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

Easy

A

924
B

792
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 ‘1’ 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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