(d)
A) There is gradual decrease in the radii of the lanthanoids with increasing atomic number-a case of lanthanide contraction, thus true.
B) Ionization potential for the formation of ${Lu}^{3 +}$ is comparatively low, hence +3 state is favourable, thus true.
C) Due to lanthanide contraction $-$Zr and Hf; Nb and Ta, Mo and W have the same size and thus similar propertites and thus separation is not easy , thus true.
D) Formation of +4 state requires very high energy, thus incorrect.