The Dhar Commission, established in 1948, had the mandate of recommending whether the States in India could be reorganized on a linguistic basis. This means that the commission was tasked with studying and evaluating the feasibility and implications of restructuring States based on the languages spoken by the people in those regions.

Option 1, which suggests that the commission was appointed to study the classification of States, is not the correct mandate of the Dhar Commission. The focus of the commission was on linguistic reorganization, not the classification of States.

Option 3, which states that the commission was meant to study Centre-State relations, is also not the correct mandate. Although Centre-State relations may have been a relevant aspect of the commission`s work, it was not the primary focus or mandate.

Option 4, which suggests that the commission examined the possibility of transferring Madras city to Andhra, is not the correct mandate either. The Dhar Commission`s mandate was to recommend on the reorganization of States based on linguistic considerations, not on specific territorial transfers.

In summary, the correct mandate of the Dhar Commission was to recommend whether the States could be reorganized on a linguistic basis.