If the sum of the coefficients in the expansion of $({\alpha ^2}{x^2} - 2\alpha x + 1)^{51}$ vanishes,then the value of $\alpha$ is

For $x \in R, x \neq -1$,if $(1+x)^{2016} + x(1+x)^{2015} + x^2(1+x)^{2014} + \dots + x^{2016} = \sum_{i=0}^{2016} a_i \cdot x^i$,then $a_{17}$ is equal to

If the sum of the coefficients in the expansion of $(1 - 3x + 10x^2)^n$ is $a$ and if the sum of the coefficients in the expansion of $(1 + x^2)^n$ is $b$,then:

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

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

The coefficient of $x^{101}$ in the expression $(5+x)^{500} + x(5+x)^{499} + x^{2}(5+x)^{498} + \ldots + x^{500}$ for $x > 0$ is: