Which of the following compounds are partially soluble or insoluble in $NH_4OH$ solution?
$(I)$ $Fe(OH)_3$
$(II)$ $Ag_2CrO_4$
$(III)$ $Al(OH)_3$
$(IV)$ $Ag_2CO_3$

If $pK_{a} = -\log K_{a} = 4$ for a weak acid $HX$ and $K_{a} = C\alpha^{2}$,then the Van't Hoff factor when $C = 0.01 \ M$ is

Blue litmus turns red in the following mixture of acid and base:

When $100 \ mL$ of $0.1 \ M$ $NaCN$ solution is titrated with $0.1 \ M$ $HCl$ solution,the variation of $pH$ of the solution with the volume of $HCl$ added will be:

At $25\, ^oC$,the dissociation constant of $CH_3COOH$ and $NH_4OH$ in aqueous solution are almost the same. The $pH$ of a $0.01\, N$ $CH_3COOH$ solution is $4.0$ at $25\, ^oC$. The $pH$ of a $0.01\, N$ $NH_4OH$ solution at the same temperature would be:

$A$ solution of $0.1 \ M$ weak base $(B)$ is titrated with $0.1 \ M$ of a strong acid $(HA)$. The variation of $pH$ of the solution with the volume of $HA$ added is shown in the figure below. What is the $pK_{b}$ of the base? The neutralization reaction is given by $B + HA \rightarrow BH^{+} + A^{-}$.