NIT

The following factors determine the BTech cut-off (admission/qualifying):

• Number of aspirants who appeared for entrance exam
• The difficulty level of the exam
• Total number of seats available
• Total number of applications received for a particular programme
• The category under which admission is sought

With an AIR of 67,353 in JEE Main, you have good chances of getting NITs like NIT Jalandhar, NIT Goa, NIT Hamirpur, and NIT Srinagar, especially in branches like Civil, Mechanical, EEE, or ECE. You may also get core branches in newer NITs like Nagaland, Mizoram, Arunachal Pradesh, and Puducherry. These NITs had closing ranks above 80,000–1,10,000 in recent years. Make sure to fill your choices carefully in JoSAA counselling and include all possible options. If you're flexible with the branch, you'll have a better chance of getting into a decent NIT. Always keep backup colleges just in case.

Yes, of course. BTech Civil Engg. is the oldest and quite popular engineering specialisation that is offered across the top IITs and NITs in India. There are integrated BTech-MTech courses in Civil Engineering as well at the IITs where you can earn a dual degree in 5 years.
Top IITs where you can study BTech Civil Engineering include IIT Bombay, IIT Madras, and IIT Kharagpur, while the top NITs are NIT Trichy, NIT Surathkal, and NIT Rourkela. You can get into these institutes via the JEE Main and JEE Advanced exam scores.