What is the remainder when $5 ^ {99}$ is divided by 13?

Which one of the following is the greatest coefficient in the expansion of $(1 + x) ^ {100}$ ?

 If $x=(1111){}^2$, $y=(1001){}^2$ and $z=(110){}^2$, then what is x³−y³−z³−3xyz equal to?

What is the number of rational terms in the expansion of $(\sqrt{3}+5^\frac{1}{4})^{12}$