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7.Binomial Theorem
medium
If the sum of the coefficients in the expansion of $(x+y)^{n}$ is $4096,$ then the greatest coefficient in the expansion is .... .
A
$111$
B
$222$
C
$924$
D
$347$
(JEE MAIN-2021)
Solution
$(\mathrm{x}+\mathrm{y})^{\mathrm{n}} \Rightarrow 2^{\mathrm{n}}=4096\quad 2^{10}=1024 \times 2$
$\Rightarrow 2^{\mathrm{n}}=2^{12} \quad\quad\quad\quad\quad\quad 2^{11}=2048$
$\mathrm{n}=12 \quad\quad\quad\quad\quad\quad\quad\quad 2^{12}=\underline{4096}$
${ }^{12} \mathrm{C}_{6}=\frac{12 \times 11 \times 10 \times 9 \times 8 \times 7}{6 \times 5 \times 4 \times 3 \times 2 \times 1}$
$= 11 \times 3 \times 4 \times 7$
$= 924$
Standard 11
Mathematics
