Metallurgy

You may check manit site for the statical data. Complete placement statistics with percentage placement is provided there. About the scope, I would suggest metalurgy had a good scope but with a lot of work on itself. Conceding your marks if you have category or belong to home state still opt for a better branch in the collage. But if you have interest, metalurgy isn't a bad. Check out NIRF data too placed on site of college or NIRF site.

Dear,
Maths and physics have an important role in every B.Tech field and you should have strong foundation and Interest in maths to get the knowledge and skills to reach a good level.
All the best.

Absolutely, there will be good future if you study in NIT but for job opportunities, you should try abroad for better salary packages. You can get nice salary packages in North India.

Hello Pavan,
There could be as many opinions as persons involved. As per me metallurgy and materials will have better prospects than mines. Lot of research is going in materials and metallurgy.
Best wishes

Civil Engineering is better option among the two as you will get more opportunities in engineering and construction companies. You can also target GATE and look to get into PSUs or can go for further studies (M.Tech).

Hello Sai,
Lateral admissions are prerogative of concerned state govt. Normally table is published indicating which branches in diploma will make you eligible for which branch in engineering. Check for PI with your polytechnic where you completed your diploma & they will inform you immediately.