The correct options are
A Lu(OH)3 is less basic than La(OH)3
B In lanthanide series, ionic radius of La3+−Ln3+ ion increases
Lu(OH)3 is less basic than La(OH)3.
Due to lanthanoid contraction, the size of the tripositive lanthanoid ion regularly decreases with increase in the atomic number from La3+ to Lu3+. This decreases the basic character.