- Physics
- Mathematical methods, mechanics and general properties of matter, oscillations waves and optics, electricity and magnetism, kinetic theory and thermodynamics, modern physics, solid state physics and devices, and electronics. Degree-level throughout.
- Chemistry
- Physical chemistry covering basic mathematical concepts, atomic and molecular structure, theory of gases, solid state, chemical thermodynamics, chemical and phase equilibria, electrochemistry, chemical kinetics and adsorption; organic chemistry covering basic concepts, stereochemistry, reaction mechanisms, organic synthesis, natural products, heterocyclic chemistry and spectroscopy; and inorganic chemistry covering periodic table, chemical bonding, main group and transition elements, bioinorganic chemistry, analytical chemistry and instrumental methods.
- Mathematics
- Sequences and series of real numbers, functions of one and two real variables, integral calculus, differential equations, vector calculus, group theory, linear algebra and real analysis. A demanding paper that rewards genuine mathematical maturity rather than technique alone.
- Mathematical Statistics
- Mathematics comprising sequences and series, differential calculus, integral calculus, matrices and differential equations; and statistics comprising probability, random variables, standard distributions, joint distributions, sampling distributions, limit theorems, estimation and testing of hypotheses. The paper is weighted towards the statistics component.
- Biotechnology
- Biology, chemistry, mathematics and physics at approximately the level of the first year of a bachelor’s degree, with biology carrying the largest share. The breadth across four subjects is what makes this paper distinctive.
- Geology
- The planet earth, geomorphology, structural geology, palaeontology, stratigraphy, mineralogy, petrology, economic geology and applied geology.
- Economics
- Microeconomics, macroeconomics, statistics for economics, Indian economy, and mathematics for economics. A paper aimed at graduates in economics and related quantitative disciplines.
The biotechnology paper deserves a specific note because its structure differs from the others: it draws on four subjects rather than one, which means a candidate with a narrow specialisation may be examined well outside it. Reading the weighting between the four before committing to that paper is worthwhile.
The published syllabus for your paper and the syllabus of your own degree course will not be identical, and the difference is where preparation gaps hide. Some topics your course covered in depth may barely appear; some the paper expects may have been optional or taught lightly at your institution. Mapping one against the other in the first week — marking each published topic as solid, rusty or never properly covered — produces a study plan calibrated to you rather than to a generic candidate.
