The correct answer is A. 1832.
The Goa State Central Library was established in 1832 by the Portuguese government. It is the oldest library in Goa and one of the oldest libraries in India. The library is located in the capital city of Panaji. It has a collection of over 100,000 books in Portuguese, English, Konkani, Marathi, Hindi, and other languages. The library also has a collection of newspapers, magazines, and journals. The library is open to the public and is a popular place for students, researchers, and the general public.
Option B is incorrect because the Goa State Central Library was not established in 1838.
Option C is incorrect because the Goa State Central Library was not established in 1846.
Option D is incorrect because the Goa State Central Library was not established in 1858.