Yes, you can apply for the jobs in the research organisation. For research posts it is a must to have completed Masters course from a reputed and recognised institute.

Also there are criteria's like –
-Candidate must be citizen of the India,
-Must have no criminal background etc to join research institutes like ISRO and DRDO.
-In the DRDO job opportunities for M.Sc Chemistry candidates will be in the area of Junior Research Fellow.
- Some of them prefer candidates who have experience in field of coatings and characterization of hazardous chemicals.
-There are also opportunities in ISRO for those who have specialised in electro chemistry background.
-There are also job opportunities in other sectors like pharma, chemical industries etc.