Arrange the following in increasing order of solubility product
Ca(OH)₂, AgBr, PbS, HgS

Based on the Ksp values and salt analysis cation identification, we can say that order of Ksp value is:
HgS < PbS < AgBr < Ca(OH)₂
Ksp values
$\begin{array}{rl} & \mathrm{HgS}\to 4\times {10}^{-53}\\ & \mathrm{PbS}\to 8\times {10}^{-28}\\ & \mathrm{AgBr}\to 5\times {10}^{-13}\\ & \mathrm{Ca}(\mathrm{OH}{)}_2\to 5.5\times {10}^{-6}\end{array}$