Based on your JEE Main rank of 11 lakh in the OBC category, it is highly unlikely that you will be allotted a seat in any government college through JoSAA counselling. Most NITs, IIITs, and GFTIs close admissions for OBC candidates well before this rank, typically under 200,000.

You may explore alternative options such as:

1. State-level counselling: Some state universities and technical institutes conduct their own counselling and may offer seats at higher ranks. Look into state quota options in your home state.

2. CSAB Special Rounds: Although limited, these are conducted after JoSAA rounds and might have seats in lower-demand branches or remote colleges. However, chances remain minimal at your rank.

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3. Private and deemed universities: Many of these institutions accept JEE scores regardless of rank or have their own admission processes. They are your most realistic option.

4. Diploma to Degree (Lateral Entry): If you’re open to it, consider pursuing a diploma now and taking lateral entry into B.Tech in the second year later through LEET or state-level entrance exams.