Four sols are available: P ($\mathrm{As}{}_2\mathrm{S}{}_3$), Q ($\mathrm{Fe}(\mathrm{OH}){}_3$), R (gold) and S ($\mathrm{Al}(\mathrm{OH}){}_3$). Which of the following pairs, when mixed in suitable proportions, show mutual coagulation?

$\mathrm{As}{}_2\mathrm{S}{}_3$ and gold sols are negative, while $\mathrm{Fe}(\mathrm{OH}){}_3$ and $\mathrm{Al}(\mathrm{OH}){}_3$ sols are positive. Mutual coagulation needs oppositely charged sols, giving P+Q and R+S. P+R are both negative and Q+S both positive, so there is no mutual coagulation.