The correct answer is: A) Kannada language and literature.
The Karnataka Vidyavardhaka Sangha was established in 1890 by a group of young Kannada scholars and activists. The main objective of the Sangha was to promote the Kannada language and literature. The Sangha also played a significant role in the freedom struggle and the development of Kannada culture.
Option B is incorrect because the Sangha was not established for the promotion of temple construction. The Sangha was a secular organization that was not involved in religious activities.
Option C is incorrect because the Sangha was not established for the promotion of trade with other states. The Sangha was a cultural organization that was not involved in economic activities.
Option D is incorrect because the Sangha was not established for the promotion of military training. The Sangha was a non-violent organization that was not involved in military activities.