What is the sum of the coefficients of $(x^2 - x - 1)^{99}$?

The coefficient of $x^{19}$ in the polynomial $(x-1)(x-2^1)(x-2^2) \dots (x-2^{19})$ 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 = $

The coefficient of $x$ in the expansion of $[\sqrt{1 + x^2} - x]^{-1}$ in ascending powers of $x$,when $|x| < 1$,is

In the expansion of $(a+1+\frac{1}{a})^n$,where $n \in N$,there are $2029$ terms. Then $n=$

The value of $^nC_1 \sum_{r=0}^1 {^1C_r} + ^nC_2 \left( \sum_{r=0}^2 {^2C_r} \right) + ^nC_3 \left( \sum_{r=0}^3 {^3C_r} \right) + \dots + ^nC_n \left( \sum_{r=0}^n {^nC_r} \right)$ is equal to