Akbar constructed 'Ibadat-Khana' in

The Ibadat-Khana ('House of Worship') was a structure Akbar built specifically to host formal religious and philosophical debates among scholars of different faiths, reflecting his broader project of religious tolerance and syncretism during his reign.

Akbar founded a new capital city in 1571 to commemorate the birth of his son and the blessing of the Sufi saint Shaikh Salim Chishti, and it was within this new capital — Fatehpur Sikri — that he constructed the Ibadat-Khana around 1575. Initially open only to Muslim theologians, its membership was later widened to include Hindus, Jains, Zoroastrians, and Christians, and the resulting debates contributed to the development of Akbar's later syncretic religious order, Din-i-Ilahi.

• Delhi: an important Mughal-era city under other rulers, but not the site Akbar chose for the Ibadat-Khana.

• Sikandara: the location of Akbar's mausoleum — begun in his lifetime and completed by Jahangir after his death — a burial site, not a debate hall built during his reign.

• Agra: an earlier Mughal seat, but the Ibadat-Khana belongs to the later capital Akbar founded, not to Agra.

Hence, among the offered options, Fatehpur Sikri is the city where Akbar constructed the Ibadat-Khana.