The only language officially permitted in the Supreme Court, for the purposes of pleadings as well as for arguments, is English.
However, in practice, the judges of the Supreme Court are liberal in this regard. In appropriate cases, the judges permit a petitioner appearing in person (or, sometimes, even an advocate) to argue in Hindi language, if he is finding it difficult to explain his points in English. In fact, I have seen once the court permitting a petitioner in person to argue even in Telugu language even though only one judge understood Telugu and the other judge did not understand Telugu (the judge who knew Telugu explained it to the other judge who did not know that language).
So, in exceptional cases, the Supreme Court may permit a person to argue in Hindi, even though it is not officially permitted. You may make a request to court to permit you to argue in Hindi, and the court may permit you, generally speaking.
At the same time, let me point out that if you are not able to communicate in English, instead of arguing the case in Hindi yourself, it may perhaps be advisable to engage an advocate who can represent you and argue the case properly before the court in the language (English) that is the only permitted language. Going against the stream may not always be taken kindly by some judges, more so, when you are also arguing in person, because though the court permits it, it may not encourage it and sometimes may not view it favourably. Anyway, the choice is yours. What I have stated is the legal position and what is seen in actual practice in the Supreme Court, whether you like it or not, there is no escape from it.
Dr. Ashok Dhamija is a New Delhi based Supreme Court Advocate and author of law books. Read more about him by clicking here. List of his Forum Replies. List of his other articles. List of his Quora Answers. List of his YouTube Videos.