A polymer blend is made up of four lots of polymers A$,$ B$,$ C$,$ and D $($with $k=1,2,3,$ and $4,$ respectively$),$

which can be described by their number$-$average $(x_n)$ and weight$-$average $(x_w)$ degree of polymerization

$x_w=2,800k^{1\mathrm{.}5},x_n=1,400k$

The blend contains $1,\frac{000}{k^2}g$ of each lot. For the blend,

a$.$ What degree of polymerization can be expected from measurement made using a light

scattering apparatus?

b$.$ What degree of polymerization can be expected from measurements of osmotic pressure

at various concentrations of this blend in a solution?