In the expansion of $(1 + x + y + z)^4$,the ratio of the coefficients of $x^2y$,$xy^2z$,and $xyz$ is:

In the expansion of $(5^{1/2} + 7^{1/8})^{1024}$,the number of integral terms is

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

The constant term in the expansion of $\left(\frac{x}{2}+\frac{1}{x}+\sqrt{2}\right)^5$ is $\frac{a \sqrt{2}}{2}$,then $a=$

Let the coefficients of three consecutive terms $T_r$,$T_{r+1}$,and $T_{r+2}$ in the binomial expansion of $(a+b)^{12}$ be in a $G.P.$ and let $p$ be the number of all possible values of $r$. Let $q$ be the sum of all rational terms in the binomial expansion of $(\sqrt[4]{3}+\sqrt[3]{4})^{12}$. Then $p+q$ is equal to:

If the coefficients of $T_r, T_{r+1}, T_{r+2}$ terms of $(1+x)^{14}$ are in $A.P.$,then $r =$