Three metals $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ with solution of their respective cations are tested in a voltaic cell with following
result.

A and B : A is cathode
B and C : C is cathode
A and C : A is anode

What is order of oxidation potentials from highest to lowest for the cations of three metals?

In voltaic cell in which longest reduction potential in cthode and lowest reduction potential is anode. So in A and B if A is cathode then it will be highest reduction potential as compared to B but C is cathode in B and C similarly in case of A. Similarly opposite of this will be oxidation potential hence the order of oxidation potential will be $\mathrm{B} > \mathrm{A} > \mathrm{C}$.