Dear Aritra,
yes aftr clearing your compartments you will be eligible for the apearing IIT and AIEEE...By the time of couselling you should get the certificate/memorandom of marks as a proof that you have passed...
For IIT , candidate must meet each of the following conditions:

1. He/she can attempt JEE only twice, in consecutive years.

2. He/she should have passed (10+2) or equivalent qualifying examination in 2008 or should be appearing in 2009, and secure at least 60% (55% for SC/ST and Person with Physical Disability PDI] marks in aggregate in his/her respective Board Examination. He/she should NOT have passed the qualifying examination earlier than October 1, 2007. If any Board awards only letter-grades, he/she should obtain a certificate from the Board specifying equivalent percentage marks. In case the respective Board awards letter-grades without providing norms for converting them to equivalent percentage marks, the norms decided by the Joint Implementation Committee, JEE-2009 shall be final.

3. He/she should NOT have accepted admission by paying full fees at
any of the IITs, IT-BHU- Varanasi or ISMU, Dhanbad through JEE.

4. He/she should have been born on or after October 1, 1984 (October
1, 1979 for SC/ST and PD candidates).
Click the link given below for the AIEEE eligiblity criteria:
http://www.askiitians.com/aieee/Eligibility-Criteria
Thanks and All the Best !!!!