Given below are two statements:
Statement I : None of the alkaline earth metal hydroxides dissolve in alkali.
Statement II : Solubility of alkaline earth metal hydroxides in water increases down the group.
In the light of the above statements, choose the most appropriate answer from the options given below:

We begin by recalling that the hydroxides of the alkaline-earth metals have the general formula $$M(OH)_2,$$ where $$M$$ stands for $$\mathrm{Be,\,Mg,\,Ca,\,Sr,\,Ba}.$$

The first point concerns their behaviour toward a concentrated external base (alkali). A hydroxide will dissolve in an alkali only if it is amphoteric, i.e. if it can react further with hydroxide ion $$\mathrm{OH^-}$$ to give a complex anion. The relevant amphoteric equilibrium is stated here:

$$M(OH)_2(s)+2\,\mathrm{OH^-}(aq)\;\rightleftharpoons\;[M(OH)_4]^{2-}(aq).$$

Experimentally, only $$\mathrm{Be(OH)_2}$$ is sufficiently amphoteric to undergo this reaction. The other hydroxides - $$\mathrm{Mg(OH)_2},\,\mathrm{Ca(OH)_2},\,\mathrm{Sr(OH)_2},\,\mathrm{Ba(OH)_2}$$ - are purely basic; they do not form the above complex and therefore do not dissolve in excess alkali. Hence the blanket statement “None of the alkaline-earth metal hydroxides dissolve in alkali” is false because $$\mathrm{Be(OH)_2}$$ is a clear counter-example.

Next we discuss the solubility of these hydroxides in water. Lattice energy ($$U_L$$) decreases more rapidly than hydration energy ($$H_h$$) when we go down the group, because the cationic radius increases markedly while the anionic radius (that of $$\mathrm{OH^-}$$) remains constant. The condition for dissolution is stated as

$$\lvert H_h\rvert \; >\; U_L.$$

As $$U_L$$ falls down the group, this inequality becomes progressively easier to satisfy, causing solubility to rise in the order

$$\mathrm{Be(OH)_2}<\mathrm{Mg(OH)_2}<\mathrm{Ca(OH)_2}<\mathrm{Sr(OH)_2}<\mathrm{Ba(OH)_2}.$$

Therefore the statement “Solubility of alkaline earth metal hydroxides in water increases down the group” is true.

Summarising, Statement I is incorrect whereas Statement II is correct. This matches Option B in the given list.

Hence, the correct answer is Option B.