Should I go for civil engineering or metallurgy and material science engineering in NIT Trichy?

I would suggest you go for metallurgy if you plan to do a job right after completing your degree. Metallurgy has more job opportunities to offer. With Metallurgy, you can easily learn coding and go for tech companies. NIT Trichy has a great coding culture, so picking up coding skills will not be difficult. 

If you plan to prepare for civil services or any other government job, I would suggest you go for civil engineering.

When compared to metallurgy, there are fewer job opportunities in the civil department.

If you plan on doing an MBA after having done your engineering, you can opt for either of them because then it does not matter anyway.