Question

The largest coefficient in the expansion of ${(1+x)}^{24}$ is

• A. ${}^{24}{C}_{24}$
• B. ${}^{24}{C}_{13}$
• C. ${}^{24}{C}_{12}$
• D. ${}^{24}{C}_{11}$

Answer 1

The correct option is C

${}^{24}{C}_{12}$

Explanation for correct option:

General formula for binomial expansion is given as

$T_{r+1}={}^{n}C_r{x}^{n-r}{y}^r$

We know that the middle term will have the greatest coefficient

Given expression is ${(1+x)}^{24}$

$T_{12+1}={}^{24}{C}_{12}{x}^{24-12}{\left(1\right)}^{12}$

$={}^{24}C_{12}{x}^{12}$

Hence, ${}^{24}C_{12}$ is the greatest coefficient.

Hence,option C is correct.