Hello aspirant A

you have passed your degree course (BE) in Karnataka, you will be eligible to apply Post graduation course in Karnataka.

Eligibility for doing PG in Karnataka  state is that a candidate must have domicile of Karnataka But candidates who have passed ug course through karnataka state can also apply

Karnataka PGCET is also open for Candidates who do not hold the domicile of Karnatka. However they will not be eligible for any reservation. According to the article https://engineering.careers360.com/articles/karnataka-pgcet, to fulfil the domicile criteria for K PGCET, either the Candidate or his/her parents should have resided in Karnataka atleast for a period of 7 years and should have studied in Govt. or Govt. recognised Institutions for a period of 7 years either consecutively or with breaks in between. But in your case if you have studied your BE in Karnataka, that amounts only for a period of 4 years. Now the clause that you mentioned "Candidates should have passed the qualifying examination within Karnataka from an institute which is run or recognized by the state government makes you eligible for participating in Govt.seats but not for reservation.