Mechanics

Yes, it is possible to get a B.Tech in Mechanical Engineering through JOSAA (Joint Seat Allocation Authority) or CSAB (Central Seat Allocation Board) in lower NITs (National Institutes of Technology). JOSAA handles the initial seat allocation for IITs, NITs, IIEST, IIITs, and other GFTIs based on JEE Main ranks. If there are any vacant seats remaining after the JoSAA rounds, CSAB conducts special rounds to fill those, also based on JEE Main scores. 

In order to move forward to study research in quantum mechanics and atomic branches, you must possess a background in Physics. Having an PCB (Physics, Chemistry, Biology) stream, you cannot be made eligible to study undergraduate in Physics, as the latter traditionally demands PCM (Physics, Chemistry, Mathematics) or PCMB (Physics, Chemistry, Mathematics, Biology) streams.If one wishes to pursue this field, they can reappear for their 12th boards with PCM or PCMB to be eligible for a Bachelor's degree in Physics. This is the basic knowledge needed to study and research quantum physics.