Most basic hydroxide among the following is

Due to lanthanide contraction, the size of $M^{3+}$ ions [ie, $\mathrm{Lu}^{3+}, \mathrm{Eu}^{3+}, \mathrm{Yb}^{3+}$ and $\mathrm{Ce}^{3+}$ ] decreases and thus, the basic strength of their hydroxides decreases. The order of size of given $M^{3+}$ ions is $\mathrm{Ce}^{3+}>\mathrm{Eu}^{3+}>\mathrm{Yb}^{3+}>\mathrm{Lu}^{3+}$ $\therefore$ The order of basic strength of hydroxides is $\mathrm{Ce}(\mathrm{OH})_{3}>\mathrm{Eu}(\mathrm{OH})_{3}>\mathrm{Yb}(\mathrm{OH})_{3}>\mathrm{Lu}(\mathrm{OH})_{3}$ (most basic)