The Union cabinet has recently (July 2016) approved setting up of a major part at Enayam near Colachel in the Indian state of _____________

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Step-by-step explanation:

1. Identification: Enayam is a coastal locality situated near the town of Colachel in the Kanyakumari district.

2. Administrative location: Kanyakumari district is part of the Indian state of Tamil Nadu, so geographically and administratively Enayam 
   belongs to Tamil Nadu. In set notation: Enayam \in Kanyakumari \subset Tamil\;Nadu.

3. Geographical coordinates (approximate) confirming southern Tamil Nadu location: Colachel/Enayam lie near $\approx 8^\circ	ext{N},\;77^\circ	ext{E}$, which is in the state of Tamil Nadu.

Conclusion: The Union cabinet approval for a major part at Enayam near Colachel refers to the state of Tamil Nadu.

FINAL_ANSWER: c

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