Step 1: Concept
Identify the structure of each alcohol and categorize the -OH groups based on the carbon they are attached to.
Step 2: Meaning
Glycerol (Propane-1,2,3-triol) structure is $CH_2(OH)-CH(OH)-CH_2(OH)$.
Step 3: Analysis
The two end carbons are primary ($1^\circ$), and the middle carbon is secondary ($2^\circ$).
Step 4: Conclusion
Glycerol contains exactly two primary and one secondary alcoholic groups.
Final Answer: (D)