Tata Institute of Fundamental Research (TIFR) is a National Centre of the Government of India, undertaking by Department of Atomic Energy, as well as a deemed University awarding degrees for master's and doctoral programs. At TIFR, carry out basic research in physics, chemistry, biology, mathematics, computer science and science education. TIFR main campus is located in Mumbai, but TIFR also have additional campuses in Pune, Bangalore and Hyderabad.
syllabus and question papers

TIFR M.Sc Entrance Test Chemistry Written Test Syllabus / TIFR Physics Syllabus / TIFR Mathematics Paper Syllabus/TIFR Ph.D Screening Test Syllabus
Main Topics of Mathematics will be Algebra, Analysis, Geometry, Topology, and General.
The screening test is mainly based on mathematics covered in a reasonable B.Sc Course. The interview need not be confined to this.
Pattern of Mathematics Test - The test paper will contains 30 questions of True/False type, 8 each from Algebra, Analysis, Geometry / Topology & 6 of General Type. The duration of the test will be 90 minutes.

Main Topics for Physics in TIFR will be Classical Mechanics, Mathematics relevant to Physics, Electricity & Magnetism, Quantum Mechanics, Heat, Thermodynamics & Statistical Physics, General Physics, Modern Physics, and Electronics & Experimental Physics.
TIFR M.SC/Ph.D Entrance Test Syllabus
Main Topics of Chemistry - Physical Organic, Inorganic, analytical, electro & quantum chemistry, bio-physics, thermodynamics, spectroscopy (NMR, Fluorescence, IR, UV & X-Ray), Logic & Statistics & mathematical methods.

The syllabus for the written test in chemistry is similar to the typical standard syllabus followed in any Indian University for the Bachelor of Science and Master of Science (B.Sc & M.Sc) Degree Course.

Computer & System Science:- Hot Topics of Computer Science will be Discrete Mathematics, Formal Language, Data Structure & Algorithms, Fundamentals of Programming Language & Compilers, Operating Systems & Concurrency, Switching Theory & Digital Circuits, and Theory of Database.

Common Topics of System Science will be carrying with Engineering Mathematics, Electrical & Computer Science.

Pattern of Computer & System Science - The question paper will have three parts. Part A is common to both streams. It will test the general mathematical aptitude of the candidate. There is no prescribed syllabus for part-A. Part-B will be oriented towards the listed topics under "Computer Science" above & Part-C will be oriented towards topics listed under "System Science" above. Only one of the part-B or C should be attempt. The duration of the question paper will be three hours. The test will be of multiple choice type with negative marking for incorrect answers.

TIFR Official site for Download the Syllabus and previous years papers for those students who are preparing the TIFR.