Correct option is : (2) \(\mathrm{HgS}<\mathrm{PbS}<\mathrm{AgBr}<\mathrm{Ca}(\mathrm{OH})_{2}\)
Based on the Ksp values and salt analysis cation identification, we can say that order of Ksp value is:
\(\mathrm{HgS}<\mathrm{PbS}<\mathrm{AgBr}<\mathrm{Ca}(\mathrm{OH})_{2}\)
Ksp values
\(\mathrm{HgS} \rightarrow 4 \times 10^{-53}\)
\(\mathrm{PbS} \rightarrow 8 \times 10^{-28}\)
\(\mathrm{AgBr} \rightarrow 5 \times 10^{-13}\)
\(\mathrm{Ca}(\mathrm{OH})_{2} \rightarrow 5.5 \times 10^{-6}\)