Explanation:

Telangana was officially bifurcated from the state of Andhra Pradesh and became the $29^{\text{th}}$ state of India on June $2$, $2014$. This was the culmination of a long-standing movement for a separate state. Options (1), (2), and (3) are incorrect dates. $2015$ is a year later, and the other dates in $2014$ are not accurate for the formation. The Andhra Pradesh Reorganisation Act, $2014$, was passed by the Parliament of India in February $2014$, paving the way for the creation of Telangana. Therefore, (4) June $2$, $2014$ is the correct answer.