2016 graduate with good percentile scores, what are the chances?

Verbal 99.8 percentile
Problem solving 97.8 percentile
Quantitative ability 99.97 percentile

2016 mechanical engineering branch passout from NIT Calicut. Where should I apply to? Will there be any job openings for 2016 batch?

Your scores are excellent but passout year can be a problem. You can try both here as well as in Amcat. Also try some placement agencies since they are aware of job openings. Best of luck!