Step 1: Structure of glucose.
Glucose is an aldohexose with the molecular formula C$_6$H$_{12}$O$_6$. Its open-chain structure is:
\[
HOCH_2 – (CHOH)_4 – CHO
\]
Step 2: Identify alcoholic groups.
- The four middle carbons each have a hydroxyl (–OH) group, making them secondary alcohols.
- The terminal –CH$_2$OH group at C-6 is a primary alcoholic group.
Step 3: Conclusion.
Thus, glucose has only one primary alcoholic group (at carbon-6).
Final Answer:
\[
\boxed{\text{(A) One}}
\]