Use known trend in transition metals

In each transition series, the melting point generally increases up to the middle due to strong metallic bonding and then decreases.

The given pairs are neighboring elements in groups 7 and 8 of the 3d, 4d, and 5d series:

• $(\text{Mn}, \text{Fe})$
• $(\text{Tc}, \text{Ru})$
• $(\text{Re}, \text{Os})$

Compare Mn and Fe

• Manganese has anomalously lower melting point because of its half-filled $3d^5 4s^2$ configuration and relatively weaker metallic bonding.
• Iron has stronger metallic bonding than Mn.

Therefore, $\text{Mn} < \text{Fe}$

Compare Tc and Ru

• In the $4d$ series, ruthenium lies closer to the peak of metallic bonding strength.
• Hence Ru has a higher melting point than Tc.

Therefore, $\text{Tc} < \text{Ru}$

Compare Re and Os

• In the $5d$ series, osmium has one of the highest melting points among transition metals.
• Thus Os has a higher melting point than Re.

Therefore, $\text{Re} < \text{Os}$

Match with the options

We obtained: $\text{Mn} < \text{Fe}, \quad \text{Tc} < \text{Ru}, \quad \text{Re} < \text{Os}$

This corresponds to Option C.

Quick numerical check with approximate melting points

• $\text{Mn} \approx 1246^\circ \text{C}$, $\text{Fe} \approx 1538^\circ \text{C}$
• $\text{Tc} \approx 2157^\circ \text{C}$, $\text{Ru} \approx 2334^\circ \text{C}$
• $\text{Re} \approx 3186^\circ \text{C}$, $\text{Os} \approx 3033^\circ \text{C}$

The first two comparisons confirm: $\text{Mn} < \text{Fe}, \quad \text{Tc} < \text{Ru}$

But for the third pair, $\text{Os} < \text{Re}$

So the actual full order is: $\text{Mn} < \text{Fe}, \quad \text{Tc} < \text{Ru}, \quad \text{Os} < \text{Re}$

Hence Option D is correct.

Conclusion

The correct option is: $\boxed{\text{D}}$