The depression in the freezing point of  $0.01 \mathrm{m}$ aqueous solution of urea, sodium chloride and sodium sulphate are in the ratio of

We know that Depression in freezing point is given by the relation:

$\Delta T_f=i\times k_f\times m$

$\Delta T_f=$ Depression in freezing point

$\mathrm{i}=$ Van'T Hoff factor

$k_f=$ freezing point constant

$\mathrm{m}=$ molality

Here, depression in freezing point is determined by Van't Hoff factor as molality is same for all solutions.

So,

$1.$ For $0.01\mathrm{m}$ $\mathrm{urea}$

$\mathrm{i}=1$  as it is a non-electrolyte and does not dissociate.

2. For $0.01\mathrm{m} \mathrm{NaCl}$

$\mathrm{NaCl}\to {\mathrm{Na}}^{+}+{\mathrm{Cl}}^{-}$

$\mathrm{i}=2$  as it is an electrolyte and dissociate to give 2 ions.

3. For  $0.01\mathrm{m}$  ${\mathrm{Na}}_2{\mathrm{SO}}_4$

${\mathrm{Na}}_2{\mathrm{SO}}_4\to 2{\mathrm{Na}}^{+}+{\mathrm{SO}}_4^{2-}$

$\mathrm{i}=3$ as it is an electrolyte and dissociate to give 3 ions.

 As Van't Hoff factor for$\mathrm{urea}:$$\mathrm{NaCl}:{\mathrm{Na}}_2{\mathrm{SO}}_4$ is in the ratio of $1: 2: 3$.

Thus, the depression in the freezing point will have also the ratio of $1: 2: 3.$

Hence, option(b) is correct.