No, you cannot get admission in Acharya Prafulla Chandra Ray Polytechnic College
It is really impossible to expect to get admission in a top notch Government Polytechnic college without having to sit for any entrance exams.
Let me inform you that to get into APC Ray Polytechnic College, which is considered to be the best college for polytechnic in West Bengal, you will need a rank within 500 for core engineering streams.
One of my friends is studying there in Civil Engineering by scoring a rank of 427 from the general category through Jexpo.