For Statement I:
The electronic configurations of the given transition metal ions are:
Ti4+:3d0 (colourless due to absence of unpaired electrons)
V2+:3d3 (coloured)
Mn2+:3d5 (coloured)
Fe3+:3d5 (coloured)
Cr2+:3d4 (coloured)
The pairs in which both ions are coloured are [V2+,Mn2+], [Mn2+,Fe3+], and [V2+,Cr2+]. The pair [Ti4+,V2+] contains Ti4+ which is colourless. Thus, there are exactly 3 pairs where both ions are coloured. Statement I is correct.
For Statement II:
The electronic configurations of the given f-block ions are:
La3+:[Xe]4f0 (diamagnetic)
Yb2+:[Xe]4f14 (diamagnetic)
Lu3+:[Xe]4f14 (diamagnetic)
Ce4+:[Xe]4f0 (diamagnetic)
Ac3+:[Rn]5f0 (diamagnetic)
Lr3+:[Rn]5f14 (diamagnetic)
All the given ions have either an f0 or f14 configuration, meaning they have no unpaired electrons and are diamagnetic. Therefore, in all 3 pairs, both ions are diamagnetic. Statement II is correct.
Both Statement I and Statement II are correct.
Answer: Both Statement I and Statement II are correct