The correct answer is A. Nizam-ul-Mulk Asaf-Jah.
Nizam-ul-Mulk Asaf-Jah was a Mughal noble who served as the Prime Minister of the Mughal Empire from 1713 to 1722. He was the founder of the Asaf Jahi dynasty, which ruled the princely state of Hyderabad from 1724 to 1948.
Mir Muhammad Amin alias Saadat Khan was a Mughal noble who served as the governor of Awadh from 1707 to 1719. He was the founder of the Saadat Khani dynasty, which ruled Awadh from 1722 to 1739.
Osman Ali Khan was the sixth Nizam of Hyderabad from 1886 to 1914. He was the last independent ruler of Hyderabad.
Qamaruddin Khan was the Prime Minister of Hyderabad from 1937 to 1948. He was the last Prime Minister of Hyderabad.
Nizam-ul-Mulk Asaf-Jah was the most likely person to have established the state of Awadh. He was a powerful and influential Mughal noble who had the resources and the ambition to establish a new state. He was also familiar with the region of Awadh, having served as its governor for several years.
Mir Muhammad Amin alias Saadat Khan was also a powerful and influential Mughal noble, but he was not as well-positioned to establish a new state as Nizam-ul-Mulk Asaf-Jah. He was not as familiar with the region of Awadh, and he did not have the same level of resources.
Osman Ali Khan and Qamaruddin Khan were not in a position to establish a new state. They were both rulers of Hyderabad, which was already an established state.