Concept:
Bond length is inversely proportional to bond order, and hybridisation depends on the steric number (number of sigma bonds + lone pairs on atom).
Step 1: Check Statement I (O–O bond lengths).
Bond orders:
\[
O_2 = 2,\quad O_3 = 1.5,\quad H_2O_2 = 1
\]
Since bond length \( \propto \frac{1}{\text{bond order}} \),
\[
\text{Bond length order: } H_2O_2 > O_3 > O_2
\]
So Statement I is correct.
---
Step 2: Check Statement II (hybridisation).
• In graphite, each carbon is \(sp^2\) hybridised (three \(\sigma\)-bonds in hexagonal planar structure).
• In pyridine, each ring carbon is also \(sp^2\) hybridised (aromatic system with trigonal planar geometry).
Thus, hybridisation of carbon in both is the same:
\[
sp^2
\]
So Statement II is correct.
---
Step 3: Conclusion.
Both statements are correct:
\[
\boxed{\text{(A) Both statements I and II are correct}}
\]
---