Which of the following districts was established by Firoz Shah Tughlaq?

Firoz Shah Tughlaq (r. 1351-1388 CE) is remembered as one of the Delhi Sultanate's most prolific town-founders -- chroniclers and inscriptions credit him with laying out several new fortified towns along the Delhi-Punjab military and trade corridor, distinct from settlements that already existed under earlier rulers or that were organised as districts only under later British/independent India administration.

Applying this to the options: Hisar (originally called Hisar-i-Firoza, meaning 'the fort of Firoz') was founded by Firoz Shah Tughlaq in 1354 CE as a fortified township on the Delhi-Multan route, complete with a fort, a palace, and irrigation canal works. This founding is recorded in his own memoir (Futuhat-i-Firoz Shahi) and is confirmed by the present-day Hisar district's own official history.

• Mewat (the historical Meo region, today's Nuh district): an older region with its own separate medieval history; it was not founded by Firoz Shah Tughlaq, and the modern district itself was carved out only in 2005.

• Jhajjar: its identity as a district comes from a later administrative reorganisation, not from a 14th-century Tughlaq foundation.

• Mahendragarh: likewise organised as a district only in the modern period; no Tughlaq-era founding is attested for it.

Among the four districts offered, only Hisar has a directly attested Firoz Shah Tughlaq-era founding, so Hisar is the correct answer.