The sum of the coefficients in the expansion of $(1+x+x^2)^n$ is

The coefficient of $x^{48}$ in $(1+x)+2(1+x)^2+3(1+x)^3+ . . . +100(1+x)^{100}$ is equal to:

If $(1 + ax)^n = 1 + 8x + 24x^2 + ....,$ then the value of $a$ and $n$ 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

If $f(x) = x^n$,then the value of $f(1) - \frac{f'(1)}{1!} + \frac{f''(1)}{2!} - \frac{f'''(1)}{3!} + ...... + \frac{(-1)^n f^n(1)}{n!}$ is

The coefficient of $x^4$ in the expansion of $(1+x-x^2-x^3)^{11}$ is