If $C_{x} \equiv^{25} C_{x}$ and $\mathrm{C}_{0}+5 \cdot \mathrm{C}_{1}+9 \cdot \mathrm{C}_{2}+\ldots .+(101) \cdot \mathrm{C}_{25}=2^{25} \cdot \mathrm{k}$ then $\mathrm{k}$ is equal to

The expression $x^3 - 3x^2 - 9x + c$ can be written in the form $(x - a)^2 (x - b)$ if the values of $c$ is

If the sum of the coefficients of all the positive powers of $x$, in the binomial expansion of $\left(x^{n}+\frac{2}{x^{5}}\right)^{7}$ is $939 ,$ then the sum of all the possible integral values of $n$ is

The value $\sum \limits_{ r =0}^{22}{ }^{22} C _{ r }{ }^{23} C _{ r }$ is $.......$

The sum of the series $\left( {\begin{array}{*{20}{c}}{20}\\0\end{array}} \right) - \left( {\begin{array}{*{20}{c}}{20}\\1\end{array}} \right)$$+$$\left( {\begin{array}{*{20}{c}}{20}\\2\end{array}} \right) - \left( {\begin{array}{*{20}{c}}{20}\\3\end{array}} \right)$$+…..-……+$$\left( {\begin{array}{*{20}{c}}{20}\\{10}\end{array}} \right)$ 

In the expansion of ${(1 + x)^5}$, the sum of the coefficient of the terms is