Which compound does not dissolve in hot dilute $HNO_3$?

Solid $Ba(NO_3)_2$ is gradually dissolved in $1 \times 10^{-4} \ M \ Na_2CO_3$ solution. At what concentration of $Ba^{+2}$ will the precipitation of $BaCO_3$ start? (Given: $K_{sp}$ of $BaCO_3 = 5.1 \times 10^{-9}$)

The $K_{sp}$ of $AgI$ is $1.5 \times 10^{-16}$. Which of the following mixtures of equal volumes will result in precipitation?

The solubility of $PbI_2$ at $25\,^{\circ}C$ is $0.7\, g\, L^{-1}$. The solubility product of $PbI_2$ at this temperature is (molar mass of $PbI_2 = 461.2\, g\, mol^{-1}$)

The molar solubility of a sparingly soluble salt $MX_4$ is $s \ mol \ L^{-1}$. If the solubility product is $K_{sp}$,then $s$ in terms of $K_{sp}$ is:

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