BHMTT

Yes, there is a course for MBA in travel and tourism. There are also post graduation diploma courses in travel and tourism.
Thank you.

I personally suggest you to go for MBA finance or dual MBA (Christ and from Germany), Virginia commonwealth USA and Christ MBA, MBA in Leadership and Management. Jobs in tourism even after doing MBA are very less paying and, mostly, it's a desk job once you gain some experience and perform well you might get a traveling job but otherwise MBA tourism is of no use. You have 600+ MAT score that makes you eligible for all MBA courses offered by Christ.
All the best.

This is very specific questions to answer. It is better you focus on one thing, either internship or job, none of the institute focus on both the things.