(C) The sum of the coefficients in the expansion of $(x+y)^{n}$ is obtained by putting $x=1$ and $y=1$.So,$(1+1)^{n} = 2^{n} = 4096$.Since $2^{12} = 4

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

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

JEE MAIN 2021 All JEE MAIN

A
$111$
B
$222$
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$924$
D
$347$

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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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