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1

Cell Biology: Structure of prokaryotic and eukaryotic cells, membrane structure, organelles

Biochemistry: Biological macromolecules, enzyme mechanisms, metabolism (glycolysis, TCA cycle)

Genetics: Mendel’s laws, inheritance patterns, chromosomal basis of inheritance

Molecular Biology: DNA replication, transcription, regulation of gene expression

Evolution: Natural selection, population genetics, speciation

2

Microbiology: Structural features of microorganisms, microbial metabolism

Plant Biology: Plant tissues and organs, plant hormones and responses

Animal Biology: Organ systems, basics of immunology

Ecology: Climate patterns, ecosystems, species interactions

Biotechnology Techniques: Plant tissue culture, DNA cloning, PCR

3

Atomic Structure and Bonding: Bohr's theory, chemical bonding

Thermodynamics and Equilibrium: Laws of thermodynamics, chemical kinetics

Organic Chemistry: Hydrocarbons, functional groups, reaction mechanisms

Instrumental Techniques: Basics of spectroscopy and calorimetry

4

Mechanics: Laws of motion, energy conservation, rotational motion

Thermodynamics: Heat, laws of thermodynamics, kinetic theory of gases

Electromagnetism: Electric charge, field, magnetism, electromagnetic induction

Optics: Geometrical optics, wave optics

5

Algebra and Functions: Sets, relations, functions, linear and quadratic equations

Calculus: Differentiation, integration, applications of derivatives

Statistics and Probability: Measures of dispersion, probability concepts

Vectors and Matrices: Basic operations, applications

6

Revise Biology topics, focusing on diagrams and key concepts

Revise Chemistry and practice numerical problems

Revise Physics and Mathematics, focusing on formulas and problem-solving techniques

7

Take full-length mock tests for all subjects

Review mistakes from mock tests, revise weak areas

1

Basic Concepts of Organic Chemistry: Electronic effects, stereochemistry, isomerism

Organic Reaction Mechanism: Reactive intermediates, nucleophilic substitution, elimination reactions

Synthetic Applications: Hofmann-Curtius rearrangement, oxidation/reduction reactions, functional group interconversions

2

Synthetic Applications: Diels-Alder, electrocyclic reactions, and organometallic reagents

Qualitative Organic Analysis: Functional group identification, UV, IR, and NMR spectroscopy

Natural Products Chemistry: Alkaloids, steroids, terpenes, carbohydrates, amino acids

3

Transition Metals (d-block): Characteristics, coordination complexes, crystal field theory

Organometallic Compounds: Structure, properties, and applications in catalysis

Bioinorganic Chemistry: Role of metal ions in biological systems

Instrumental Methods: Conductometry, potentiometry, UV-vis spectrophotometry

4

Chemical Kinetics: Order, molecularity, rate laws, Arrhenius equation

Chemical Kinetics: Steady state approximation, enzyme catalysis

Electrochemistry: Conductivity, Nernst equation, electrochemical series

Applications of Electrochemistry: Potentiometric titrations

5

Chemical Thermodynamics: Laws of thermodynamics, enthalpy, entropy, Gibbs free energy

Phase Equilibria: Law of mass action, Le-Chatelier principle, ionic equilibria

Gaseous State: Ideal gas behavior, van der Waals equation, Maxwell-Boltzmann distribution

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Liquid State: Properties of liquids, vapor pressure, surface tension

Solid State: Unit cells, crystal systems, X-ray diffraction

Revise Organic Chemistry topics, focusing on mechanisms and synthetic applications

7

Revise Inorganic Chemistry topics, focusing on transition metals and their properties

Revise Physical Chemistry topics, focusing on kinetics and thermodynamics

Solve previous years' question papers for all subjects

8

Take full-length mock tests for Organic, Inorganic, and Physical Chemistry

Review mistakes from mock tests, focus on weak areas

Last-minute revision of key concepts and formulas

1

Microeconomics: Consumer Theory - Preference, utility and representation theorem, budget constraint, choice, demand (ordinary and compensated), Slutsky equation, revealed preference axioms

Microeconomics: Theory of Production and Cost - Production technology, isoquants, production functions, returns to scale, short run vs. long run costs, cost curves in the short run and long run

Microeconomics: General Equilibrium and Welfare - Equilibrium and efficiency under pure exchange and production, welfare economics, theorems of welfare economics

2

Microeconomics: Market Structure - Perfect competition, monopoly, pricing with market power, price discrimination, monopolistic competition and oligopoly

Microeconomics: Game Theory - Strategic form games, Nash equilibrium, mixed strategies, examples: Cournot, Bertrand duopolies, Prisoner's dilemma

Microeconomics: Public Goods and Market Failure - Externalities, public goods, markets with asymmetric information (adverse selection and moral hazard)

3

Macroeconomics: National Income Accounting - Structure, key concepts, measurements, circular flow of income, fiscal and foreign sector variables

Macroeconomics: Behavioral and Technological Functions - Consumption functions, investment functions, money demand and supply

Macroeconomics: Business Cycles and Economic Models (Closed Economy) - Business cycles facts and features, Classical and Keynesian models, IS-LM model

4

Macroeconomics: Business Cycles and Economic Models (Open Economy) - Mundell-Fleming model, Keynesian flexible price model

Macroeconomics: Inflation and Unemployment - Inflation theories, measurement, causes, and effects; types of unemployment

Macroeconomics: Growth Models - Harrod-Domar, Solow, Neoclassical growth models

5

Statistics for Economics: Probability Theory - Sample space, events, properties of probability, random variables, probability distributions

Statistics for Economics: Mathematical Statistics - Random sampling, estimation of population parameters, sampling distribution, confidence intervals

Statistics for Economics: Hypothesis Testing - Test statistics, hypothesis testing, Type I and II errors

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Statistics for Economics: Correlation and Regression - Correlation types, regression analysis, OLS method, goodness of fit

Indian Economy: Before 1991 - Transfer of tribute, deindustrialization, planning models

Indian Economy: After 1991 - 1991 balance of payments crisis, economic reforms, trade and foreign investment

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Indian Economy: Banking, Finance and Macroeconomic Policies - Banking aspects, CRR and SLR, financial sector reforms

Indian Economy: Social Development Inequalities - Health, education, human development disparities

Indian Economy: Poverty and Labor Market - Methodology of poverty estimation, unemployment, labor force participation rates

8

Review all topics covered, focus on weak areas, summarize key concepts

Take practice exams covering all topics, review answers and explanations

1

Mineralogy: Symmetry and forms in common crystal classes, Physical properties of minerals, Classification of minerals, Structure of silicates, Optical properties of common rock-forming minerals

2

Petrology: Definition and classification of rocks, Igneous rocks: forms and evolution of magma

Petrology: Sedimentary rocks: classification and structures, Metamorphic rocks: types and controls

3

Structural Geology: Orientation of planes and lines, Geological maps and cross-section construction

Structural Geology: Classification and origin of folds, faults, and joints, Numerical problems related to outcrop data

4

Planet Earth: Origin of the Solar System and the Earth, Geosphere and the composition of the Earth, Shape and size of the Earth, Earth-Moon system, Dating rocks and age of the Earth, Volcanism and volcanic landforms

5

Planet Earth: Interior of the Earth, Earthquakes, Earth’s magnetism and gravity, Isostasy, Basic elements of Plate Tectonics, Orogenic cycles.

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Paleontology: Major steps in the evolution of life forms, Fossils and their preservation, Morphology and evolutionary trends of important groups, Gondwana plant fossils

Geomorphology: Weathering and erosion, Soil formation and landforms

7

Additional topics like Stratigraphy, Economic Geology & Applied Geology

8

Take full-length mock tests

Review mistakes from mock tests, focus on weak areas

Last-minute revision of key concepts and formulas

1

Sequences and Series of Real Numbers: Convergence of sequences, Bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem, Power series

2

Differential Equations: Bernoulli’s equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, method of separation of variables, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.

3

Functions of One Real Variable: limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, Taylor’s series, maxima and minima, Riemann integration (definite integrals and their properties), fundamental theorem of calculus

4

Integral Calculus: Double and triple integrals, Change of order of integration, Calculating surface areas and volumes using double integrals, Calculating volumes using triple integrals

5

Calculus: Functions of two or three real variables: limits, continuity, partial derivatives, total derivative, Maxima and minima for multivariable functions

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Additional Topics like: systems of linear equations, rank, nullity, rank-nullity theorem, linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange's theorem

8

Take full-length mock tests

Review mistakes from mock tests, focus on weak areas

Last-minute revision of key concepts and formulas

1

Sequences and Series of real numbers: Sequences of real numbers, their convergence, D’Alembert’s ratio test, Cauchy’s test, Leibnitz’s test

2

Differential Calculus of one and two real variables: Limits of functions of one real variable, Continuity and differentiability of functions of one real variable, Properties of continuous and differentiable functions of one real variable, Rolle's theorem and Lagrange's mean value theorems, Higher order derivatives, Lebnitz's rule, Integral Calculus:

3

Matrices and Determinants: Vector spaces with real fields, Subspaces and sum of subspaces, Span of a set, Linear dependence and independence, Dimension and basis, all matrices

4

Probability: Random Experiments, Sample Space and Algebra of Events (Event space), Convergence in probability, convergence in distribution and their inter relations, Weak law of large numbers and Central Limit Theorem (i.i.d. case) and their applications.

5

Univariate & Multivariate Distributions: Definition of random variables,Cumulative distribution function (c.d.f.) of a random variable, Discrete and Continuous random variables, Definition of random vectors. Joint and marginal c.d.f.s of a random vector, Discrete and continuous type random vectors.

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Sampling Distributions: Definitions of random sample, parameter and statistic, Sampling distribution of a statistic, Order Statistics

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Estimation: Unbiasedness, Sufficiency of a statistic, Factorization theorem, Complete statistic, Consistency and relative efficiency of estimators

Testing of hypothesis: Null and alternative hypotheses (simple and composite), Type-I and Type-II errors, Critical region

8

Take full-length mock tests

Review mistakes from mock tests, focus on weak areas

Last-minute revision of key concepts and formulas

1

Mathematical Methods: Calculus of single and multiple variables, partial derivatives, Vector algebra, Vector Calculus, Multiple integrals, Algebra of complex numbers.

2

Mechanics and General Properties of Matter: Newton’s laws of motion and applications, Velocity and acceleration in Cartesian, Motion under a central force, Kepler’s laws, Kinematics of moving fluids, equation of continuity, Euler’s equation, Bernoulli’s theorem

3

Oscillations, Waves and Optics: Differential equation for simple harmonic oscillator and its general solution, Wave equation, traveling and standing waves in one dimension

4

Electricity and Magnetism: Coulomb’s law, Gauss’s law, Electric field and potential, particles in electric and magnetic fields

5

Kinetic Theory, Thermodynamics: Elements of Kinetic theory of gases, Velocity, Laws of thermodynamics, Carnot cycle. Maxwell’s thermodynamic relations and simple applications

6

Modern Physics: Inertial frames and Galilean invariance, Postulates of special relativity, Lorentz transformations, Bohr’s atomic model, X-rays, Schrödinger equation and its solution for one, two and three dimensional boxes

7

Solid State Physics, Devices and Electronics: Crystal structure, Bravais lattices and basis, Miller indices, X-ray diffraction and Bragg's law

8

Take full-length mock tests

Review mistakes from mock tests, focus on weak areas

Last-minute revision of key concepts and formulas

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