me, went for check up during 1st day of work.. 

Btw, why you worry about your report? 

I signed one. The offer letter you signed should be a conditional one subject to a confirmed offer only after the medical and background check up are satisfactory. Which means if your medical report has issues or your background check doesn't tally with what you told them, the offer will be taken back. It's standard procedure.

When I went for my medical check, I was told that it is hard to fail it unless you have some severe hypertension, alcoholic habits or chainsmoking. Emphasis on severe illnesses. Take a look at the company's HR policies and guidelines, they should have something on discrimination and etc.

It's normal to worry about losing two jobs at once, I had the same experience too after informing everyone in my soon-to-be ex company that I am leaving. What I did was I informed the company I'm going to after I completed my medical check and followed up with them by a call a week later to see whether there were any issues with the results and my background check.

So far there has been no news of the offer being withdrawn. I believe if there is anything, they will let you know as soon as possible, in a week or so. If they leave you hanging then it's not that good of a company to join.

Everything was stated clearly in my offer letter about how it is conditional after background and medical check. Yours didn't state anything?

Background check includes your educational qualifications, they might call up your university/college to check whether you exist and or reference checks from your universities or previous employers based on the references you provided.

In my current company, they even ask your references whether the stories you told them during the interview tallies with what you did. For example, if you said you are a very friendly and open person in your previous job, they will include that in the reference check that will be sent to your previous employer for verification.

I think it is a valid point that it can waste both parties' time this way but I guess it's standard procedure for them to only actually dig real deep about you once you pass all the interviews and they are sure you're the one for the job.