CUET PG Syllabus 2027: Subject-Wise Topics, Topic-Wise Syllabus and PDF Download

Vector algebra, Vector calculus (divergence, curl, gradient), Multiple integrals, Divergence theorem, Green’s theorem, Stokes’ theorem, Ordinary and partial differential equations, Complex analysis (analytic functions, Cauchy-Riemann equations), Laplace and Fourier transforms, Matrices and determinants.

Newton’s laws and conservation principles, Rotational dynamics and rigid body motion, Lagrangian and Hamiltonian formulations, Central force problems and planetary motion, Elasticity and fluid mechanics, Small oscillations and normal modes, Special theory of relativity (Lorentz transformation, mass-energy equivalence).

Simple harmonic motion, Damped and forced oscillations, Resonance, Wave equation and wave propagation, Interference and diffraction, Polarisation of light, Coherence, Laser principles, Optical instruments.

Electrostatics (Gauss’s law, Laplace and Poisson equations), Magnetostatics (Biot-Savart law, Ampere’s law), Faraday’s law and electromagnetic induction, Maxwell’s equations, Electromagnetic wave propagation, AC circuits (impedance, resonance), Dielectric and magnetic materials.

Kinetic theory of gases (Maxwell-Boltzmann distribution, mean free path), Laws of thermodynamics, Entropy and the Clausius inequality, Thermodynamic potentials (free energy, Gibbs potential), Heat engines and Carnot cycle, Phase transitions, Statistical mechanics (microcanonical, canonical, and grand canonical ensembles).

Wave-particle duality and de Broglie hypothesis, Schrödinger equation (particle in a box, harmonic oscillator, hydrogen atom), Quantum numbers and atomic spectra, Operators and expectation values, Perturbation theory basics, Spin and Pauli matrices, Photoelectric effect and Compton scattering.

Nuclear structure (binding energy, radioactivity, fission, fusion), Particle physics basics (elementary particles, quarks), Band theory of solids, Semiconductors (p-n junction, transistors, FETs), Rectifiers and amplifiers, Logic gates and Boolean algebra, Digital circuits (combinational and sequential).

Quantum mechanical model of the atom, Molecular orbital theory, VSEPR theory, Hybridisation, Ionic and covalent bonding, Intermolecular forces, Hydrogen bonding, Band theory of solids.

Laws of thermodynamics, Free energy and chemical equilibria, Chemical kinetics (rate laws, activation energy, Arrhenius equation), Reaction mechanisms and transition state theory, Electrochemistry (Nernst equation, electrolysis, galvanic cells), Colligative properties.

Schrödinger equation applications in chemistry, UV-Vis, IR, NMR, and mass spectroscopy, Surface chemistry and colloidal systems, Photochemistry basics.

Nucleophilic and electrophilic substitution reactions (SN1, SN2, E1, E2), Addition reactions to alkenes and alkynes, Aromaticity and electrophilic aromatic substitution, Named reactions (Aldol, Claisen, Diels-Alder, Wittig, Grignard), Chirality, enantiomers, diastereomers, conformations.

Alcohols, ethers, aldehydes, ketones, carboxylic acids and their derivatives, Nitrogen compounds (amines, amides, nitro compounds), Carbohydrates, amino acids, proteins, lipids, nucleic acids basics.

Periodic trends in properties, s-block and p-block elements (reactions and compounds), d-block and f-block elements (electronic configurations, oxidation states, catalytic properties), Coordination compounds (naming, isomerism, Crystal Field Theory, magnetic properties), Organometallic chemistry basics, Bioinorganic chemistry (haemoglobin, chlorophyll).

Groups, subgroups, cyclic and abelian groups, cosets, normal subgroups, quotient groups, Rings, ideals, integral domains, fields, Vector spaces, linear independence, basis, dimension, Linear transformations, eigenvalues, eigenvectors, diagonalisation, Inner product spaces.

Sequences and series (convergence tests, absolute convergence), Limits, continuity, and differentiability of functions, Mean value theorems, Riemann integration, Uniform convergence, Power series, Functions of several variables (partial derivatives, Taylor series, maxima and minima).

Complex numbers and functions, Analytic functions and Cauchy-Riemann equations, Complex integration and Cauchy’s theorem, Taylor and Laurent series, Residues and contour integration.

Ordinary differential equations (first order, linear ODEs, Bernoulli equations), Higher-order linear ODEs with constant coefficients, Systems of ODEs, Laplace transforms and their applications, Partial differential equations (heat equation, wave equation, Laplace equation), Separation of variables and Fourier series.

Numerical solutions of equations (bisection, Newton-Raphson method), Interpolation (Newton’s forward/backward, Lagrange), Numerical differentiation and integration (trapezoidal rule, Simpson’s rule), Numerical solutions of ODEs (Euler’s method, Runge-Kutta), Linear programming (simplex method, duality), Game theory basics.

Arrays, stacks, queues, linked lists, trees (BST, AVL, heap), Graphs (representation, BFS, DFS), Sorting algorithms (bubble, merge, quick, heap sort), Searching algorithms (binary search, hashing), Time and space complexity analysis (Big-O notation), Dynamic programming and greedy algorithms.

Number systems (binary, octal, hexadecimal), Boolean algebra and logic gates, Combinational and sequential circuits, CPU architecture (instruction set, registers, fetch-decode-execute cycle), Memory hierarchy (cache, RAM, virtual memory), I/O organisation and DMA.

Process management (scheduling algorithms, PCB, context switching), Memory management (paging, segmentation), Deadlock (detection, prevention, avoidance), File systems and I/O management, Relational database model (ER diagrams, normalisation 1NF–BCNF), SQL (DDL, DML, joins, aggregates), Transaction management and concurrency control.

OSI and TCP/IP reference models, Network layers (physical, data link, network, transport, application), IP addressing and subnetting, Routing protocols (OSPF, BGP), TCP/UDP protocols, HTTP, FTP, DNS, SMTP, Network security basics (firewalls, encryption, SSL/TLS).

C and C++ programming (pointers, memory management, OOP concepts), Java fundamentals (classes, interfaces, exception handling), Software development life cycle (SDLC), Software design models (waterfall, agile, spiral), Software testing (unit, integration, system), Formal languages and automata (DFA, NFA, PDA, Turing machines).

Consumer theory (utility, indifference curves, budget constraints), Demand and supply analysis, Elasticity of demand and supply, Production theory (short run, long run, returns to scale), Cost curves, Market structures (perfect competition, monopoly, monopolistic competition, oligopoly), Game theory basics, Welfare economics.

National income accounting, Aggregate demand and supply, Consumption function and investment multiplier, IS-LM model, Keynesian and classical economics, Open economy macroeconomics, Growth theories (Harrod-Domar, Solow model), Business cycles.

Functions of money, Quantity theory of money, Monetary policy (tools, transmission mechanism), Inflation (types, causes, effects), Phillips curve, Banking system and credit creation, RBI and monetary policy in India.

Theories of international trade (comparative advantage, Heckscher-Ohlin), Terms of trade, Balance of payments and balance of trade, Exchange rate determination (fixed vs. floating), WTO, IMF, and World Bank, Trade policy instruments (tariffs, quotas, subsidies).

Sectors of Indian economy (agriculture, industry, services), Five-year plans and economic planning, Economic reforms (1991 liberalisation and beyond), Poverty and income inequality, Employment and unemployment, Infrastructure development, Government budget and fiscal policy.

Probability theory, Probability distributions (binomial, Poisson, normal), Sampling and estimation, Hypothesis testing, Regression analysis, Time series analysis, Index numbers.

Differential calculus and optimisation, Matrix algebra and linear equations, Constrained optimisation (Lagrangian method), Difference equations and dynamic analysis, Linear programming.

Prehistoric cultures, Indus Valley Civilisation (urban planning, trade, decline), Vedic Age (Rig Vedic and later Vedic society), Mahajanapada period and the rise of cities, Mauryan Empire (Ashoka, administration, dhamma), Post-Mauryan period (Kushans, Satavahanas), Gupta Empire (golden age, arts, science), Sources and historiography of ancient India.

Early medieval kingdoms, Delhi Sultanate (different dynasties, Iqta system, administration), Vijayanagara and Bahmani kingdoms, Bhakti and Sufi movements, Mughal Empire (Akbar, Aurangzeb, administration, agrarian system), Provincial kingdoms and their cultural contributions, Indo-Persian culture and society.

British expansion in India (Battle of Plassey, Buxar), Economic impact of British rule (de-industrialisation, drain of wealth), Socio-religious reform movements (Brahmo Samaj, Arya Samaj, Aligarh Movement), 1857 revolt, Indian National Congress and freedom movement, Gandhian nationalism (Non-Cooperation, Civil Disobedience, Quit India), Partition and Independence.

Renaissance and Reformation, French and American Revolutions, Industrial Revolution and its social impact, World War I (causes, consequences, Paris Peace Settlement), World War II (causes, Holocaust, aftermath), Cold War and decolonisation, United Nations and contemporary world order.

Concepts of state, sovereignty, and power, Liberty, equality, rights, and justice, Democracy (types and theories), Political ideologies (liberalism, Marxism, socialism, fascism, anarchism), Political thinkers (Plato, Aristotle, Locke, Rousseau, Marx, Rawls), Feminism and multiculturalism in political theory.

Constitutional framework (Preamble, Fundamental Rights, DPSP), Parliament (Lok Sabha, Rajya Sabha, legislative process), President and Prime Minister (powers and roles), Judiciary (Supreme Court, High Courts, judicial review), Federalism and Centre-State relations, Electoral system and Election Commission, Political parties and coalition politics.

Comparative methods in political science, Presidential vs. parliamentary systems, Federal and unitary systems, Political culture and socialisation, Political parties and party systems, Democratisation and democratic transitions, State-building and governance in the Global South.

IR theories (realism, liberalism, constructivism, dependency theory), Foreign policy concepts (national interest, power, decision-making), India’s foreign policy (Non-Alignment, Look East/Act East, Neighbourhood First), United Nations system, Regional organisations (SAARC, ASEAN, EU), Contemporary issues (terrorism, climate change, nuclear proliferation).

Forms of business organisation, Management functions (planning, organising, directing, controlling), Leadership styles and motivation theories, Human resource management basics, Business communication.

Financial accounting (journal, ledger, trial balance, final accounts), Company accounts (shares, debentures, dividends), Ratio analysis and fund flow/cash flow statements, Cost accounting (marginal costing, standard costing), Capital structure, leverage, and capital budgeting, Working capital management.

Demand analysis and forecasting, Cost and revenue concepts, Market structures and pricing, National income and business cycles, Business cycles and economic indicators, Indian economy and government policy.

Marketing mix (4Ps), Consumer behaviour, Market segmentation and targeting, Basic statistics (mean, median, mode, standard deviation), Probability, Index numbers, Time series analysis, Operations research basics.