Correct option is A
(B) Jam'at-Khanah Masjid : The Jamaat Khana Masjid, also known as the Khilji Mosque, is Delhi's oldest functioning mosque, built between 1315 and 1325 by Khizr Khan. It is the largest structure within the Nizamuddin Basti Dargah enclosure, which is also the Nizam-ud-Din Auliya Shrine Complex. The mosque is the main mosque of the Dargah Hazrat Nizamuddin.
(C) Begumpuri Masjid: The Begumpur Mosque also known as the Jam'i Masjid of Jahanpanah, is a former Friday mosque, now in partial ruins, located in an urban village called Begumpur, which now bears its modern name, Jahanpanah. The former mosque was built in the centre of the sultanate capital of the Tughluq dynasty, in c. 1343 CE. The former mosque is large, measuring 94 by 90 metres (307 by 295 ft). Jahanpanah means "the centre of the world," and the village was built by the order of Muhammad bin Tughluq in 1327 CE.
(D) Khidki Masjid (constructed in 1360): The mosque was built by Khan-i-Jahan Junan Shah, the prime minister of Feroz Shah Tughlaq (1351–1388) of the Tughlaq Dynasty.
(A) Moth-Ki-Masjid (constructed in 1500 by Muhammad Ghazi Shahid): The mosque was built in 1505 by Wazir Miya Bhoiya, Prime Minister during the reign of Sikander Lodi of the Lodi dynasty. It was a new type of mosque developed by the Lodis in the fourth city of the medieval Delhi Sultanate. This mosque was considered a beautiful domed (gumbad) structure of the period.