The correct answer is option 4, Arunachal Pradesh. Arunachal Pradesh is the only state among the given options that does not have a Legislative Council.

Option 1, Karnataka, is incorrect because Karnataka does have a Legislative Council. A Legislative Council is also known as the upper house or the Vidhan Parishad in some states and is a part of the bicameral legislature system.

Option 2, Telangana, is incorrect because Telangana does have a Legislative Council. The Legislative Council in Telangana is known as the Telangana Legislative Council or the Telangana Vidhan Parishad.

Option 3, Jammu and Kashmir, is incorrect because Jammu and Kashmir did have a Legislative Council until 2019. However, following the reorganization of the state into two union territories - Jammu and Kashmir, and Ladakh - in October 2019, the Legislative Council was abolished.

Therefore, the only correct option is 4, Arunachal Pradesh, as it does not have a Legislative Council.