First slide

Binomial theorem for positive integral Index

Question

If the sum of the coefficients in the expansion of (a + b)ⁿ is 4096, then the greatest coefficient in the expansion is

Moderate

A

924
B

729
C

1594
D

none of these

Solution

We know that the sum of the coefficients in a binomial
expansion is obtained by replacing each variable by unit in
the given expression. Therefore, sum of the coefficients in
(a + b)ⁿ is given by (1 + 1)ⁿ
$∴ 4096 = 2^{n} or 2^{n} = 2^{12} or n = 12$
Hence, n is even. So, the greatest coefficient is $^{n} C_{n / 2}$ i.e., $^{12} C_{6} = 924$

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