Hello Aspirant

With a rank of 13400 you have almost no chances chances to get Computer Science Engineering in Amrita Coimbatore campus even if you have home state quota. You need a rank less than 11500 to get into Amrita Coimbatore CSE with state quota.
You cannot get into other Amrita campuses with CSE branch as you will be an open category candidate for other branches. For other campuses you need a rank below 4000 for open category students.
In Amrita Coimbatore campus you can get into other branches like ECE, EIE, EEE and all others based upon preference except CSE.

You can check the previous year's cutoffs for different branches from the link given below:
https://engineering.careers360.com/articles/aeee-cutoff

Hope this helps
Good Luck

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