Based on your CMR of 4186, it won't be possible to get FD, TD, AD courses in Hyderabad as the last rank admitted in the previous year in obc category is as follows :-
FD - 1679
TD - 2753
AD - 2533
But, you can try in another branches. For FD, you may get NIFT shillong and NIFT srinagar. For TD, You may get NIFT kangra. For AD, you may get NIFT bhopal, NIFT raebareli, NIFT shillong, NIFT kangra and NIFT jodhpur.
All the best !
Yes, you may get admission in NIFT colleges on the basis of your category rank. The probability of admission also depend upon the course you opt.
It is difficult to get FD, but you might get AD or TD.
for cut off, visit the link provided below -
Hope this helps,