Hi

Yes, you can do diploma  and graduation both at the same time.

This is because,

UGC has given its approval that one can go for pursuing two courses at the same time, the only condition is that one cannot pursue both these courses in regular mode i.e for both the courses to be legal, one  course can be in regular mode and other course in distance mode from Open University or online.

So, there will be no problem even if you do diploma in regular mode and your graduation as a distance program , just make sure that you do it from recognised Open Universities like IGNOU and afterwards you won't face any problem even in the case of government examinations like SSC CGL etc

For your reference,

SSC CGL eligibility criteria is provided below

*You must have a graduation/ bachelor's degree in any discipline   from a recognised university.

So, it doesn't matter even if you do your graduation from open university in distance mode what all matters is that it should be recognised one.

*Minimum age limit :-  you need to be at least 18 years old to be eligible

*Maximum age limit :-  32 years , also there's 3 year relaxation on upper age limit for obc and of 5 years for sc/st category

For detailed information related to SSC CGL eligibility criteria , you can visit our page at

https://competition.careers360.com/articles/ssc-cgl-eligibility-criteria

I hope that you find this helpful

Thank you