Admission to Integrated Mathematics programmes consists of 2 stages. The 1st stage is an entrance examination. The syllabus and exam pattern are enlisted at: http://univ.tifr.res.in/gs2020/Files/Maths_Syllabus.pdf . The exam pattern is MCQs and True or False. The syllabus includes topics like Algebra, Analysis, Toplogy and General. The chapter wise topics are available in the link. You need to practise them in English if not for the entrance exam but atleast for studying Masters. This is because the medium of instruction will be in English. During the interview, they do not check your communication skills but they check for your subject knowledge. So they might understand that you are coming from Hindi Medium and might be okay if you answer questions in Hindi too. But should you be shortlisted for Interview, please ask their permission if you can answer in Hindi.

Hello Aspirant,

TIFR is a nationwide entrance exam conducted by Tata Institute of Fundamental Research (TIFR) in order to provide admission to candidates in postgraduate Science courses offered by it. For admission into PHD maths a student mus have completed M.A./M.Sc./M.Tech or should be in final year. There's no bar on the basis of english/ hindi medium. Everyone meeting the eligibility criteria can sit for the exam. TIFR checks your knowledge and skills so you don't have to worry about being passed out from hindi medium.

All the best