B}$, then n is equal to :

Question

Suppose A and B are the coefficients of $30^{	ext {th }}$ and $12^{	ext {th }}$ terms respectively in the binomial expansion of $(1+x)^{2 \mathrm{n}-1}$. If $2 \mathrm{~A}=5 \mathrm{~B}$, then n is equal to :

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{A}={ }^{2 \mathrm{n}-1} \mathrm{C}_{29} \quad \mathrm{~B}={ }^{2 \mathrm{n}-1} \mathrm{C}_{11} \ & 2^{2 \mathrm{n}-1} \mathrm{C}_{29}=5{ }^{2 \mathrm{n}-1} \mathrm{C}_{11} \ & 2 \frac{(2 \mathrm{n}-1)!}{29!(2 \mathrm{n}-30)!}=5 \frac{(2 \mathrm{n}-1)!}{(2 \mathrm{n}-12)!11!} \ & \frac{1}{29 \ldots 12 \cdot 5}=\frac{1}{(2 \mathrm{n}-12)(2 \mathrm{n}-13) \ldots(2 \mathrm{n}-29) 2} \ & \frac{1}{30 \cdot 29 \ldots 12}=\frac{1}{(2 \mathrm{n}-12)(2 \mathrm{n}-13) \ldots(2 \mathrm{n}-29) 12} \ & 2 \mathrm{n}-12=30 \ & \mathrm{n}=21\end{aligned}$

Suppose A and B are the coefficients of $30^{\text {th }}$ and $12^{\text {th }}$ terms respectively in the…

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