Question

If the sum of the coefficients in the expansion of $(x+y{)}^n$ is $4096$, then the greatest coefficient in the expansion is

• A. 924.0
• B. 924.00
• C. 924

Answer 1

Answer: (A), (B), (C)

Sum of coefficient in $(x+y{)}^n=4096$
Put $x=y=1\Rightarrow 2^n=2^{12}$
$\Rightarrow n=12$
Greatest coefficient in $(x+y{)}^{12}=$ coeff. of middle term $={}^{12}{C}_6$
$=\frac{12!}{6!\times 6!}$
$=\frac{12\times 11\times 10\times 9\times 8\times 7}{6\times 5\times 4\times 3\times 2\times 1}=924$