The solubility of $CaCO_3$ in water is $3.05 \times 10^{-4} \, mol/L$. Its solubility product will be:

If $K_{sp}$ of $CaF_2$ at $25\,^{\circ}C$ is $1.7 \times 10^{-10}$,the combination amongst the following which gives a precipitate of $CaF_2$ is

Assertion : $BaCO_3$ is more soluble in $HNO_3$ than in plain water.
Reason : Carbonate is a weak base and reacts with the $H^+$ from the strong acid,causing the barium salt to dissociate.

Precipitation occurs if the ionic product is ........

$A$ solution which is $10^{-3} \ M$ each in $Mn^{2+}, Fe^{2+}, Zn^{2+},$ and $Hg^{2+}$ is treated with $10^{-16} \ M$ sulphide ion. If $K_{sp}$ of $MnS, FeS, ZnS,$ and $HgS$ are $10^{-15}, 10^{-23}, 10^{-20},$ and $10^{-54}$ respectively,which one will precipitate first?

When equal volumes of the following solutions are mixed,precipitation of $AgCl$ $(K_{sp} = 1.8 \times 10^{-10})$ will occur only with: