Given below are two statements :
Statement (I) : The first ionisation enthalpy of group 14 elements is higher than the corresponding elements of group 13.
Statement (II) : Melting points and boiling points of group 13 elements are in general much higher than those the corresponding elements of group 14.
In the light of the above statements, choose the most appropriate answer from the options given below :

In each period, the electronic configuration of a group 13 element ends with $$ns^{2}np^{1}$$ whereas that of the adjacent group 14 element ends with $$ns^{2}np^{2}$$.

Because the group 14 atom has one more proton and one more valence-shell electron, its effective nuclear charge ($$Z_{\text{eff}}$$) is higher. A higher $$Z_{\text{eff}}$$ holds the outermost electrons more strongly, so more energy is required to remove the first electron.

Observed first-ionisation enthalpies (in $$\text{kJ mol}^{-1}$$) confirm this:
B 800 < C 1086  Al 577 < Si 786  Ga 579 < Ge 762  In 558 < Sn 709  Tl 589 < Pb 716

Thus, the first ionisation enthalpy of a group 14 element is indeed higher than that of the corresponding group 13 element. Statement I is correct.

Melting and boiling points depend mainly on the type and strength of bonding present. From group 13 to group 14 the bonding becomes more covalent and the lattice (or giant covalent network) becomes much stronger.

Typical melting points (in °C) and boiling points (in °C):
B 2300 / 2550  C 3550 / 4027  Al 660 / 2467  Si 1414 / 3265  Ga 30 / 2403  Ge 938 / 2830  In 156 / 2080  Sn 232 / 2600  Tl 304 / 1473  Pb 327 / 1749

For every pair, the group 14 element has the higher melting and boiling points. Therefore Statement II is incorrect.

Conclusion: Statement I is correct while Statement II is incorrect. Hence the correct option is Option A.