Hello Aspirant,

PhD Mathematics program is a minimum of 3 years to a maximum of 5-6 years course.Admission will either be based on your merit or entrance exam depending on the university.But is always ideal to clear the top entrance exams in order to become eligible for PhD in Math anywhere in India.Some top Ph.D. Mathematics entrance exams are NBHM (National Board for Higher Mathematics)Entrance Exam, CSIR UGC NET, UGC NET, and other relevant entrance exams.Top university to pursue the same are:

Tata Institute of Fundamental Research (TIFR)

Harishchandra Research Institute (HRI)

Indian Statistical Institute (ISI)

Chennai Mathematical institute (CMI)

Institute of Mathematical Sciences (IMSc)IISc (Bangalore)

Banaras Hindu University

Aligarh Muslim University

Ramakrishna Mission Vivekananda College,Kolkata and many more.

You can try for prestigious abroad universities as well if interested and have a good merit. Some of them are Massachusetts Institute of Technology (MIT),Harvard University,Stanford University,University of Cambridge,University of Oxford,University of California, Berkeley (UCB),Princeton University,ETH Zurich (Swiss Federal Institute of Technology),UCLA etc.

Some universities may admit based on their own entrances, but anyways in general the entrance questions(in India) will mostly be from the following topics:

Abstract Algebra

Complex Analysis

Elements of Numerical Analysis

Linear Algebra

Ordinary Differential Equations

Partial Differential Equations

Real Analysis

You may visit the below link , to explore Indian universities:

https://university.careers360.com/colleges/list-of-phd-in-mathematics-universities-in-india

All the best