With a JEE Mains rank of 51,600, you have a chance of getting into some NITs and IIITs, although you may need to opt for lower-demand branches or newer campuses. Here are some possibilities:

NITs:

1. NIT Meghalaya - Possible Branches: Civil, Mechanical.
   
   
2. NIT Mizoram - Possible Branches: Electrical, Civil.
   
   
3. NIT Agartala - Possible Branches: Production Engineering, Biotechnology.
   
   IIITs:
   
   
4. IIIT Pune - Possible Branches: Electronics and Communication Engineering.
   
   
5. IIIT Bhagalpur - Possible Branches: Computer Science, Electronics.
   
   
6. IIIT Una - Possible Branches: Information Technology.
   
   Other Options:

• Newer NITs like NIT Sikkim or NIT Nagaland might offer seats in branches like Electrical or Mechanical.
  
  
• State Engineering Colleges accepting JEE Mains scores could also be a good backup option.
  
  
  I would recommend you to use JEE college predictor tool by Careers360 to get the list of possible colleges you can get with your rank.
  
  Here is the link to the tool:
  
  https://engineering.careers360.com/jee-main-college-predictor?utm_source=qna&utm_medium=jee_cp
  
  Click on the above link, fill the required details and you will get the list of possible colleges at your rank.
  
  
  I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
  
  Thank you and wishing you all the best for your bright future.