Question

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

• A. $924$
• B. $792$
• C. $1594$
• D. None of these

Answer 1

The correct option is A $924$

We know that, the coefficients in a binomial expansion is obtained by replacing each variable by unit in the given expression.

Therefore, sum of the coefficients in $(a+b{)}^n$

$=4096=(1+1{)}^n$

$\Rightarrow 4096=2^n$

$\Rightarrow 2^{12}=2^n\Rightarrow n=12$

Here $n$ is even, so the greatest coefficient is

${}^n{C}_{n/2}$ i.e., ${}^{12}{C}_6=\frac{12\times 11\times 10\times 9\times 8\times 7}{6\times 5\times 4\times 3\times 2\times 1}=924$.