The coefficient of $x^{10}$ in the expansion of $(1 + x)^2 (1 + x^2)^3 (1 + x^3)^4$ is equal to

The coefficient of $x^{13}$ in the expansion of $(1 - x)^5(1 + x + x^2 + x^3)^4$ is :-

Let $(5 + 2\sqrt{6})^n = p + f$,where $n \in N$,$p \in N$,and $0 < f < 1$. Then the value of $f^2 - f + pf - p$ is:

Let $(1+x+x^2)^{2014} = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \ldots + a_{4028} x^{4028}$. Let $A = a_0 - a_3 + a_6 - \ldots + a_{4026}$,$B = a_1 - a_4 + a_7 - \ldots - a_{4027}$,and $C = a_2 - a_5 + a_8 - \ldots + a_{4028}$. Then,

The fractional part of a real number $x$ is defined as $x - [x]$,where $[x]$ is the greatest integer less than or equal to $x$. Let $F_1$ and $F_2$ be the fractional parts of $(44 - \sqrt{2017})^{2017}$ and $(44 + \sqrt{2017})^{2017}$,respectively. Then,$F_1 + F_2$ lies between the numbers:

The coefficient of $t^{24}$ in the expansion of $(1 + t^2)^{12}(1 + t^{12})(1 + t^{24})$ is