I would suggest you to go to DCE
M&C at Dhanbad is good but the first INTEGRATED batch of M&C is to pass out by 2010. Although only Msc programs(Not throug JEE) have passed out.
IF placements are your CUP OF TEA then I can surely say that DCE will give you much better options.
Having said that the placement scenario may change sooner as it is a very booming branch.
If you have more queries, feel free to ask.
AND about the BITs thing!!...........EDUCATION LOANS are everywhere yaar. You will be paying it. So why worrying about that?
Try to convince your parents
All the Best!