With a JEE Main rank of 120000, securing a seat in a top NIT or IIT is highly unlikely. Your chances of getting into a good government college for any core branch are slim.

However, you can explore these options:

• Lower Tier NITs or IIITs: You might have a chance in some lower-tier NITs or IIITs for less preferred branches like Biotechnology, Metallurgy, or other similar branches.
• State Government Colleges: Consider state government engineering colleges in your home state. These might offer better chances based on state quotas.
• Private Colleges: A wide range of private engineering colleges are available, offering various branches. However, weigh the pros and cons, including fees and placement records.
• Other Entrance Exams: Explore other engineering entrance exams conducted by state governments or private universities.

It's crucial to research colleges, their cutoffs, and placement records before making a decision. Consider factors like location, branch preferences, and future career goals.

hope this helps you!!