Question

If the coefficient of $pth$ term in the expansion of $(1+x{)}^{44}$ is $p$ and that of $(p+1)$th term is $q$, then $(p+q-1)=$

• A. $n$
• B. $2n$
• C. $3n$
• D. $4n$

Answer 1

The correct option is A $n$

Binomial Coefficient of $pth$ term ${}^n{C}_{p-1}=p$
Binomial Coefficient of $(p+1)th$ term ${}^n{C}_p=q$
Therefore, with respect to the above question.
$\frac{{}^n{C}_{p-1}}{{}^n{C}_p}=\frac{p}{q}$
$\frac{n!(n-p)!p!}{n!(n-p+1)!(p-1)!}=\frac{p}{q}$
$\frac{p}{n-p+1}=\frac{p}{q}$
$n-p+1=q$
$n=p+q-1$
Hence answer is $n$