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7.Binomial Theorem
medium
The sum of the coefficients in the expansion of ${(x + y)^n}$ is $4096$. The greatest coefficient in the expansion is
A
$1024$
B
$924$
C
$824$
D
$724$
(AIEEE-2002)
Solution
(b) By hypothesis, ${2^n} = 4096 = {2^{12}} \Rightarrow n = 12$
Since $n$ is even, hence greatest coefficient
$ = {\,^n}{C_{n/2}} = {\,^{12}}{C_6} = \frac{{12.11.10.9.8.7}}{{1.2.3.4.5.6}} = 924$.
Standard 11
Mathematics