Concept:
Lanthanoid contraction refers to the gradual decrease in atomic and ionic radii across the lanthanoid series due to poor shielding by 4f electrons.
Step 1: Examine Statement-I carefully.
Because of lanthanoid contraction, the size of 5d elements becomes nearly equal to that of corresponding 4d elements.
Examples:
\[
Zr \approx Hf
\]
\[
Nb \approx Ta
\]
Thus Statement-I is correct.
Step 2: Examine Statement-II carefully.
Actinoids show a larger number of oxidation states because 5f, 6d and 7s orbitals have comparable energies.
Examples:
\[
U(+3,+4,+5,+6)
\]
\[
Np(+3,+4,+5,+6,+7)
\]
\[
Pu(+3,+4,+5,+6,+7)
\]
Lanthanoids predominantly show
\[
+3
\]
oxidation state with only a few exceptions.
Therefore actinoids exhibit more variable oxidation states than lanthanoids.
\[
\text{Statement-II is false}
\]
Step 3: Final conclusion.
Statement-I is true.
Statement-II is false.
Hence the correct option is
\[
\boxed{\text{Statement I is correct but Statement II is not correct}}
\]