Let $n\in N. $ Which of the following inequalities are TRUE.
$(a)$ For every $n>1$, $ \quad {{2n}\choose{n}}^{1/n}> 2.$
$(b)$ For every $n\geq1$ , $\quad {{2n}\choose{n}}< \frac{1}{\sqrt{2n+1}}.$
$(c)$For every $n>1$,$ \quad n!{{2n}\choose{n}}< (2n)^n.$
Kindly help I have no idea how to solve these type of combinatorial inequalities. Thank you.