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

1594

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792

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924

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2924

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Solution

The correct option is C 924
Sum of coefficients in the expansion of $(a + b)^{n}$ is equal to $2^{n}$
We have $2^{n} = 4096 = 2^{12} \Rightarrow n = 12;$
So, middle term is $t_{7}$
$t_{7} = t_{6 + 1} =^{12} C_{6} = \frac{12!}{6! 6!} = 924.$

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