The sum of the coefficients in the expansion of $(1 + x - 3x^2)^{2163}$ will be

If the sum of all the coefficients of $(\alpha x^2 - 2x + 1)^{2019}$ is equal to the sum of all the coefficients of $(x - \alpha y)^{2019}$,then $\alpha = $

For natural numbers $m, n$,if $(1 - y)^m(1 + y)^n = 1 + a_1y + a_2y^2 + \ldots$ and $a_1 = a_2 = 10$,then $(m, n) = \_\_\_\_\_\_$.

When $|x| < 2$,the coefficient of $x^2$ in the power series expansion of $\frac{x}{(x-2)(x-3)}$ is

Using the Binomial Theorem,evaluate $(99)^{5}$.

The remainder obtained when $(2m + 1)^{2n}$ $(m, n \in N)$ is divided by $8$ is