At which of the following ancient centres of learning did the grammarian…

Concept

Questions about ancient centres of learning are solved by matching a scholar with the institution consistently linked to that scholar in historical and educational accounts.

Chronology is a useful control: an institution that arose centuries after a scholar cannot be the place where that scholar studied.

Application

Panini, the author of the Ashtadhyayi and a major grammarian of ancient India, is traditionally listed among the noted pupils of Takshashila. Therefore, the scholar–institution association required here is Panini–Takshashila.

Contrast

• Nalanda became a major monastic university in Magadha in a considerably later period.

• Sridhanya Katak (Dhanyakataka) is remembered as a Buddhist learning centre in the Andhra region, especially in later Buddhist traditions.

• Odantapuri was a Buddhist monastic centre in Bihar that developed under the Pala rulers, much later than Panini.

Cross-check

The chronology supports the documented association: Nalanda and Odantapuri belong to later institutional traditions, while Takshashila was already an established centre in the north-western region associated with Panini.

Hence, the answer is Takshashila.