If you are dead sure about joining the Core companies then it would not be a cake piece for you.
I was from the same branch & tried a lot.
Options are:
1. try searching as many CORE based companied on internet & mail their recruitment/HR team directly, chances are few that they will reply but they may.
2. Anytime you can consult a consultancy for getting opportunities in CORE field.
3. CORE companies have a different procedure to follow, There are plenty of opportunities coming on freshersworld etc. you have to apply online/purchase their forms.
Prepare for their Exams all over India.
