Which exams should I give other than JEE?

As a backup plan for the JEE, you can give the following exams:

BITSAT (Birla Institute of Technology & Science Admission Test)

VITEEE (Vellore Institute of Technology Engineering Entrance Exam)

NATA (National Aptitude Test in Architecture)

WBJEE (West Bengal Joint Entrance Examination)

MHTCET (Maharashtra Common Entrance Test)

AP EAPCET (Andhra Pradesh Engineering, Agriculture and Pharmacy Common Entrance Test)

TS EAMCET (Telangana Engineering, Agriculture and Pharmacy Common Entrance Test)

KEAM (Kerala Engineering Architecture Medical Examination)

COMEDK (Consortium of Medical, Engineering and Dental Colleges of Karnataka)

KCET (Karnataka Common Entrance Test)

OJEE (Odisha Joint Entrance Examination)

CUET (Common University Entrance Test) for admission to undergraduate programmes like BSc in all the Central Universities and their affiliated colleges in India.