Step 1: Understanding the Question:
Evaluate statements about the color (due to d-d transitions) and magnetic property (diamagnetic vs paramagnetic) of various d-block and f-block ions.
Step 2: Detailed Explanation:
Evaluating Statement-I (Color):
Ions are coloured if they have partially filled d-orbitals ($d^1$ to $d^9$).
1. $Cr^{+3} (d^3)$, $Mn^{+2} (d^5)$ : Both have unpaired electrons, both coloured.
2. $Ti^{+4} (d^0)$, $V^{+2} (d^3)$ : $Ti^{+4}$ is colourless ($d^0$), $V^{+2}$ is coloured.
3. $Sc^{+3} (d^0)$, $V^{+4} (d^1)$ : $Sc^{+3}$ is colourless ($d^0$), $V^{+4}$ is coloured.
4. $Co^{+3} (d^6)$, $Cu^{+2} (d^9)$ : Both have unpaired electrons, both coloured.
Only two sets have both ions coloured. Statement-I says "three sets", hence it is incorrect.
Evaluating Statement-II (Magnetism):
Ions are diamagnetic if they have no unpaired electrons ($f^0$ or $f^{14}$).
1. $Lu^{+3} (f^{14})$, $La^{+3} (f^0)$ : Both diamagnetic.
2. $Lr^{+3} (f^{14})$, $Ce^{+4} (f^0)$ : Both diamagnetic.
3. $Yb^{+2} (f^{14})$, $Eu^{+2} (f^7)$ : $Eu^{+2}$ is paramagnetic (7 unpaired electrons).
4. $Nd^{+3} (f^3)$, $Sm^{+3} (f^5)$ : Both are paramagnetic.
Only two sets have both ions diamagnetic. Statement-II says "three sets", hence it is incorrect.
Step 3: Final Answer:
Both Statement I and Statement II are incorrect.