Hey,
To apply for the Integrated PhD program at any IISER basic eligibility is 60% at your graduation level. Along with that you need to have good JAM score. For Integrated PhD in Physics JEST score is also accepted. Based on that you'll be shortlisted for interview. Now some IISER also have a written test for shortlisted candidates after which they select for interview.
In order to be shortlisted you need to first apply to your preferred IISER before deadlines.
Duration of integrated PhD is around 6 years. After completion of 6 years they will be given both master's and doctoral degree .
First four semesters that is two years is mostly course work after which doctoral research work starts. Students can also exit after successfully completing their two year course work. However, they will have to complete one more year of research as part of their MSc thesis.
As for direct recruitment in ISRO/DRDO, there is no direct placement by IISER. You'll have to look for vacancies and apply for position in ISRO on your own. You will surely be at advantage because of all the skills and knowledge you have gained at IISER. Applying and looking for vacancies you'll have to do that on your own.
I hope I have answered your questions.
ALL THE BEST!
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