This is a bit tricky question and here is the reason why : It is combining two different themes together. You have to discuss the architecture of the Delhi Sultanate period in terms of the socio-politico-economic conditions of that time.
Your answers should be based on how the conditions of that era reflected on its architecture. Points like third phase of Urbanisation in Indian history, concentration of wealth in certain pockets, rising inequalities between rulers and ruled, communal bonhomie of the time, amalgamation of two different religions into architecture should be discussed.
Perhaps the greatest artistic achievement of the Delhi sultanate was architecture. Even more than literature and music. As with the musicians, the creativity of the Muslim architects was nourished by the mature styles of both the existing Islamic and Hindu traditions. The rulers of that time brought to India the experience gained in the great buildings of other parts of the world, and they were able to draw upon the skill of Indian stonemasons. The result was a profusion of mosques, palaces, and tombs unmatched in any other Islamic country. At the same time, the architecture of that era gave us insights into the prevailing socio-economic-politico conditions.
Architecture of Delhi Sultanate period reflecting contemporary socio politico economic realities:
India witnessed third phase of Urbanisation.
Delhi, Lahore, Multan, and Lakhnauti were centers of new industries, such as metal work, paper making, and textile.
Urban centres in Bengal, Gujarat and present day Uttar Pradesh came up.
Reflects the distance between the rulers and the ruled, the despotism of the sultans:
Each monument reflects the tastes of the sultan as because of their scale each sultan tried to build according to his likes to expand his glory.
Ala-ud-din built Alai Darwaza which was majestic in scale. This reflects the despotism of the sultan and his ability to extract surplus from the peasants.
The Sultan and his nobles lived a lavish life, by owning a palace. The artisans and shopkeepers were included in the middle classes.. The rest of population lived in very small and conjusted ghettos.
The turkish rulers extracted all the agriculture surplus in their hands. This surplus had to be put to use and it happened in the form of grand monuments.
Most of the monuments were Islamic which showed the distribution of power in the urban society was in the hands of Muslims.
Expanding muslim population in India and subsequent rise of Indian muslim class was reflected in the increasing numbers of mosques and citadels owned and build by muslim population.
The trade was dominated by the Arabs, but the Tamils, the Kalingas, and Gujaratis also participated in trade. Grand Sarais (Inns) built on the trade routes by these traders, bore testimony to it.
Nobles lived a luxurious and lavish life because of their position and monetary condition. Warrior noble’s gradually transformed into patrons of culture.
Exchange of skills and traditions between Indian and Islamic architectural forms:
Iltutmish changed architectural methods. Previously material from Hindu buildings had been used for constructing mosques, but in 1230, when he extended the Quwwat-ul-Islam mosque, he used stone especially quarried for the purpose. This gave the addition a more Islamic appearance.
Not only scholars but artisans as well came to Delhi as refugees, and they found a ready market for their skills in the expanding Muslim state
One important result was that the indigenous Indian artistic element ceased to be dominant in Delhi during this period.
Islam doesn’t permit images of birds and animals so floral designs, geometric designs and calligraphy came up which was an Indian style.
Decentralisation of Political power reflected in the architecture:
In the provincial capitals, however, the influence of the refugee artisans was slight, and the indigenous styles remained important.
In Bengal the Muslim rulers decorated their buildings with carving which is obviously the work of Hindu craftsmen, and in Gujarat they adapted the local style to Muslim needs to create some of India’s most beautiful buildings.
This went against the more islamic designs of buildings in the Delhi region.
Threat of Mongol invasion:
The cities developed as Military Camps. In order to protect Delhi from the ravages of Mongols, Sultan Alauddin Khilji fortified a camp at Siri.
Personality of the ruler
Economy and Outside disturbances reflected on the architecture:
The Tughluqs in the fourteenth century introduced a new and austere phase in architecture.
Muhammad Tughluq, who shifted his capital from Delhi to Daulatabad, had no interest in the old city.
Construction of sarais reflected the continuity and ease of trade in Indian sub-continent.
The many buildings erected in Delhi during the reign of his successor Firuz show a severe simplicity, possibly due as much to the need for economy as Firuz’s own strict orthodoxy.
Under the Lodis there reemerged a vigorous and catholic spirit of design, replete with creative energy and imagination.
The explanation is probably that with the conversion of the Mongols to Islam and the reduction of chaos in Central Asia, inspiration from Persia was now available in architecture as in literature.
In architecture, as in other spheres of culture, the Indo-Islamic society was enriched by the dislocation in Central Asia and Persia caused by the Mongol invasion.
Architecture took a new direction in the Delhi Sultanate period. It was a combination of Arabic and Indian styles. The genius of both Hindu and Muslim craftsmen blended to achieve a unique genre of art and architecture during this time. There was indeed distinct character of architecture in different Sultan’s era which reflected the socio-economic-political character of the time. When society was at peace and trade was flourishing, we saw the construction of great forts and mosques while disarray in the construction activity during Sayyid Dynasty era reflected the state of affairs and instability of the time.