Step 1: Analyze Statement I.
Boron is a hard solid with strong covalent bonding in its crystal structure.
Due to these strong bonds, boron possesses a very high melting point.
Hence, Statement I is correct.
Step 2: Analyze Statement II.
Boron is actually a low-density element compared to many metals.
It is not known for high density.
Hence, Statement II is incorrect.
Step 3: Analyze Statement III.
Pure boron is not a good conductor of electricity at ordinary temperature.
It behaves more like a semiconductor rather than a highly conducting metal.
Hence, Statement III is incorrect.
Step 4: Analyze Statement IV.
The isotope \(^{10}B\) has a very high neutron absorption capacity.
Because of this property, boron is used in nuclear reactors as a control rod material.
Hence, Statement IV is correct.
Step 5: Determine the correct combination.
The correct statements are
I and IV only
Step 6: Final conclusion.
Hence, the correct answer is
\[
\boxed{\text{I, IV only}}
\]