Question

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

• A. $1594$
• B. $792$
• C. $924$
• D. $2924$

Answer 1

Answer: (C)

$924$

For the sum of the coefficients, we substitute $a=b=1$

Then, we get

$2^n=4096=2^{12}$

Thus

$n=12$

Hence

$(a+b{)}^n=(a+b{)}^{12}$

The greatest binomial coefficient will be the coefficient of the middle term.

The middle term will be the 7th term.

$T_7$

$=T_{6+1}$

Thus coefficient if

$={}^{12}{C}_6$

$=924$