The value of $4 \{^nC_1 + 4 \cdot ^nC_2 + 4^2 \cdot ^nC_3 + \dots + 4^{n-1} \cdot ^nC_n\}$ is:

If $\{ p \}$ denotes the fractional part of the number $p$,then $\left\{\frac{3^{200}}{8}\right\}$ is equal to

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 $(m, n) = \_\_\_\_\_\_$.

By neglecting $x^4$ and higher powers of $x$, find the approximate value of $\sqrt[3]{x^2+64}-\sqrt[3]{x^2+27}$.

$(3+\sqrt{8})^5+(3-\sqrt{8})^5=$

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 = $