Binomial Theorem

If the ratio of coefficient of the three consecutives terms in binomial expansion of $$(1+x)^n$$ is $$2:15:70$$.
Then the average of these coefficient is
If $$ (1-x)^{-n}=a_{0}+a_{1}x+a_{2}x^{2}+.......+a_{r}x^{r} +........,$$ then $$a_{0}+a_{1}+a_{2}+.....a_{r} $$ is equal to
Write the general term in the expansion of $$(x^2 - yx)^{12}, x \neq 0$$
Show that the expansion of $$\left( x^2 + \dfrac{1}{x} \right)^{12}$$ does not contain any term involving $$x^{-1}$$.
Remainder when $$2 ^ { 30 } 3 ^ { 20 }$$ is divided by 7 is