Sum of coefficients in expansion of {(x + y)^n} is 4096 . greatest coefficient in expansion is

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7.Binomial Theorem

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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

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