Question

If for some positive integer $n$, the coefficients of three consecutive terms in the binomial expansion of $(1+x{)}^{n+5}$ are in the ratio $5:10:14,$ then the largest coefficient in this expansion is :-

• A. 792
• B. 252
• C. 462
• D. 330

Answer 1

Answer: (C)

Let $n+5=N$
$N_{C_{t-1}}:N_{C_t}:N_{C_{n-1}}=5:10:14$
$\Rightarrow \frac{N_{C_s}}{N_{C_{t-1}}}=\frac{N+1-r}{r}=2$
$\frac{N_{C_{t+1}}}{N_{C_t}}=\frac{N-r}{r+1}=\frac{7}{5}$
$\Rightarrow r=4,N=11$
$\Rightarrow (1+x{)}^{11}$
Largest coefficient $={}^{11}{C}_6=462$