$\text{ The sum of the coefficient of all the terms in the expansion }$$\text{ of }(2x-y+z{)}^{20}\text{ in which }y\text{ do not appear at all while }x$$\text{ appears in even powers and }z\text{ appears in odd powers is - }$

$\begin{array}{l}coefficient of general term=\frac{20!}{\text{p}!\text{q}!\text{r}!}=\frac{20!}{\text{p}!\text{q}!\text{r}!}{2}^{\text{p}}{\text{x}}^{\text{p}}{\text{y}}^{\text{q}}{\text{z}}^{\text{r}}\\ \text{where p}+\text{q}+\text{r}=20,\text{q}=0\\ \text{⇒p}+\text{r}=20\text{ (p is even and r is odd). }\\ \text{ ⇒even }+\text{ odd }=\text{ even (not possible) }\\ \text{⇒ Coefficient of such power never occur }\\ \therefore \text{ coefficient is zero }\end{array}$