The total number of terms in the expansion of $(x+a)^{47}-(x-a)^{47}$ after simplification is

The sum of coefficients in the expansion of $(1 + x + x^2)^n$ is

The remainder when $19^{200} + 23^{200}$ is divided by $49$ is $.........$.

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

Evaluate $(\sqrt{3}+\sqrt{2})^{6}-(\sqrt{3}-\sqrt{2})^{6}$ (in $\sqrt{6}$)

Let $n$ be a positive integer. Let $A = \sum_{k=0}^{n} (-1)^{k} {}^{n}C_{k} \left[ \left(\frac{1}{2}\right)^{k} + \left(\frac{3}{4}\right)^{k} + \left(\frac{7}{8}\right)^{k} + \left(\frac{15}{16}\right)^{k} + \left(\frac{31}{32}\right)^{k} \right]$. If $63A = 1 - \frac{1}{2^{30}}$,then $n$ is equal to ......