With a JEE Main rank of 686,220 , it's very unlikely to secure admission in competitive government engineering colleges like Government Engineering College, Bhavnagar or Government Engineering College, Ajmer , where even the least competitive branches have closing ranks in the hundreds to low thousands —for example, IT at Bhavnagar had closing ranks around 22,332 (All India) and 34,161 (Home State) in 2025 (https://collegedunia.com/college/28236-government-engineering-college-gec-bhavnagar/jee-main-2025-cutoff?utm_source=chatgpt.com) .

Recommendation: You’re more likely to find seats in state-level or less competitive government colleges through entrance exams like GUJCET or REAP (depending on your state). These options may include branches like IT or EEE and typically offer affordable fee structures. Consider using tools like the Careers360 college predictor to explore affordable colleges with realistic cutoffs and good placements