Which is better chemical or instrumentation and control or production engineering at NIT Trichy (no specific interest)?

In order to determine the right branch for yourself, you will have to go through a list of questions related to these branches individually.

Production Engineering:

• Are you okay with drilling a hole, shaping a metal part with a lathe, or polishing a metal piece for microscopic inspection
• Can you handle distorted schedules?
• Do you have an interest in drawing and designing? 

If yes, then go for Production Engineering.

Instrumentation and control engineering:

• Can you withstand extreme peer pressure, and strict professors.
• Can you give multiple internals before semester exams
• Can you handle extremely long lab sessions?

If yes, then go for Instrumentation and Control Engineering.

Chemical engineering:

• Can you attend multiple and frequently held lab sessions.
• Do you have any interest in thermodynamics?

If yes then go for Chemical Engineering.