Concept:
- Sucrose is non-reducing because the anomeric carbon of each monosaccharide is used in the glycosidic bond.
- Finding those two anomeric carbons identifies the linkage positions.
Step 1: Identify the two monosaccharide units.
Sucrose contains $\alpha$-D-glucose and $\beta$-D-fructose.
Step 2: Locate each anomeric carbon.
The anomeric carbon of glucose is $C_1$.
Because fructose is a ketose, its anomeric carbon is $C_2$.
Step 3: Join the two anomeric centres.
The glycosidic oxygen connects glucose $C_1$ to fructose $C_2$. Since both anomeric groups are tied up, sucrose has no free reducing end.
Final Answer: $C_1-C_2$ glycosidic linkage, option B.