Among the leaders mentioned, the one who did not believe in the drain theory of Dadabhai Naoroji was Sir Syed Ahmed Khan (Option 4).

Dadabhai Naoroji, a prominent Indian political leader and social reformer, propounded the "drain theory" in the late 19th century. According to this theory, India was being drained of its wealth by the British colonial rule through the systematic transfer of resources and capital from India to Britain. Naoroji argued that the economic exploitation of India by the British was a significant cause of India`s impoverishment.

Now, let`s analyze the other options to understand why Sir Syed Ahmed Khan did not believe in Naoroji`s drain theory.

1. B.G. Tilak (Option 1):

Bal Gangadhar Tilak, a nationalist leader and one of the early advocates of Swaraj (self-rule), supported the drain theory. He highlighted the economic exploitation of India by the British and believed that it was essential for India to regain control over its resources to achieve prosperity and independence. Thus, Tilak believed in the drain theory.

2. R.C. Dutt (Option 2):

Romesh Chunder Dutt, an economist and political leader, was one of the prominent voices in support of the drain theory. Dutt`s work, "The Economic History of India," extensively discussed the drain of wealth from India to Britain. He argued that this economic exploitation hindered India`s development and led to widespread poverty. Therefore, it is evident that R.C. Dutt believed in the drain theory.

3. M.G. Ranade (Option 3):

Mahadev Govind Ranade, a social reformer, and one of the founding members of the Indian National Congress, also subscribed to the drain theory. Ranade emphasized the importance of economic self-sufficiency for India`s progress and highlighted the negative consequences of British economic policies on Indian industries and agriculture. Thus, M.G. Ranade believed in the drain theory.

4. Sir Syed Ahmed Khan (Option 4):

Sir Syed Ahmed Khan was a notable Muslim philosopher, educationist, and politician during the British colonial era. Unlike the other leaders mentioned above, Sir Syed Ahmed Khan did not endorse the drain theory. His focus was more on social and educational reforms for the upliftment of the Muslim community in India. While he acknowledged the challenges faced by India under British rule, he did not attribute the country`s economic woes solely to the drain of wealth. Instead, Sir Syed Ahmed Khan believed in fostering a spirit of cooperation and understanding between the Indian Muslims and the British administration.

In summary, among the leaders mentioned, Sir Syed Ahmed Khan (Option 4) did not believe in the drain theory of Dadabhai Naoroji. While the drain theory was supported by B.G. Tilak, R.C. Dutt, and M.G. Ranade, Sir Syed Ahmed Khan focused on other aspects of reform and did not attribute India`s economic problems solely to the drain of wealth by the British.