Question

If three consecutive coefficients in the expansion of $(1+x{)}^n$ be 165, 330 and 462, then ${}^n{C}_2$ =

• A. 55
• B. 66
• C. 45
• D. does not exist

Answer 1

The correct option is A

55

${}^n{C}_{r-1}$ = 165, ${}^n{C}_r$ = 330, ${}^n{C}_{r+1}$ = 462

⇒ $\frac{r}{n-r+1}$ = $\frac{1}{2}$, $\frac{r+1}{n-r}$ = $\frac{5}{7}$ ⇒ n = 11.

∴ ${}^n{C}_2$ = ${}^{11}{C}_2$ = $\frac{11\times 10}{2}$ = 55.