JEST

JEST is joint entrance screening test. It is conducted in the month of February once every year. Where can I write JEST exam? JEST exams are conducted across major cities of india, it is conducted in many cities like Ahmadabad, Aligarh, Allahabad, Bangalore, Mumbai, Nagpur, Pune, Raipur, etc. Eligibility for JEST:
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M.Sc/ME/M.Tech/MCA and related disciplines, interested in maths aspect with computer science will be considered for Ph.D programme.
-Talented B.Sc/BE/B.Tech graduates are eligible for Master's degree.
JEST is the exam via which students are selected for interview, JEST is conducted for Ph.D and integrated Ph.D programs for physics and computer science every year.
-GATE score cannot be used instead of written exam of JEST but it is used for shortlisting candidates for direct interview for Ph.D programs.

Neil Menon's answer provides satisfactory details, and I don't differ when it comes to Classical Mechanics and Quantum Mechanics, but have a point to add about Special Relativity (classical):
I would say that to really appreciate Special Relativity, one needs to read Introduction to Special Relativity by Robert Resnick a very thin book, with 4 chapters and many excellent examples and exercises once in life. I would suggest try to solve each and every problem, know the book from cover to cover. D. J. Griffiths Introduction to Electrodynamics also delves into Relativity in the last chapter, dealing with the very useful 4-vector formulation, unlike Resnick, in his usual elegant and simple style: it might also be very useful as far as problem-solving is concerned.