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

We have $2^{n} = 4096 = 2^{12} \Rightarrow n = 12;$
so middle term $= t_{7}; t_{7} = t_{6 + 1} =^{12} C_{6} = \frac{12!}{6! 6!} = 924.$

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