Engineering

No, you can can't apply without physics in class 12th.

Hello Udai,
There are good possibilities to get admission in PSGIM with 43.33 under SC Quota, because 42 is the last years lowest cut off under BC Quota to get admission in PSGIM. Still, it depends on student's choices on MBA institutions this year. All the best.

Hello Sheeba,
There are good possibilities to get admission in PSGIM with 58.33 under BC Quota, because 56 is the last years the lowest cut off under BC Quota to get admission in PSGIM. Still, it depends on student's choices on MBA institutions this year. All the best.

Yes, there are many colleges like -
FIEM
BBIT
Dr. Sudhir Chandra Sur Degree Engineering College
Techno India University
UEM.

Yes, you can, provided you had PCM in class 12th and scored 50% marks in that. You need to understand that Pilot training is governed and regulated by DGCA and it is irrespective of the flying school you choose to train with. For becoming a commercial pilot, there is a specific eligibility criteria,

No, with this rank for lateral entry, you'll not get any government college, but probably you can good private colleges like:
Galgotias University
BBD
SRGI
Ajay Kumar Garg Engineering College

It totally depends on your choice, because we can't compare two branches. If you desire for CSE, go for IIIT, or else go for NIT -Hamirpur. Choose wisely. If you are asking for infrastructures, then NIT Hamirpur is well established and IIIT is running inside NIT-Jamshedpur.

Yes, on the basis of your rank in IMT, you can get admission in AEMS and SIMS, but not in IMU.

Yes, you can get admission in ECE through ACPC in DDU after your class 12-Science.