The official languages of Karnataka as recognized by the Census:

Kannada
Kannada, English
Kannada, Hindi, English
Kannada and all other languages included in the 8th Schedule of the Constitution

The correct answer is: B) Kannada, English

Kannada is the official language of the Indian state of Karnataka. It is the primary language spoken in the state, and is also spoken by significant populations in the neighboring states of Andhra Pradesh, Telangana, Tamil Nadu, Kerala, and Maharashtra. Kannada is a Dravidian language, and is one of the 22 scheduled languages of India.

English is the second official language of Karnataka. It is used in government and education, and is also widely spoken in the business community. English is a Germanic language, and is one of the most widely spoken languages in the world.

The other options are incorrect because they do not include Kannada as one of the official languages of Karnataka. Option C includes Hindi, but Hindi is not an official language of Karnataka. Option D includes all other languages included in the 8th Schedule of the Constitution, but the 8th Schedule does not include Kannada.