JEE Main

Hello nikhil, you are eligible for a college even if you score cutoff marks in boards and JEE since you have got 22428 rank yes you are eligible for admission to any college.
now coming to admission
for NITs:
http://josaa.nic.in/webinfo/Handler/FileHandler.ashx?i=File&ii=62&iii=Y
this is last years cutoff ,you can get branches like civil,electrical,manufacturing in newer NITs and branches like biotech in older ones.
for DTU/NSIT:
http://jacdelhi.nic.in/publicinfo/Public/View.aspx?page=78
last years cutoff
considering delhi quota you can get ice,mpae,bt in NSIT and pie,ep,civil(if you are lucky),bt, environmental.
choose according to your interests not for money.
best of luck

Sorry, But I guess you have Very less chance of getting MANIT.
Well Check out last year cutoff
Chemical Engineering BC HS 7066 8158
Chemical Engineering BC OS 4413 4776
Civil Engineering BC HS 4619 7298
Civil Engineering BC OS 3068 3564
Computer Science Engineering BC HS 1834 4071
Computer Science Engineering BC OS 898 2004
Electrical Engineering BC HS 4299 6766
Electrical Engineering BC OS 2511 3041
Electronics and Communication Engineering BC HS 4018 7162
Electronics and Communication Engineering BC OS 1792 2545
Mechanical Engineering BC HS 3132 5300
Mechanical Engineering BC OS 1757 2880
Metallurgical and Materials Engineering BC HS 7695 8851
Metallurgical and Materials Engineering BC OS 5965 7149
Planning Engineering BC HS 1157 1354
Planning Engineering BC OS 704 977
Architecture Engineering BC HS 616 1154
Architecture Engineering BC OS 470 780