Which statements are correct about lactose?

Options

A. `(C_(1)-beta)(OH)` of glucose is linked with `(C_(4)-OH)` of galactose.
B. `(C_(1)-beta)-(OH)` of galactose is linked with `(C_(4)-OH)` of `beta`-glucose.
C. It is hydrolysed both by amylase and lactase.
D. It exhibits mutarotation.

Explanation

To determine which statements are correct about lactose, we will analyze the structure of lactose and the properties associated with it.

### Step-by-Step Solution:

1. **Understanding the Structure of Lactose**:
- Lactose is a disaccharide composed of two monosaccharides: beta-D-galactose and D-glucose.
- The linkage between these two sugars occurs between the first carbon (C1) of beta-D-galactose and the fourth carbon (C4) of D-glucose.

2. **Identifying the Glycosidic Linkage**:
- The glycosidic bond formed in lactose is a beta (β) linkage. Specifically, it is a β(1→4) glycosidic bond.
- This means that the hydroxyl group (OH) on the C1 of galactose is in the beta configuration and is linked to the C4 of glucose.

3. **Analyzing Hydrolysis**:
- Hydrolysis of lactose can occur through the action of the enzyme lactase, which specifically breaks down the β-glycosidic bond.
- Amylase, on the other hand, is an enzyme that hydrolyzes alpha (α) glycosidic bonds and is not effective for lactose.

4. **Mutarotation**:
- Mutarotation refers to the change in optical rotation due to the conversion between different anomeric forms of a sugar.
- In lactose, the glucose part can undergo mutarotation because it has a hemiacetal linkage at its C1 position, allowing it to interconvert between its alpha and beta forms.

5. **Conclusion**:
- Based on the analysis:
- Statement regarding the linkage between galactose and glucose (C1 of galactose and C4 of glucose) is correct.
- Statement about hydrolysis by amylase and lactase is incorrect since lactase is the enzyme that acts on lactose.
- Statement about mutarotation is correct due to the presence of the hemiacetal linkage in glucose.

### Final Answer:
The correct statements about lactose are:
- The linkage between beta C1 of galactose and C4 of glucose is correct.
- The hydrolysis by amylase and lactase is incorrect.
- Mutarotation is possible due to the hemiacetal linkage in glucose.

Thus, the correct options are **b and d**.