To solve the question, we need to compare the atomic properties of beryllium and boron in terms of nuclear charge and first ionisation enthalpy.
Based on these properties, in comparison to boron, beryllium has a lesser nuclear charge because it has fewer protons. However, beryllium has a greater first ionisation enthalpy due to its filled 2s orbital configuration making its electrons harder to remove.
Therefore, the correct answer is: lesser nuclear charge and greater first ionisation enthalpy.
In general, the properties that decrease and increase down a group in the periodic table respectively are: