The coefficients of $${x^p}$$ and $${x^q}$$ in the expansion of $${\left( {1 + x} \right)^{p + q}}$$ are

$$r$$ and $$n$$ are positive integers $$\,r > 1,\,n > 2$$ and coefficient of $$\,{\left( {r + 2} \right)^{th}}$$ term and $$3{r^{th}}$$ term in the expansion of $${\left( {1 + x} \right)^{2n}}$$ are equal, then $$n$$ equals

If the sum of the coefficients in the expansion of $$\,{\left( {a + b} \right)^n}$$ is 4096, then the greatest coefficient in the expansion is

The positive integer just greater than $${\left( {1 + 0.0001} \right)^{10000}}$$ is