# The largest coefficient in the expansion of $(1+x)^{30}$ is __________

$\begin{array}{1 1}(A)\;30C_{15}\\(B)\;30C_{10}\\(C)\;30C_{14}\\(D)\;30C_5\end{array}$

Toolbox:
• $T_{r+1}=nC_r a^{n-r} b^r$
The coefficient in $(1+x)^{30}$ is $30C_0,30C_1,30C_2$..........$30C_{30}$
$\therefore$ Greatest coefficient =$30C_{30/2}$
$\qquad\qquad\quad\quad\quad\;=30C_{15}$
(If n is even the $nC_r$ is greatest where $r=\large\frac{n}{2}$)
Hence (A) is the correct answer.