The correct IUPAC nomenclature for the following compound is:

The molecule contains:

$$-COOH$$ and $$C=O$$ functional groups.

According to IUPAC priority rules, the carboxylic acid has higher priority and is taken as the principal functional group.

Hence the suffix used is: $$\text{-oic acid}$$

The longest carbon chain containing the carboxylic acid group has:

$$6 \text{ carbon atoms}$$

Therefore the parent chain is: $$\text{hexanoic acid}$$

Numbering starts from the carboxylic acid carbon.

Thus:

$$C1 : COOH$$

$$C2 : CH \text{ carrying a methyl group}$$

$$C3 : CH_2$$

$$C4 : CH_2$$

$$C5 : C=O$$

$$C6 : CH_3$$

The substituents present are:

A methyl group at:

$$C2$$ and a ketone group represented by the prefix: $$\text{oxo-}$$ at: $$C5$$

Combining all parts of the name:

$${\text{2-methyl-5-oxohexanoic acid}}$$
Hence, Option A is correct