If $n$ is even and ${ }^n{C}_0{<}^n{C}_1{<}^n{C}_2<\dots {<}^n{C}_r{>}^n{C}_{r+1}{>}^n{C}_{r+2}>\dots ..{>}^n{C}_n,$ then,  $r=$

From the given relation it is evident that ${ }^n{C}_r$  is the

greatest ;1mong the values ${ }^n{C}_n{,}^n{C}_1,\dots {,}^n{C}_r$ 

We know that ${ }^n{C}_r$ is greatest for $r=\frac{n}{2}.$ Hence $r=\frac{n}{2}.$