With a JEE Main percentile of 78.53 in the OBC-NCL female category from West Bengal, securing admission to top NITs or IIITs for branches like Electrical Engineering (EE), Electronics and Communication Engineering (ECE), or Mechanical Engineering (ME) may be challenging. However, you might have opportunities in certain institutions with lower cutoffs.

For instance, NITs such as NIT Agartala, NIT Raipur, and NIT Jalandhar have previously had closing ranks for EE and ME branches within the range of 90,000 to 1,50,000, which could be within reach for your percentile. Similarly, IIITs like IIIT Bhagalpur and IIIT Kottayam have had closing ranks for ECE around 40,000 to 50,000. These figures suggest that with your current percentile, you might have a chance in these institutions, though it's advisable to verify the latest cutoffs during the JoSAA counseling process.

Additionally, considering Government Funded Technical Institutes (GFTIs) could be beneficial, as they often have more accessible cutoffs. Institutions like NIT Durgapur in your home state of West Bengal might offer opportunities in branches like IT, EE, or ME. It's recommended to monitor the official JoSAA counseling portal for the most accurate and up-to-date information.

In summary, while top-tier NITs and IIITs may be competitive, exploring options in NITs with lower cutoffs and GFTIs could align better with your current percentile. Staying informed during the counseling process will be crucial in making the best decision.

With 78.53 percentile (OBC-NCL, Female, Home State: West Bengal), chances for NIT, IIIT, or GFTI in core branches like ECE, EE, or ME are very low. You may get lower NITs or GFTIs with Civil or lesser-preferred branches in spot rounds.