There are many Top engineering colleges in India which cater to the need to Indian origin students.
Please also check Engineering colleges and Exams in South India.
The students in UAE and Middle east region can apply online for IIT JEE/AIEEE and AIPMT exams.
For IIT JEE form and applications in Dubai , you need to visit askiitians website.
The Govt. of India has made this provision, so if you want, you can keep your test centre in Dubai.