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

If $A$ denotes the sum of all the coefficients in the expansion of $\left(1-3 x+10 x^2\right)^n$ and $B$ denotes the sum of all the coefficients in the expansion of $\left(1+x^2\right)^n$, then :

If $\frac{1}{n+1}{ }^n C_n+\frac{1}{n}{ }^n C_{n-1}+\ldots+\frac{1}{2}{ }^{ n } C _1+{ }^{ n } C _0=\frac{1023}{10}$ then $n$ is equal to

If $(1 + x) (1 + x + x^2) (1 + x + x^2 + x^3) ...... (1 + x + x^2 + x^3 + ...... + x^n)$

$\equiv  a_0 + a_1x + a_2x^2 + a_3x^3 + ...... + a_mx^m$ then $\sum\limits_{r\, = \,0}^m {\,\,{a_r}}$ has the value equal to

Let $n$ be an odd integer. If $\sin n\theta = \sum\limits_{r = 0}^n {{b_r}{{\sin }^r}\theta } $ for every value of $\theta $, then

The sum of the coefficients of three consecutive terms in the binomial expansion of $(1+ x )^{ n +2}$, which are in the ratio $1: 3: 5$, is equal to