Will i be eligible to appear for mht-cet if i do private 12th science?

I completed my 11th in science but could not appear for 12th exams due to health related issues. If i appear for 12th privately then will i be eligible to appear for mht cet and aieee exams as i want to do engineering or graduation in IT. Will private 12th mark sheet have any impact on my job and career in future? how to prepare for science practicals if i appear for 12th privately? please help i need your suggestions and advice.