I have never recognised or endorsed a Mukhyagraha nor an ishtdev. They are all local connotations unrelated to astrology.
You are a potential IIT aspirant and have some reasoning on these matters. These are all tantrums of local astro specialists designed to enrich themselves.
All the planets work in tandem in a horoscope some of them behave as benefics and some of them malefics. I have given the planetary dispositions above. Look at which are the benefics and perhaps the planet with maximum benefic points could be taken as MukhyaGraha.(Important). in your case it could be Sun. And He could as well be your ishtadev.
You should try to learn the science behind astrology rather than listening to loose talk spread by the astro community, most of whom do not know how to compute the strengths of horoscopes.