NIT

With a 10,000-15000 or 20000-25000 rank in JEE Mains,  you can still get admission into NIT, IIIT, GFTIs and other engineering colleges. These colleges may accept different rank ranges depending on the type of college and B.Tech Course .

Getting admission in MNIT totally depends on your rank, reservation and branch. For getting seat in MNIT, you should score above 98 percentile for general category student. So, it depends on reservation category and you have scored 87 percentile which is good and you have good chances of getting seat in MNIT in some branches.

Assuming You have a rank ~40k to ~55k, It is Not possible in general category if you are aiming for top NITs or IIITs . You may have  limited options with lower branches but  not CSE and definately not best nit's. It is possible to get into some good NITs and IIITs if you are from a  sc (scheduled caste) or st(scheduled tribe.

With 77.92 percentile in JEE Main and SC category, your SC rank would be around 12k–15k.
Chances are low for top branches like CSE in NITs/IIITs, but possible in lesser-known ones.
You may get lower branches (like Mechanical, Civil, or Production) in newer NITs.
Some IIITs with newer campuses may also be within reach.
Participate in JoSAA counseling and also consider state counseling options for better chances.

With a JEE Main score of 53.06 and a SC category rank of 55137 in JEE Mains, securing admission in top NITs, IIITs, or GFTIs may be challenging. you better try other universities or private B.Tech colleges.

A JEE Main percentile of 74 is unlikely to secure admission to top tier National Institutes of Technology (NITs) or Indian Institutes of Information Technology (IIITs). 

Your friend is likely referring to the Study Grant offered by Lovely Professional University (LPU). Under this initiative, LPU provides a study grant of 1 Lacs per student to those who qualify the LPUNEST exam and secure admission to prestigious institutions such as IITs, NITs, IIMs, NLUs, IHMs, NIDs, and other government universities and colleges.