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

$(\sqrt{2} + 1)^6 - (\sqrt{2} - 1)^6 = $

If in the expansion of $(1+x)^p(1-x)^q$,the coefficients of $x$ and $x^2$ are $1$ and $-2$ respectively,then $p^2+q^2$ is equal to :

If $(1+2x+3x^2)^{10} = a_0+a_1x+a_2x^2+\ldots+a_{20}x^{20}$,then $\frac{a_2}{a_1}$ is equal to

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

Let $a$ be the largest real root and $b$ be the smallest real root of the polynomial equation $x^6-6x^5+15x^4-20x^3+15x^2-6x+1=0$. Then $\frac{a^2+b^2}{a+b+1}$ is