Question

If $A$ and $B$ are coefficients of $x^n$ in the expansions of ${(1+x)}^{2n}$ and ${(1+x)}^{2n-1}$ respectively, then $\frac{A}{B}$ is equal to

• A. $4$
• B. $2$
• C. $9$
• D. $6$

Answer 1

Answer: (B)

$2$

Given $A=$ Coefficient of $x^n$ in ${(1+x)}^{2n}$
and $B=$ Coefficient of $x^n$ in ${(1+x)}^{2n-1}$
$\therefore A={{}^{2n}C}_n;B={{}^{2n-1}C}_{n-1}$
$\therefore \frac{A}{B}=\frac{{{}^{2n}C}_n}{{{}^{2n-1}C}_{n-1}}=\frac{2n}{n}=2$