For $x\, \in \,R\,,\,x\, \ne \, - 1,$ if ${(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^2}{(1 + x)^{2014}} + ....{x^{2016}} = \sum\limits_{i = 0}^{2016} {{a_i\,}{\,x^i}} ,$ then $a_{17}$ is equal to

${n^n}{\left( {\frac{{n + 1}}{2}} \right)^{2n}}$ is

For natural numbers $m,n$ ,if ${\left( {1 - y} \right)^m}{\left( {1 + y} \right)^n} = 1 + {a_1}y + {a_2}{y^2} + \ldots \;$ and $a_1= a_2=10,$ then $(m,n)$ =______. 

$(1 + x) (1 + x + x^2) (1 + x + x^2 + x^3) ...... (1 + x + x^2 + ...... + x^{100})$ when written in the ascending power of $x$ then the highest exponent of $x$ is ______ .

If  the number of terms in the expansion  of ${\left( {1 - \frac{2}{x} + \frac{4}{{{x^2}}}} \right)^n},x \ne 0$ is $28$ then the sum of the coefficients of all the terms in this expansion, is :

The coefficient of $x^{256}$ in the expansion of $(1-x)^{101}\left(x^{2}+x+1\right)^{100}$ is: