(B) The sum of the coefficients in the expansion of $(x + y)^n$ is given by putting $x = 1$ and $y = 1$,which is $(1 + 1)^n = 2^n$.Given $2^n = 4096 =

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(B) The sum of the coefficients in the expansion of $(x + y)^n$ is given by putting $x = 1$ and $y = 1$,which is $(1 + 1)^n = 2^n$.Given $2^n = 4096 = 2^{12}$,so $n = 12$.The greatest coefficient in the expansion of $(x + y)^n$ when $n$ is even is given by the middle term coefficient,which is $^nC_{n/2}$.For $n = 12$,the greatest coefficient is $^{12}C_6 = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7}{6 \times 5 \times 4 \times 3 \times 2 \times 1} = 924$.

Class 11 Mathematics Binomial Theorem General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

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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

AIEEE 2002 All AIEEE

A
$1024$
B
$924$
C
$824$
D
$724$

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Binomial Theorem

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General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

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