Compound A gives D-Galactose and D-Glucose on hydrolysis. The compound A is:

We have to identify the disaccharide that, on hydrolysis, produces $$\text{D-Galactose}$$ and $$\text{D-Glucose}$$.

First, let us recall the basic fact that hydrolysis of a disaccharide splits the glycosidic bond and gives its two monosaccharide constituents. Symbolically we can write the general reaction as $$\text{Disaccharide} + \text{H}_2\text{O} \;\xrightarrow{\text{acid / enzyme}}\; \text{Monosaccharide}_1 + \text{Monosaccharide}_2.$$

Now we list the well-known disaccharides and their hydrolysis products:

1. $$\text{Sucrose} \;(\text{C}_{12}\text{H}_{22}\text{O}_{11})$$ $$\longrightarrow$$ $$\text{D-Glucose} + \text{D-Fructose}$$

2. $$\text{Maltose} \;(\text{C}_{12}\text{H}_{22}\text{O}_{11})$$ $$\longrightarrow$$ $$\text{D-Glucose} + \text{D-Glucose}$$

3. $$\text{Lactose} \;(\text{C}_{12}\text{H}_{22}\text{O}_{11})$$ $$\longrightarrow$$ $$\text{D-Galactose} + \text{D-Glucose}$$

4. $$\text{Amylose}$$ is not a disaccharide at all; it is a linear polymer of $$\text{D-Glucose}$$ units, so its hydrolysis gives many $$\text{D-Glucose}$$ molecules and no $$\text{D-Galactose}$$.

Comparing these facts with the requirement in the question—formation of $$\text{D-Galactose}$$ and $$\text{D-Glucose}$$—we see that only the third entry fits. Thus, the compound A must be $$\text{Lactose}$$.

The option list shows that $$\text{Lactose}$$ corresponds to Option 4.

Hence, the correct answer is Option 4.