Yes, you can get admission in Government college with 20,000 rank. Here are the list of possible colleges, with the branches that you'll have maximum chances in for the General category.

• GEC Kozhikode (Applied Electronics and Instrumentation)
  
• GEC Mananthavady (Electronics and Communication Engineering)
  
• GEC Idukki (Information Technology)
  
• GEC Sreekrishnapuram (Information Technology)
  

You also have a good shot at some sel-financing Government colleges