Choose the incorrect statement among the following:
A. The chemistry of different lanthanides are very similar.
B. $4\,{\text{f}} - $ and $5{\text{f}} - $orbitals are equally shielded.
C. d-block elements show irregular and erratic chemical properties among themselves.
D. La and Lu have partially filled d-orbitals.

Hint: Lanthanides have deeply buried f-orbitals. $4\,{\text{f}} - $ orbitals are more attracted to the nucleus than $5{\text{f}} - $ orbitals. Elements of d-block do not have deep-buried valence orbitals. The atomic number of La and Lu is 57 and 79 respectively.

Complete answer:
The valence orbitals that is $4\,{\text{f}} - $ orbitals, are deep buried so, they are not affected by the ligand field, so, all lanthanides show a few oxidation states, basicity, sharp electronic spectra, etc. so, the statement that the chemistry of different lanthanides is very similar, is true. So, option (A) is incorrect.
$4\,{\text{f}} - $ orbital is closer to the nucleus than the $5{\text{f}} - $ orbitals so, electrons in $4\,{\text{f}} - $ orbital feel more attraction so, $4\,{\text{f}} - $ orbital has more density of electrons than $5{\text{f}} - $ orbitals so, $4\,{\text{f}} - $ orbital has high shielding power than $5{\text{f}} - $ orbitals. So, the statement that $4\,{\text{f}} - $ and $5{\text{f}} - $ orbitals are equally shielded, is incorrect. So, option (B) is correct.
d-block elements are known as inner transition elements because they lie in between metals and non-metals so, their shows irregular properties also the valence orbitals that are d-orbitals, are of not deeply buried so, they get affected by ligand field. So, they show variation in properties such as magnetic and electronic spectra, oxidation states etc.so, the statement that d-block elements show irregular and erratic chemical properties among themselves, is true. So, option (C) is incorrect.
The electronic configuration of La and Lu is as follows:
${\text{La}}\, = \,\left[ {{\text{Xe}}} \right]{\text{6}}{{\text{s}}^{\text{2}}}{\text{5}}{{\text{d}}^{\text{1}}}$
${\text{Lu}}\, = \,\left[ {{\text{Xe}}} \right]{\text{6}}{{\text{s}}^{\text{2}}}{\text{4}}{{\text{f}}^{14}}{\text{5}}{{\text{d}}^{\text{1}}}$
So, the statement that La and Lu have partially filled d-orbitals, is true. So, option (D) is incorrect.

Therefore option (B) $4\,{\text{f}} - $ and $5{\text{f}} - $ orbitals are equally shielded, is correct.

Note: All lanthanides have lower energy valence shells whereas the actinides have higher energy valence shells, so all lanthanides show similar physical and chemical properties whereas all actinides show variation in physical and chemical properties.