(a) Hydrolysis of lactose
Lactose is a disaccharide, so it gives two monosaccharide units :
$$\underset{\text{lactose}}{C_{12}H_{22}O_{11}} + H_2O \xrightarrow{\text{lactase}} \underset{\text{galactose}}{C_6H_{12}O_6} + \underset{\text{glucose}}{C_6H_{12}O_6}$$
Products : $\beta$-D-galactose and $\beta$-D-glucose
Structure note : the two units are joined by a $\beta$-1,4-glycosidic linkage between C-1 of galactose and C-4 of glucose.
Why lactose is a reducing sugar : the glucose unit keeps a free anomeric carbon at C-1, so a potential aldehyde group remains and the sugar reduces Tollens' and Fehling's reagents.
Lactose is the sugar of milk, which is why it is also called milk sugar.
(b) Hydrolysis of a DNA nucleotide containing thymine
A nucleotide has three components, and complete hydrolysis releases all three :
$$\text{Nucleotide} + H_2O \rightarrow \text{Thymine} + \beta\text{-D-2-deoxyribose} + \text{Phosphoric acid}$$
The three products are :
- Thymine — the nitrogenous base
- $\beta$-D-2-deoxyribose — the pentose sugar. Note the deoxy, since this is DNA and the sugar has no $-OH$ at C-2
- Phosphoric acid, $H_3PO_4$
Partial hydrolysis would stop at the nucleoside (thymidine) plus phosphoric acid :
$$\text{Nucleotide} \rightarrow \text{Nucleoside} + H_3PO_4$$
A point worth noting : if the question had said RNA, two of the three answers would change — the sugar would be $\beta$-D-ribose and the base would be uracil instead of thymine.