If the ratio of the coefficient of third and fourth term in the expansion of ${\left( {x – \frac{1}{{2x}}} \right)^n}$ is $1 : 2$, then the value of $ n$ will be

If the coefficient of the second, third and fourth terms in the expansion of ${(1 + x)^n}$ are in $A.P.$, then $n$ is equal to

Find the middle terms in the expansions of $\left(3-\frac{x^{3}}{6}\right)^{7}$

Let $\mathrm{m}$ and $\mathrm{n}$ be the coefficients of seventh and thirteenth terms respectively in the expansion of $\left(\frac{1}{3} \mathrm{x}^{\frac{1}{3}}+\frac{1}{2 \mathrm{x}^{\frac{2}{3}}}\right)^{18}$. Then $\left(\frac{\mathrm{n}}{\mathrm{m}}\right)^{\frac{1}{3}}$ is :

Sum of co-efficients of terms of degree $m$  in the expansion of $(1 + x)^n(1 + y)^n(1 + z)^n$ is