The correct answer is the University of Mumbai.
The University of Mumbai is a public state university located in Mumbai, Maharashtra, India. It is the oldest university in the state of Maharashtra and the second oldest university in India. The university was established in 1857 as the University of Bombay, and it was renamed the University of Mumbai in 1996.
The university has over 600 affiliated colleges and institutes, and it offers a wide range of undergraduate, postgraduate, and doctoral programs in arts, science, commerce, engineering, law, medicine, and other disciplines. The university is also home to a number of research centers and institutes.
The University of Mumbai is a member of the Association of Indian Universities and the Association of Commonwealth Universities. It is also accredited by the National Assessment and Accreditation Council (NAAC).
The university has produced a number of notable alumni, including former Prime Minister of India Indira Gandhi, former Chief Justice of India P. N. Bhagwati, and Nobel laureate Rabindranath Tagore.
The other options are incorrect because they are not state universities responsible for affiliating colleges in the Mumbai region.
Savitribai Phule Pune University is a public state university located in Pune, Maharashtra, India. It was established in 1948 as the University of Pune, and it was renamed Savitribai Phule Pune University in 2014.
Dr. Babasaheb Ambedkar Marathwada University is a public state university located in Aurangabad, Maharashtra, India. It was established in 1958 as the Marathwada University, and it was renamed Dr. Babasaheb Ambedkar Marathwada University in 1994.
Rashtrasant Tukadoji Maharaj Nagpur University is a public state university located in Nagpur, Maharashtra, India. It was established in 1923 as the Nagpur University, and it was renamed Rashtrasant Tukadoji Maharaj Nagpur University in 2014.