If your JEE Main percentile is 61.67, then your rank is likely between 3,30,000 and 10,00,000. With this rank, it is very difficult to get admission in top engineering colleges in Pune, Bangalore, Hyderabad, or Chennai through JEE Main counselling.

In Pune, popular colleges like COEP, VIT Pune, or MIT WPU usually need a higher percentile. But small private colleges may give admission through management quota or other state-level exams.

In Bangalore, good colleges like RV College, BMSCE, and MSRIT also need high percentiles. But you can try small private colleges if they accept JEE Main score or if you apply directly.

In Hyderabad, top colleges like IIIT Hyderabad or CBIT usually take students with high percentiles. With 61.67 percentile, it’s very hard to get admission there through JEE. You can check smaller colleges or go for management quota.

In Chennai, big colleges like VIT or SRM may give admission if you clear their entrance exam or have good class 12 marks. But for JEE Main admission, 61.67 percentile is too low.

So, your chances in top colleges of these cities are low with this score. But you can try for small private colleges, use your state board marks if they are good, or go for direct admission or management quota.

You can also check if any state-level counselling in your home state accepts your score for local colleges.