Bangladesh

Hi
IITs offer only B.tech and not B.Sc. and admissions are through JEE and so far there is no lateral entry admissions offered. Check here for more details.
http://www.iitkgp.ac.in/topfiles/acad_progs.php
If you wish to try another universities, here is the list.
List of Engineering Lateral Entry Entrance Exams
AIEEE All India Engineering Entrance Exams
Calicut University Lateral Entry Entrance Exams
Delhi technical University Lateral Entry Entrance Examination
Kerala University Lateral Entry Exam
KIIT University Lateral Entry Entrance Examination
Lateral Entry Entrance Test LEET
LPU NEAT (National Engineering Aptitude Test)
MIT-Manipal BE Lateral Entry Entrance Exam
Mumbai University Lateral Entry Entrance Examination
Punjab Technical University Lateral Entry Entrance Test (PTU LEET)
UKSEE B.Tech (Lateral Entry) Entrance Exam
Uttarakhand Technical University Lateral Entry Entrance Test
West Bengal University Joint Entrance Exam for Lateral Entry (JELET)

Hi, please check the details below :
For Admission of NRI (Non Resident Indians) and Foreign Nationals to various courses of Study at Aligarh Muslim University, some of the rules must be taken into consideration, the following must be strictly adhered to:
Foreign National candidate shall not be allowed to complete his/her admission unless he/she is in possession of a valid Student Visa. However, the candidates from the Commonwealth Countries with which the Government of India has treaties shall be exempted from visa restriction.
If a document/certificate is in a language other than English, a true translation of the same in
English duly attested by the Indian Embassy /High Commission/ Consulate, should be enclosed alongwith the Application Form.
Candidates applying under ICCR Category are required to be sponsored / nominated by the Government of India through Ministry of External Affairs, Human Resource Development/ Indian Council for Cultural Relations, New Delhi.
Foreign Nationals are required to undergo a Medical Test at Aligarh and obtain a certificate from the Chief Medical Officer, University Health Service certifying the medical fitness for completion of admission. Further an HIV Negative certificate by an approved laboratory is also essential to confirm the admission in the University. The admission of a Foreign National who is found medically unfit at any stage can be discontinued/cancelled.
As a student of this University, a Foreign National is entitled to the Medical Facilities available at the University Health Service.
For seeking admission under Children of NRIs Category, it is mandatory for the parents of the candidate to hold NRI status at the time of admission. However, if at any stage after admission the parent of the candidate admitted under Children of NRI Category ceases to be an NRI, he/she may be allowed to deposit the remaining Institutional Economic Fee in Indian Rupees at the prevalent exchange rate as per the contract.
Any dispute with regard to any matter relating to admission in the University and its Centres shall be subject to the jurisdiction of Local Courts at Aligarh and High Court of Judicature at Allahabad, Uttar Pradesh, India only.
If still you are confused then submit your inquiry on this web link :
http://www.amu.org.in/p/ask-your-query.html