M.Tech

If you pursue integrated course other then IITs, then you will get M.Tech degree also but you will lose chance to do M.Tech from IITs, which will get through GATE after B.Tech.
Otherwise, go to any educational web portal, you will get the list of best private colleges for integrated course.
But lastly

Hello Kishore,
It will be better, but if you pursue integrated course then you will get M.Tech degree also, but you will lose a chance to do M.Tech from IITs, which you will get through GATE after B.Tech. Otherwise, VIT is also a good college to do this course. It is ranked under top 10 by MHRD.*
Last

All colleges’ fees are different, so you tell me the name of college, and then I’ll tell you about the college fees.

In Mains, you should score at least 50 marks to clear and 180+ in advance to get into IIT.
Best of luck.

You should get 60 to 80% marks in JEE.

There is a good chance but the competition is too high. If you get scholarship for your graduation then chances of getting job will be higher. If you do your Masters from New Zealand you will get one year guaranteed job after your graduation, however, Australia do not have any such commitment.

BITS Pilani does not provide BE(Hons)+ ME integrated course. But it has a programme of transfer where bright and promising students of the BE (honors) can seek transfer to a higher degree (ME) and/or Ph.D degree.

Dear Arshdeep,
Yes, it's a good choice to do MS i.e. M.Tech from abroad. Germany is considered for mechatronics and mechanical engineering so I would suggest you to do it from Germany universities.