The official languages of Jammu and Kashmir are:

Urdu, Dogri, Kashmiri
Hindi, Dogri, Kashmiri
Urdu, Hindi, English
Kashmiri, Urdu, Ladakhi

The correct answer is: a) Urdu, Dogri, Kashmiri

Urdu, Dogri, and Kashmiri are the official languages of Jammu and Kashmir. Urdu is the most widely spoken language in the state, followed by Dogri and Kashmiri. English is also used as a language of administration and education.

Urdu is an Indo-Aryan language that is spoken by about 50 million people in India, Pakistan, and Bangladesh. It is the national language of Pakistan and one of the 22 official languages of India. Urdu is written in the Perso-Arabic script.

Dogri is an Indo-Aryan language that is spoken by about 3 million people in Jammu and Kashmir. It is the official language of the Jammu region of Jammu and Kashmir. Dogri is written in the Devanagari script.

Kashmiri is an Indo-Aryan language that is spoken by about 7 million people in Jammu and Kashmir. It is the official language of the Kashmir Valley region of Jammu and Kashmir. Kashmiri is written in the Sharada script.

English is a West Germanic language that is the most widely spoken language in the world. It is the official language of 53 countries and is spoken by about 1.5 billion people. English is written in the Latin script.

The official languages of Jammu and Kashmir are Urdu, Dogri, and Kashmiri. These languages are used in government, education, and the media. English is also used in government and education, but it is not an official language.