Dear Kanishka,
Yes, you can apply for Indian Air Force after graduation being a girl.
After you graduation in any technical stream in BSc with Physics, Chemistry and Math background you can apply for AFCAT or CDS. There is one other way too which is the special entry through NCC, this can be done by the help of you NCC cell of college or universities.
To check about exam pattern, syllabus and details like these, you can go through the link below.
https://competition.careers360.com/exams/iaf-afcat
To check the eligibility criteria of AFCAT, you can check the link below.
https://competition.careers360.com/articles/afcat-eligibility-criteria
To check the same about CDS, you can follow the link below.
https://competition.careers360.com/exams/cds
https://competition.careers360.com/articles/cds-eligibility-criteria
Now coming to your second question which is what degrees are needed to be an astronaut.
See, if you want to become an astronaut after joining Air force, then you can be it by performing well in your job be it pilot or any posts and second important thing is you have to show the interest in astronaut related field like volunteer for astronaut related projects and if such situations arise during the works you have to show some skill in it. In fact some institutions related to astronaut prefer Airforce personal more over normal applicants.
Other than that if you normally want to be an astronaut then below is the educational qualification and eligibility criteria needed for it.
I hope this answer helps you.
Al the very best!!
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