B.Tech

Please go through this link
http://bhavans.ac.in/wp-content/uploads/2014/05/Eligibility-for-Admission-2017-18-1.jpg.

Defence Institute of Advanced Technology - DIAT
Girinagar, Haveli Pune, Maharashtra (020) 24389318, 24389411 (020) 24304021, 24304424
Courses Offered
M.Tech. (Mechanical (weapons)
M.Tech. (Automotive Engineering)
Ph.D. (Mechanical Engineering).

You don't need to be confused. Simply choose what you love to do, but for further knowledge, you'll get more job opportunities in commercial arts.

Yes, you are eligible for IET-Lucknow, but you have to crack the UPSEE LEET entrance exam, and your rank should be less than 5.

You'll need to qualify through JEE Main and JEE Advanced and you can get admission for first year of four year degree course. [Many state or private colleges will admin Diploma holder in second year directly, but not the IITs or NITs.]
Diploma holders are eligible to get direct admission in second year of B.Tech through different CETs of state governments.

Well, it varies every year. Since last 4 years, the placement is constantly down. TCS was the major recruiter this year. 69 B.Tech students got placed. And, around 30to 40 students got placed in Tech Mahindra (off campus). Bhushan 30, Vednat 15 (approximately), Praxiar 2 (offcampus), JK Papers (10 to 15 at maximum). Placement is really worse in IGIT. Out of 400 students in our batch more than 250 are unplaced. It is not how a government college should have placement.

Yes, you are eligible, but you have to crack the entrance exam for lateral entry and yours rank should be around 150.

Hello,
Visit Shiksha's college predictor to know the colleges you might get-
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwiomMOV8ILcAhXFOI8KHdVpCDwQFjAAegQIAhAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H

Sure, you can do MS in Engineering & Management field, but you like technical. So, it means, go with MS in Engineering.
If you like Management, then go for MBA.
Following college are good for doing MS or MBA:
IIT, NIT, IIIT, IISc, MIT BITs, SRM.