Step 1: Concept
DNA contains deoxyribose sugar.
Step 2: Meaning
"Deoxy" indicates the loss of an oxygen atom compared to ribose.
Step 3: Analysis
- In DNA, the hydroxyl group at the second carbon position ($C_2^{\prime}$) is replaced by a hydrogen atom.
Step 4: Conclusion
Hence, the $C_2^{\prime}$ carbon lacks the oxygen.
Final Answer: (B)