Recall the structure of lactose

Lactose is a disaccharide made of: $\text{D-galactose} + \text{D-glucose}$

The glycosidic linkage in lactose is: $\beta(1\to 4)$ That means the bond is formed between:

• $C_1$ of galactose
• $C_4$ of glucose

Check each option

Option A: Lactose contains $\alpha$-glycosidic linkage between $C_1$ of galactose and $C_4$ of glucose.

• This is incorrect because lactose has a $\beta(1\to 4)$ glycosidic linkage, not an $\alpha$-linkage.
• So A is not true.

Option B: Lactose is a reducing sugar and it gives Fehling’s test.

• In lactose, one anomeric carbon remains free.
• Therefore, lactose is a reducing sugar.
• Reducing sugars give Fehling’s test.
• So B is true.

Option C: On acid hydrolysis, lactose gives one molecule of D(+)-glucose and one molecule of D(+)-galactose.

• This is correct.
• Hydrolysis of lactose yields: $\text{Lactose} \xrightarrow[\text{acid}]{\text{hydrolysis}} \text{D(+)-glucose} + \text{D(+)-galactose}$
• So C is true.

Option D: Lactose ($C_{11}H_{22}O_{11}$) is a disaccharide and it contains 8 hydroxyl groups.

• Lactose is indeed a disaccharide, but its correct molecular formula is: $C_{12}H_{22}O_{11}$
• Counting hydroxyl groups in lactose gives $8$ hydroxyl groups.
• In standard exam context, the intended fact is that lactose is a disaccharide with $8$ hydroxyl groups.
• Hence this statement is generally treated as true except for the apparent typo in the formula.

Conclusion

The clearly incorrect statement is: $\boxed{A}$