Introduction:
The establishment of a madarsa in 1781 aimed to promote the study of Arabic, Persian, and Islamic law. This educational institution played a crucial role in the dissemination of knowledge in these subjects. However, the question remains: where was this madarsa set up? Let's explore the options and provide a detailed explanation for each.

Options:
(a) Bombay
(b) Murshidabad
(c) Calcutta
(d) Lucknow

Explanation:

(a) Bombay:
Bombay, now known as Mumbai, was an important center of trade and commerce during the British colonial period. While it had a significant Muslim population, there is no historical evidence to suggest that a madarsa was established there in 1781. Furthermore, Bombay was not a prominent center for Islamic education at that time.

(b) Murshidabad:
Murshidabad, located in present-day West Bengal, was the capital of Bengal during the 18th century. It was an important cultural and educational center, attracting scholars from various disciplines. Given its historical significance, it is possible that a madarsa was established in Murshidabad in 1781. Islamic studies and religious education flourished in this region, making it a plausible option for the location of the madarsa.

(c) Calcutta:
Calcutta, now known as Kolkata, emerged as a major center of British influence in India during the colonial period. It became the capital of British India in 1772. While Calcutta had a diverse population and witnessed the establishment of numerous educational institutions, including the prestigious Calcutta Madrasah in 1780, there is no specific evidence to suggest that another madarsa was set up there in 1781.

(d) Lucknow:
Lucknow, the capital of Awadh (Oudh) in present-day Uttar Pradesh, was renowned for its cultural and intellectual vibrancy during the 18th and 19th centuries. Many madarsas and educational institutions were established in Lucknow during this period. Hence, it is plausible that the madarsa in question was set up in Lucknow in 1781.

Conclusion:
After careful consideration of the options, it is likely that the madarsa mentioned in the question was established in Lucknow in 1781. Lucknow's rich cultural heritage, intellectual environment, and historical significance make it a plausible location for the establishment of an educational institution focused on Arabic, Persian, and Islamic law studies.

Madrasa was set up in Calcutta in 1781 to promote the study of Arabic,Persian and Islamic law.