First of all congratulations for your result. The cutoffs change every year as it depends on various factors. And Jadavpur University is among the top government Engineering colleges of India. So the cutoffs are enough higher compared to other colleges. Now you don't have West Bengal State Domicile that means you'll he applying through Other state quota and the cutoffs for other state candidates are generally higher than home state candidates. For home state general candidates, mechanical and electrical seats in Jadavpur University are filled within 300 and 200 GMR respectively after round 3 counselling. So the cutoffs for other state candidates will be higher than this. So with 350 rank it will be a bit difficult to get Mechanical or Electrical in Jadavpur Univeristy. You can expect other branches such as, printing Engineering or Food Technology & Bio-Chemical Engineering etc. But you can surely get good private Engineering colleges like IEM, Heritage Institute if Technology, Techno India Salt Lake etc. This is based on last few years' cutoff and this year it might get changed. But you can get into Jadavpur University, may not be Electrical but other branches mentioned above can be achievable. You can use our WBJee college Predictor tool to know where you have good chances
http://www.careers360.com/wbjee-college-predictor