Is there any problem in Appearing for IIT and 12th after failing in 12th last year???

No, there is no problem in Appearing for IIT JEE and 12th after failing in 12th last year, but this time you should concentrate on your studies and try to get minimum 65% marks in your physics, chemistry and mathematics, after you will be eligible for the JEE examination.

After cracking the JEE examination you can take admission in one of following courses:

B.Tech (Instrumentation & Control Engineering)
B.E (Electronics and Communication Engineering)
BTech (Physics)
B.Tech ( Aero Space Engineering)
BTech (Applied Mechanics)
B.Tech (Dairy Technology)
B.E.(Hons) Mechanical
B.Tech (Automobile Engineering)
B.E. (Computer Science & Engineering)
B.E.(Hons) Manufacturing
B.E (Aeronautical Engineering)
BTech (Production Engineering)
B.Tech.- Aerospace Engg.+M.Tech.-Avionics (Dual Degree)
B.E (Bio-Medical Engineering)
B.Tech ( Metallurgical and Materials Engineering)
B.Tech (Bio-technology)
B.Tech (Bioinformatics)
B.E (Petroleum and off-shore Engineering)
B.Tech (Electrical & Electronics Engineering)
BTech (Paper Technology)
B.E (Applied Marine Information Technology and Communitcation)
B.E (Mechanical Engineering)
B.Tech (Electronics & Telecommunications) & MBA (Telecom) Dual Degree
B.Tech.(H) in Manufacturing Science and Engineering
B.E. (Marine Engineering)
B.Tech (Information Technology Engineering)
B.Tech (Mining Engineering)
BTech (Biological Sciences and Bio-Engineering)
B.Tech (Paint Tech.)
B.E ( Manufacturing Processes and Automation Engineering)
BTech (Civil Engineering)
B.Tech. Textile Technology
BTech ( Materials Science)
B.E (Chemical Engineering)