(a) Due to lanthanoid contraction, the size of Lu3+ is smaller than that of La3+ ion. Thus, Lu-OH bond is stronger than La-OH bond. Hence, La(OH)3 is stronger base than Lu(OH)3.
(b) This is due to comparable energies of 5f,6d and 7s orbital in actinoids
(c) This is due to poor shielding effect by 5f electrons in actinoid as compared to that by 4f electron in the lanthanoids.