Hello Aspirant,
Your question as to how many government colleges for AME there are will be tough to quantify. But the good news is that there are many such colleges which offer AME.
To be eligible for the course, you just need to have passed 10+2 in Science (PCM).
Also, you'll need to appear for the Aircraft Maintenance Engineering Common Entrance Test (AME CET) and hopefully clear it.
All the best!
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