The number of terms in the expansion of $(x^{2}+y^{2})^{25}-(x^{2}-y^{2})^{25}$ after simplification is

If the sum of the coefficients in the expansion of $(\alpha x^2 - 2x + 1)^{35}$ is equal to the sum of the coefficients in the expansion of $(x - \alpha y)^{35}$,then $\alpha = $

If $n$ is a positive integer,then $(\sqrt{3} + 1)^{2n} - (\sqrt{3} - 1)^{2n}$ is

The coefficient of $x^2$ in the expansion of the product $(2 - x^2)((1 + 2x + 3x^2)^6 + (1 - 4x^2)^6)$ is

For $x \in R, x \neq -1$, if $(1+x)^{2016} + x(1+x)^{2015} + x^2(1+x)^{2014} + \dots + x^{2016} = \sum_{i=0}^{2016} a_i \cdot x^i$, then $a_{17}$ is equal to

Find $a, b$ and $n$ in the expansion of $(a+b)^{n}$ if the first three terms of the expansion are $729, 7290$ and $30375$ respectively.