Coeff. of $x^4={ }^n C_4$
Coeff. of $x^5={ }^n C_5$
Coeff. of $x^6={ }^n C_6$
$ { }^n C_4,{ }^n C_5,{ }^n C_6 \ldots . \text { AP } $
2. ${ }^n C_5={ }^n C_4+{ }^n C_6$
$ \begin{aligned} & 2=\frac{{ }^n C_4}{{ }^n C_5}+\frac{{ }^n C_6}{{ }^n C_5}\left\{\frac{{ }^n C_r}{{ }^n C_r-1}=\frac{n-r+1}{r}\right\} \\ & 2=\frac{5}{\mathrm{n}-4}+\frac{\mathrm{n}-5}{6} \\ & 12(n-4)=30+n^2-9 n+20 \\ & \mathrm{n}^2-21 \mathrm{n}+98=0 \\ & (\mathrm{n}-14)(\mathrm{n}-7)=0 \\ & \mathrm{n}_{\max }=14 \mathrm{n}_{\min }=7 \end{aligned} $