My Aeee rank is 19755 and belong to tamilnadu (state quota) with 75% in 12th board exam . will I be able to enter coimbatore campus?

Congratulations for your result. Based on your rank you can expect Amrita School of Engineering, Coimbatore. You have secured 19755 rank in AEEE and you belong to Tamil Nadu which means you'll be treated as Home State quota candidate for getting admission into Amrita School of Engineering, Coimbatore. Now if we go through last few years' cutoff, then getting CSE in Amrita School of Engineering with this rank would be very difficult as the closing rank lies around 13000. Almost all the branches get filled within 19000 rank. And Except Electronics and Communication engineering, you can get all other branches there such as Electrical - Electronics, Chemical, Civil Engineering, Instrumentation, Aerospace Engineering etc. Now this is based on previous few years' data and this year it might change. You can check the cutoffs here http://engineering.careers360.com/articles/aeee-cutoff
And to be eligible for AEEE, you need at least 60% of aggregate marks in PCM and a minimum of 55% marks individually in these three subjects. As you have written AEEE this means you have met this criteria. So you board marks will not matter so much now.