There is an updated post on the topic at below link
There are 3 ways in which children of NRIs can be admitted to engg institutes in India. NRI students desirous of seeking MBBS admissions in medical colleges have only one way to get admitted- private medical colleges under NRI Quota (there is a separate post on this topic here) . Following discussions is useful for engineering admissions:
1) The DASA scheme for NRIs in NITs: Main criteria is that the NRI student has to study 2 years (11th and 12th) outside india, get SAT 2(Subject Tests) score above 1440 in physics, chemistry & Maths and pass 12th qualifying exam with min. 60% marks. More than 30 reputed NITs, IIIT and PEC are covered under this scheme. Annual fee is about $7000.
The details of DASA Scheme 2010-11 has been published by NIT-Surathkal and details are available at separate post link per below
The list of colleges/institutes under this scheme, number of seats/branches for each institute and the application form can be downloaded from DASA/NRI Quota . The admissions to IITs is not applicable under DASA Scheme or NRI Quota or any other scheme. The admissions to IIIT Hyd is conducted separately , also called DASA Scheme by IIIT-Hyd, for which the details are available here.
2) NRI Quota: The key criteria is that the student has to to pass 11 & 12 from outside india with min 60% marks. VIT, PSG College, Thapar Institute-Patiala, RV College, DAI-IT-Ghandinagar, VJTI and Manipal are some of the other reputed colleges with NRI Quota (However, the fee varies from $8000 to $11000 per year). For more information on NRI Quota, please visit DASA/NRI Quota section of this website.
3) NRI sponsored Quota: The key difference being the NRI sponsored student need not pass 11 & 12th from outside india. The sponsor (father/mother/brother/sister) should be an NRI as per IT rules. Many private colleges (including VIT-Vellore) have few seats under this scheme. NO NIT has this quota. Please see below list of prominent private Institutes with whom EdCIL has MOU and offer NRI Quota including NRI sponsored category. However, it is advisable to contact these institutes to confirm if they still have a valid MOU for NRI Quota. The annual fee for NRI Sponsored Quota can range between US$7000 (RV College Bangalore), VIT-Vellore ($9000) to US$9000 (Thapar -Patiala)
Now, list of NITs most preffered by NRIs (in the order of ranking under DASA scheme)
DTU, NIT-Surathkal, NIT-Trichy, NIT-Warangal, NIT-Calicut, IIIT-Delhi, PEC, MNNIT-Allahabad and IIIT-Allahabad are the most popular per previous years preference by NRIs/PIOs.
The above list is followed by NIT -Jaipur, MANIT-Bhopal, VNIT-Nagpur, NIT-Kuru, NIT-Rourkela, SVNIT-Surat, NIT-Durgapur and NIT Jalandhar.
Starting from 2010, DASA scheme merit list would be based on SAT II scores in Maths II, Physics and Chemistry. It would be prudent to score in excess of 730(out of 800) in each of the 3 subjects in SAT II to have any hope of getting the branch and college of your choice.