Question

If the sum of the coefficient in the expansion of $ (x + y)^n $ is $ 1024 $ , then the value of the greatest coefficient in the expansion is

• A. 356
• B. 252
• C. 210
• D. 120

Answer 1

Answer: (B)

Given that the sum of the coefficient in the expansion of $(x+y)^{n}=1024$ i.e.,
$2^{n}=1024 $
$2^{n}=2^{10} \Rightarrow n=10$
Since, $n$ is even, hence greatest coefficient
$={ }^{n} C_{n / 2}={ }^{10} C_{5} $
$=\frac{10 !}{5 ! \times 5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}=252$