(A) Magnesium chloride solution coagulates a negatively charged gold solution readily than positively charged iron (III) hydroxide solution. In Magnesium chloride, the charge on cation is twice the charge on the anion. Higher is the charge on ion, higher will be its coagulating power. Hence, statement A is correct.
(B) Sodium sulphate solution causes coagulation in both solutions. It provides sodium ions which coagulate negatively charged gold sol and sulphate ions coagulate positively charged iron (III) hydroxide sol. Hence, statement B is correct.
(C) The dispersed phase in colloidal iron (III) hydroxide and colloidal gold is positively and negatively charged respectively.
When two solutions are mixed, they will affect mutual coagulation. This is because the charge on one sol is neutralized by the opposite charge on the other sol. Hence, statement C is not correct.
(D) Coagulation in both solutions can be brought about by electrophoresis.
During electrophoresis, an electric current is passed through a colloidal solution and the experiment is arranged so that only the particles can move (and no liquid medium). Hence, the statement D is correct.