Both IIT Roorkee and ISM Dhanbad are reputed Engineering institutions offering excellent education as well as opportunities. Being an IIT, Roorkee does have a slight advantage over ISM, though ISM too is going to be an IIT one day.

The infrastructure of both institutes is equally good with IIT Roorkee having a slight advantage over ISM because of its early establishment. However, ISM is fast developing and has a beautiful campus. It’s going to house Asia's largest library soon.

Branch-wise, both Applied Mathematics and MNC comprise Mathematical concepts but with a different perspectives. Applied Mathematics has pure math and only those who want to pursue research in the same should go for it. MNC on the other hand is a blend of Maths as well as Computing (coding) and is more in demand than Applied Mathematics. Its scope is also wider than APM and has better placement opportunities.

Eventually, it’s a matter of preferences and not the credibility and worth of the branch that you should focus on.