APPSC FAO/TO & STO Syllabus 2026 — Commercial Maths + 4 Optionals

APPSC FAO/TO & STO Updated: 06 Sep 2026

Syllabus

APPSC FAO/TO & STO has published the syllabus for this recruitment. Download it only from the official website appsc.gov.in.

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The PDF opens on the official site. Every topic in it is explained in plain language below — you do not have to open the PDF to read the syllabus.

Compiled from the official syllabus · check it against the official link

What this notification actually contains — its seven parts ↑

On 16 July 2026 APPSC issued notification No. PSC-R/10/2026 fixing the syllabus for direct recruitment to the FAO/TO and STO posts. The document runs to 20 pages in five annexures — one for the Recruitment Test, and four for optional subjects.

Every one of those five annexures is set out below, topic by topic, with our own plain-language note against each. Where the notification is silent we say so in as many words instead of filling the gap with a guess.

What the notification states	What it means for you
Finance and Accounts Officer/ Treasury Officer (FAO/ TO) and Sub-Treasury Officer (STO)	The syllabus is for direct recruitment to these two posts. The notification issues one common syllabus for both.
No.PSC-R/10/2026, Dated Itanagar, the 16th July, 2026	The notification's number and date. This is the reference you quote in any query or representation, so note it down.
Syllabus of Commercial Mathematics (200 Marks) for Recruitment Test (RT) in Annexure-I	This is the only place the notification states marks — 200 for Commercial Mathematics in the Recruitment Test. That paper's full syllabus is set out unit by unit below.
Syllabus of Optional Papers (Commerce) in Annexure-II	The Commerce optional syllabus. It has two papers: Paper-I (accounting, taxation, auditing and finance) and Paper-II (organisation, HRM and industrial relations).
Syllabus of Optional Papers (Economics) in Annexure-III	The Economics optional syllabus — Paper-I is theory (micro, macro, money, international trade, growth) and Paper-II is the Indian economy.
Syllabus of Optional Papers (Mathematics) in Annexure-IV	The Mathematics optional syllabus — two papers of degree and post-degree level pure and applied mathematics.
Syllabus of Optional Papers (Statistics) in Annexure-V	The Statistics optional syllabus — Paper-I is probability and inference, Paper-II is industrial statistics, optimisation and official statistics.

Commercial Mathematics (200 marks) — the twelve units the notification lists ↑

Marks appear at exactly one place in the whole notification: 200 for Commercial Mathematics in the Recruitment Test. That makes this paper the first and firmest claim on your preparation. Its syllabus runs in twelve numbered units, and the notification itself lists sub-topics under each.

The twelve units are set out first in one view; after that, two tables carry every sub-topic under each unit, in the order the notification prints them.

Unit as the notification prints it	What it covers, and how to approach it
1. Percentage	Percentage — the base of the whole paper. Interest, profit and loss and discount all stand on it, so finish this unit first and finish it properly.
2. Profit, Loss and Discount	Profit, loss and discount — the market arithmetic of cost price, selling price, marked price and chains of discount.
3. Simple Interest (SI)	Simple interest — the direct relationship between principal, rate and time. One formula, but the question can be asked from any end.
4. Compound Interest (CI)	Compound interest — interest upon interest. Directly connected to treasury work, so do not treat it lightly.
5. Banker's Discount and Bills of Exchange	The arithmetic of cashing a bill before the day it falls due. It rarely turns up in general competitive preparation, which is exactly why it needs its own slot in your timetable.
6. Partnership and Division of Money	Partnership and division of money — splitting profit in the ratio of capital and time.
7. Ratio and Proportion	Ratio and proportion — comparing quantities. Rarely asked on its own, but hidden inside almost every other unit.
8. Time and Interest Applications	Time and interest applications — questions that join time to money: present value and the settling of accounts.
9. Probability	Probability — kept at a basic level in this paper, as its own sub-list below makes clear.
10. Linear Equations/Algebraic Word Problems	Linear equations and algebraic word problems — turning a story into an equation and solving it.
11. Time and Work	Time and work — the notification also files averages (mean, average speed, average age) under this unit, which the name does not suggest. Read its sub-list below.
12. Basic Statistics	Basic statistics — only three items: mean, median and mode. Nothing beyond that is asked.

Units 1 to 6 — every sub-topic the notification lists ↑

The first six units are percentage, profit and loss, interest, banker's discount and partnership. Watch unit 5 in particular — bills of exchange and banker's discount rarely appear in general competitive preparation, and that is exactly where otherwise-prepared candidates leave marks behind.

Topic as the notification prints it	What it means and how to prepare it
Percentage — Conversion between fraction, decimal, percentage	Converting between fraction, decimal and percentage. Knowing conversions like 1/8 = 0.125 = 12.5% by heart halves the time on everything else.
Percentage — Percentage increase and decrease	How much a number rises or falls in percentage terms, and working back to the original figure from the changed one.
Percentage — Comparison of percentages	Comparing two percentages. The real question is always what each one is a percentage of.
Percentage — Successive percentage change	Percentage changes applied one after another. A 10% rise followed by a 10% fall does not return you to the original figure — that is the whole point of this item.
Percentage — Relationship between quantities using percentage	Stating the relation between two quantities in percentage terms — 'A is what percent more than B' type questions.
Profit, Loss and Discount — Cost Price (CP), Selling Price (SP)	Cost price and selling price — the two base terms of this entire unit.
Profit, Loss and Discount — Profit and Loss percentage	Profit or loss as a percentage, always calculated on cost price — the single commonest place to slip.
Profit, Loss and Discount — Marked Price (MP)	Marked price — the price written on the goods, the one the discount comes off.
Profit, Loss and Discount — Trade discount	Trade discount — the reduction allowed on the marked price.
Profit, Loss and Discount — Successive discount	Two discounts one after the other — 20% then 10% is not 30%. This is the twin of successive percentage change.
Profit, Loss and Discount — Profit or loss after discounts	How much profit or loss actually remains after the discounts are given — the shopkeeper's real question.
Profit, Loss and Discount — Equal profit and loss situations	Situations of equal profit and loss — sell two items, one at the same percentage gain and one at that loss, and the net result is still a loss.
Simple Interest (SI) — Principal, Rate, Time relationship	The relationship between principal, rate and time — the one formula simple interest runs on.
Simple Interest (SI) — Finding rate, time, principal	The interest is given and the rate, time or principal is asked — running the same formula backwards.
Simple Interest (SI) — Interest over different periods	Interest over different periods — this is where months and days must be converted into years.
Simple Interest (SI) — Multiple loans at different rates	Several loans taken at different rates — questions asking for the total interest or the average rate.
Compound Interest (CI) — Compound Interest	The concept itself — each period's interest joins the principal and earns interest in the next period.
Compound Interest (CI) — Annual compounding	Annual compounding — interest added once a year, the simplest form.
Compound Interest (CI) — Half-yearly/Quarterly compounding	Half-yearly and quarterly compounding — halve or quarter the rate and double or quadruple the periods. That one rule is the whole item.
Compound Interest (CI) — Difference between SI and CI	The difference between simple and compound interest — remember the short formula for the two-year gap; it is asked directly.
Compound Interest (CI) — Compound Interest for factional	Compound interest for a part period, such as two years and six months. (The notification prints this line exactly this way, incomplete; we have left it as printed rather than completing it for the commission.)
Banker's Discount and Bills of Exchange — Bill of exchange	A bill of exchange — a written undertaking to pay a fixed sum on a fixed date. Every question in this unit starts here.
Banker's Discount and Bills of Exchange — True Discount	True discount — the gap between the bill's face value and what it is worth today.
Banker's Discount and Bills of Exchange — Banker's Discount	Banker's discount — the interest a bank charges on the bill's full face value, not on its present worth. That is exactly what separates it from true discount.
Banker's Discount and Bills of Exchange — Banker's Gain	Banker's gain — the difference between banker's discount and true discount, which is what the bank actually makes.
Banker's Discount and Bills of Exchange — Present worth of a bill	The present worth of a bill — the sum which, paid today, would grow to the bill's face value by its due date.
Banker's Discount and Bills of Exchange — Time of bill	The time of the bill — how long is left until it falls due, which is what the whole calculation hangs on.
Partnership and Division of Money — Investment sharing	Investment sharing — how much each partner put in, and for how long.
Partnership and Division of Money — Profit distribution	Profit distribution — in the ratio of capital multiplied by time. That single idea solves most of these questions.
Partnership and Division of Money — Division of sum with equal interest conditions	Dividing a sum so that, on the stated conditions, each share earns the same interest.
Partnership and Division of Money — Loans at different rates	Loans split across different rates — working out which part was lent at which rate.

At a glance

Conducting Body	Arunachal Pradesh Public Service Commission (APPSC)
Post Name	Finance and Accounts Officer/Treasury Officer (FAO/TO) and Sub-Treasury Officer (STO)
Official Website	appsc.gov.in
State	Andhra Pradesh

Units 7 to 12 — every sub-topic the notification lists ↑

The remaining six units are ratio, time-and-interest, probability, equations, time-and-work and basic statistics. One thing to look at closely: the notification files arithmetic mean, average speed and average age under the 'Time and Work' unit, which its name does not suggest at all. Skip that unit on the strength of its title and you lose a whole topic.

Topic as the notification prints it	What it means and how to prepare it
Ratio and Proportion — Ratio formation	Forming a ratio — writing two or more quantities in their simplest comparable form.
Ratio and Proportion — Ratio from percentage difference	Getting a ratio out of a percentage difference — turning 'A is 25% more than B' into 5:4.
Ratio and Proportion — Comparison between numbers	Comparison between numbers — which is larger, and by what multiple.
Ratio and Proportion — Proportion relationships	Proportion relationships — finding the fourth quantity when three are known.
Ratio and Proportion — Direct/Indirect proportions	Direct and inverse proportion — whether the second quantity rises or falls with the first. The root of every time-and-work question.
Time and Interest Applications — Time value of money	The time value of money — a hundred rupees today is worth more than a hundred rupees a year from now. For a treasury post, that way of thinking is the real subject.
Time and Interest Applications — Settling accounts	Settling accounts — clearing several sums falling due on different dates as one payment.
Time and Interest Applications — Present value calculations	Present value calculations — what a future sum is worth today.
Time and Interest Applications — Interest for fractional time periods	Interest for part periods — converting months and days into years correctly.
Probability — Probability formula	The probability formula — favourable outcomes over total outcomes. This paper does not go past that.
Probability — Coin toss probability	Coin toss probability — writing out every possible outcome for one, two or three coins is the safest method.
Probability — Simple problems on Event outcome	Simple problems on event outcomes — the familiar dice, ball and card examples.
Linear Equations/Algebraic Word Problems — Forming equations from statements	Forming equations from statements — the difficulty is never the solving, it is writing the right equation.
Linear Equations/Algebraic Word Problems — Solving single variable equations, Quadratics Equations	Solving single-variable equations and quadratic equations. Note that the notification asks for quadratics right here, which the unit's name does not reveal.
Linear Equations/Algebraic Word Problems — Percentage equations	Percentage equations — the point where unit 1 and unit 10 meet.
Time and Work — Arithmetic Mean, Problems on Average Speed, Average Age etc.	Arithmetic mean, average speed and average age problems. The notification files these under 'Time and Work', so do not skip averages thinking they are a separate subject.
Time and Work — Work rate problems	Work rate problems — think in terms of how much is done in one day and every question opens up.
Time and Work — Efficiency comparison	Efficiency comparison — who works how much faster, and what that does to the time taken.
Time and Work — Work-Wages problems	Work and wages — the wage divides in the same ratio as the work done.
Basic Statistics — Mean	Mean — add them all and divide by how many. Look at the weighted mean alongside the simple one.
Basic Statistics — Median	Median — the middle value once the data is put in order; the average of the middle two when the count is even.
Basic Statistics — Mode	Mode — the value that occurs most often. A set of data can have more than one.

The four optional subjects — and what the notification does not say about choosing one ↑

The notification gives the syllabus for four optional subjects: Commerce, Economics, Mathematics and Statistics. Each has two papers, and each is set out in full below.

One thing has to be said plainly here. The notification nowhere states how many optional subjects a candidate offers, on what basis the choice is made, or what these papers carry in marks. That comes with the recruitment advertisement. We will not fill the gap with a guess — on a page you plan a year around, an invented figure is the most dangerous thing on it.

Optional subject	What its two papers contain
Commerce (Annexure-II)	Two papers. Paper-I: financial accounting, cost accounting, taxation, auditing, financial management and financial markets. Paper-II: organisation theory and behaviour, human resource management and industrial relations.
Economics (Annexure-III)	Two papers. Paper-I: advanced micro and macro economics, money-banking-finance, international economics, growth and development. Paper-II: the Indian economy since independence, split into the pre-liberalization and post-liberalization eras.
Mathematics (Annexure-IV)	Two papers. Paper-I: linear algebra, calculus, analytic geometry, ordinary differential equations, dynamics and statics, vector analysis. Paper-II: algebra, real and complex analysis, linear programming, partial differential equations, numerical analysis and computer programming, mechanics and fluid dynamics.
Statistics (Annexure-V)	Two papers. Paper-I: probability, statistical inference, linear inference and multivariate analysis, sampling theory and design of experiments. Paper-II: industrial statistics, optimization techniques, quantitative economics and official statistics, demography and psychometry.

Commerce, Paper-I — accounting, cost, taxation and auditing ↑

The notification heads this half of the paper 'Accounting and Finance Accounting, Taxation & Auditing' and runs it in four numbered units. The heaviest ground is accounting standards and taxation.

There is one piece of relief inside the taxation unit that most candidates read past: the notification says in as many words that the computation problems are of individuals only. That narrows what you have to prepare considerably.

Topic as the notification prints it	What it means and how to prepare it
Financial Accounting — Accounting as a financial information system; Impact of behavioural sciences	Accounting seen as an information system — the books are not just a record but the basis of decisions; and how human behaviour bends that information.
Financial Accounting — Accounting Standards for Depreciation, Inventories, Research and Development Costs, Long-term Construction Contracts, Revenue Recognition, Fixed Assets, Contingencies, Foreign Exchange Transactions, Investments and Government Grants, Cash Flow Statement	Accounting standards across ten areas, from depreciation to the cash flow statement. Take each standard separately — this is the heaviest and most-asked part of the unit.
Financial Accounting — Accounting for Share Capital Transactions including Bonus Shares, Right Shares	The entries a company passes when it hands shares to its existing owners — free in one case, at a concession in the other. Keep clear which is which.
Financial Accounting — Employees Stock Option and Buy-Back of Securities	Employee stock options and the buy-back of securities — in both the company deals in its own shares, so study them together.
Financial Accounting — Preparation and Presentation of Company Final Accounts	Preparing and presenting a company's final accounts — the balance sheet and profit and loss account in their prescribed form.
Financial Accounting — Amalgamations, Absorption and Reconstruction of Companies	Amalgamation, absorption and reconstruction of companies — three distinct situations; keep the distinction clear, because the question usually turns on it.
Cost Accounting — Nature and functions of cost accounting; Installation of Cost Accounting System	What cost accounting is and does, and how a cost accounting system is installed in an organisation.
Cost Accounting — Cost Concepts related to Income Measurement, Profit Planning, Cost Control and Decision Making	Cost concepts tied to four uses — measuring income, planning profit, controlling cost and taking decisions. The same cost is read differently for different purposes; that is the core idea.
Cost Accounting — Methods of Costing: Job Costing, Contract Costing, Process Costing, Activity Based Costing	Four costing methods. Learn them paired with the kind of industry each suits.
Cost Accounting — Volume-cost-Profit Relationship as a tool of Profit Planning	The volume-cost-profit relationship. Break-even point and contribution are the tools that live under this item.
Cost Accounting — Incremental Analysis/Differential Costing as a Tool of Pricing Decisions, Product Decisions, Make or Buy Decisions, Shut-Down Decisions etc.	Incremental analysis applied to pricing, product choice, make-or-buy and shut-down decisions. These are the four real management decisions and they usually arrive as numerical questions.
Cost Accounting — Techniques of Cost Control and Cost Reduction: Budgeting as a Tool of Planning and Control; Standard Costing and Variance Analysis	Cost control techniques — budgeting, standard costing and variance analysis. For a treasury post the budgeting half is directly job-relevant.
Cost Accounting — Responsibility Accounting and Divisional Performance Measurement	Responsibility accounting — each division answerable for its own costs, and measured on that basis.
Taxation — Income Tax: Basis of charge; Incomes which do not form part of total income	The foundation of income tax — on what basis tax is charged, and which incomes are left out of total income altogether.
Taxation — Simple problems of Computation of total Income and tax liability (of individuals only) under various heads i.e., Salaries, Income from House Property, Profits and Gains from Business or Profession, Capital Gains, Income from other sources, Income of other Persons included in Assessee's Total Income	Computing total income and tax liability across the five heads, including other persons' income clubbed in. Note that the notification limits these problems to individuals only, not companies — that narrows your preparation considerably.
Taxation — Set-off and Carry forward of Loss; Deductions from Gross Total Income	Setting off and carrying forward losses, and the deductions allowed from gross total income.
Taxation — Salient Features/Provisions Related to VAT and Good and Services Tax	The salient features of VAT and GST. Note that the notification asks for salient features here, not a section-by-section reading of the statute.
Auditing — Internal check and control	Internal check and control — the arrangements inside an organisation that stop error and fraud before they happen. Directly related to treasury work.
Auditing — Company Audit: Audit related to Divisible Profits, Dividends, Special investigations, Tax audit	Company audit — divisible profits, dividends, special investigations and tax audit.
Auditing — Audit of Banking, Insurance, Non-Profit Organization and Charitable Societies/ Trusts/ Organizations	Audit of banks, insurers, non-profit bodies and charitable trusts — each type carries its own rules, so read them separately.

Commerce, Paper-I continued — financial management, financial institutions and markets ↑

The second half of the same paper is finance, which the notification places under its own heading, 'Financial Management, Financial Institutions and Markets'. Much of it is numerical — cost of capital, leverage, dividend models — so it is learned by solving, not by reading.

Topic as the notification prints it	What it means and how to prepare it
Financial Management — Finance Function: Nature, Scope and Objectives of Financial Management: Risk and Return Relationship	The nature, scope and objectives of the finance function, and the risk-return relationship — more return demands more risk, the first rule of finance.
Financial Management — Tools of Financial Analysis: Ratio Analysis, Funds-Flow and Cash- Flow Statement	Reading a company's health out of its own statements. Ratios are the examiner's favourite here because they can be asked both as a small calculation and as a one-line interpretation.
Financial Management — Capital Budgeting Decisions: Process, Procedures and Appraisal Methods; Risk and Uncertainty Analysis and Methods	Capital budgeting decisions — the process and methods for appraising long-term investment, and the analysis of risk and uncertainty within it.
Financial Management — Cost of Capital: Concept, Computation of Specific Costs and Weighted Average Cost of Capital; CAPM as a Tool of Determining Cost of Equity Capital	The cost of capital — the cost of each source, the weighted average, and CAPM as the way to find the cost of equity.
Financial Management — Financing Decisions: Theories of Capital Structure—Net Income (NI) Approach, Net Operating Income (NOI) Approach, MM Approach and Traditional Approach	Financing decisions and the four theories of capital structure. Study all four side by side — the question always turns on how they differ.
Financial Management — Designing of Capital Structure: Types of Leverages (Operating, Financial and Combined), EBIT-EPS Analysis, and other Factors	Designing the capital structure — the three kinds of leverage and EBIT-EPS analysis. This part is numerical, so it only sticks by solving problems.
Financial Management — Dividend Decisions and Valuation of Firm: Walter's Model, MM Thesis, Gordon's Model, Lintner's Model; Factors Affecting Dividend Policy	Dividend decisions and firm valuation — four named models plus the factors that shape dividend policy. The models are asked by name, so tie each name to its conclusion.
Financial Management — Working Capital Management: Planning of Working Capital; Determinants of Working Capital; Components of Working Capital— Cash, Inventory and Receivables	Working capital management — its planning, its determinants, and its three components: cash, inventory and receivables. This is the centre of day-to-day finance.
Financial Markets and Institutions — Indian Financial System: An Overview	An overview of the Indian financial system — which institution sits where. Draw this map before reading the rest.
Financial Markets and Institutions — Money Markets: Participants, Structure and Instruments; Commercial Banks; Reforms in Banking Sector; Monetary and Credit Policy of RBI; RBI as a Regulator	The money market — its participants, structure and instruments; commercial banks; banking sector reform; the RBI's monetary and credit policy and its role as regulator.
Financial Markets and Institutions — Capital Market: Primary and Secondary Market; Financial Market Instruments and Innovative Debt Instruments; SEBI as a Regulator	The capital market — primary and secondary markets, market instruments and innovative debt instruments, and SEBI as regulator.
Financial Markets and Institutions — Financial Services: Mutual Funds, Venture Capital, Credit Rating Agencies, SEBI, Insurance and IRDA	The institutions that stand between a saver and a borrower, and the two regulators watching them. Which regulator covers which is where the question is made.

Commerce, Paper-II — organisation, human resources and industrial relations ↑

The notification heads this paper 'Organisation Theory and Behaviours, Human Resource Management and Industrial Relations'. It is theory throughout, with no calculation, so marks here come from holding the names of the theories and the differences between them.

Topic as the notification prints it	What it means and how to prepare it
Organisation Theory — Nature and Concept of Organisation	The nature and concept of an organisation — what it is, and how it differs from a mere group of people.
Organisation Theory — External Environment of Organisation—Technological, Social, Political, Economical and Legal	The organisation's external environment across five heads — technological, social, political, economic and legal. Fix each with its own example.
Organisation Theory — Organizational Goals Primary and Secondary Goals, Single and Multiple Goals; Management by Objectives	Organisational goals — primary and secondary, single and multiple — and management by objectives.
Organisation Theory — Evolution of Organisation theory: Classical, Neo-classical and system approach	The evolution of organisation theory — the classical, neo-classical and systems approaches. Remember their order and their differences.
Organisation Theory — Modern Concepts of Organisation Theory: Organisational Design, Organisational Structure and Organisational Culture	The modern concepts — organisational design, structure and culture. Design is decided, structure is visible, culture is felt.
Organisation Theory — Organisational Design—Basic Challenges; Differentiation and Integration Process; Centralization and Decentralization Process; Standardization/Formalization and Mutual Adjustment; Coordinating Formal and Informal Organizations	The basic challenges of organisational design — differentiation and integration, centralization and decentralization, standardization and mutual adjustment, and coordinating the formal with the informal organisation.
Organisation Theory — Designing Organizational structures—Authority and Control; Line and Staff Functions, Specialization and Coordination; Types of Organization Structure — Functional, Matrix Structure, Project Structure	How a company draws its own chart — who answers to whom, and who is allowed to decide. The three types are best learned through one real company that uses each.
Organisation Theory — Nature and Basis of Power, Sources of Power, Power Structure and Politics; Impact of Information Technology on Organizational Design and Structure	The nature, basis and sources of power, power structure and organisational politics; and how information technology has reshaped design and structure.
Organisation Behaviour — Meaning and Concept; Individual in organization: Personality, Theories and Determinants; Perception—Meaning and Process	The meaning of organisational behaviour; the individual in the organisation — personality theories and determinants; and the process of perception.
Organisation Behaviour — Motivation: Concepts, Theories and Applications; Leadership— Theories and Styles	Motivation — concepts, theories and applications; and leadership theories and styles. Both are asked by the name of the theory.
Organisation Behaviour — Quality of Work Life (QWL): Meaning and its impact on Performance, Ways of its Enhancement; Quality Circles (QC)—Meaning and their Importance	Quality of work life — its meaning, its effect on performance and the ways to improve it; and quality circles and why they matter.
Organisation Behaviour — Management of Conflicts in Organizations; Transactional Analysis; Organizational Effectiveness; Management of Change	Managing conflict in organisations, transactional analysis, organisational effectiveness and the management of change.
Human Resources Management (HRM) — Meaning, Nature and Scope of HRM; Human Resource Planning	The meaning, nature and scope of HRM, and human resource planning — how many people with what skills are needed, and when.
Human Resources Management (HRM) — Job Analysis, Job Description, Job Specification	Job analysis, job description and job specification — three different things, and the exam builds its question on that difference.
Human Resources Management (HRM) — Recruitment Process, Selection Process, Orientation and Placement, Training and Development Process	The recruitment and selection process, orientation and placement, and the training and development process.
Human Resources Management (HRM) — Performance Appraisal and 360° Feed Back, Salary and Wage Administration, Job Evaluation; Employee Welfare, Promotions, Transfers and Separations	Everything that happens to an employee after joining — being judged, being paid, being moved, and finally leaving. A long list, but the part of HRM whose questions are easiest to predict.
Industrial Relations (IR) — Meaning, Nature, Importance and Scope of IR	The meaning, nature, importance and scope of industrial relations — the study of the three-way relationship between employer, worker and the state.
Industrial Relations (IR) — Formation of Trade Union, Trade Union Legislation, Trade Union Movement in India	The formation of a trade union, the legislation governing it, and the history of the trade union movement in India.
Industrial Relations (IR) — Recognition of Trade Unions, Problems of Trade Unions in India; Impact of Liberalization on Trade Union Movement	Recognition of trade unions, the problems Indian unions face, and the effect of liberalization on the movement.
Industrial Relations (IR) — Nature of Industrial Disputes: Strikes and Lockouts, Causes of Disputes, Prevention and Settlement of Disputes	Industrial disputes — strikes and lockouts, the causes of disputes, and how they are prevented and settled.
Industrial Relations (IR) — Worker's Participation in Management: Philosophy, Rationale, Present Day Status and Future Prospects	Workers' participation in management — its philosophy, its rationale, where it stands today and where it may go.
Industrial Relations (IR) — Adjudication, Reconciliation and Collective Bargaining	Adjudication, reconciliation and collective bargaining — three routes out of a dispute. The difference asked about is who decides in each.
Industrial Relations (IR) — Industrial Relations in Public Enterprises; Absenteeism and Labour Turnover in Indian Industries and their Causes and Remedies	Industrial relations in public enterprises; and absenteeism and labour turnover in Indian industry, their causes and their remedies.
Industrial Relations (IR) — ILO and its Functions	The International Labour Organisation and its functions — the only international item in this whole paper, so do not skip it.

Economics, Paper-I — units 1 to 3: micro, macro and money ↑

Economics Paper-I has five units. The first three are theory: advanced micro-economics, macro-economics, and money-banking-finance. Most items here are asked by economist's name, so tie one central argument to each name.

Topic as the notification prints it	What it means and how to prepare it
Advanced Micro-Economics — (a) Marshallian and Walrasian Approaches to Price determination	Two approaches to price determination — Marshall's partial equilibrium and Walras's general equilibrium. One looks at a single market, the other at all markets together.
Advanced Micro-Economics — (b) Alternative Distribution Theories; Ricardo, Kaldor, Kaleeki	Alternative theories of distribution from three named economists. They are asked by name, so tie each name to its central argument.
Advanced Micro-Economics — (c) Markets Structure: Monopolistic Competition, Duopoly, Oligopoly	Market structure — monopolistic competition, duopoly and oligopoly. The real difference between them is the number of sellers and how far each depends on the others.
Advanced Micro-Economics — (d) Modern Welfare Criteria: Pareto Hicks and Scitovsky, Arrow's Impossibility Theorem, A. K. Sen's Social Welfare Function	How economists judge whether a change leaves society better off, and the famous proof that no voting rule can settle it perfectly. Sen's answer to that problem is the part asked most often.
Advance Macro- Economics — Approaches to Employment Income and Interest Rate determination: Classical, Keynes (IS)-LM) curve, Neo-classical synthesis and New classical	Approaches to the determination of employment, income and the interest rate — classical, Keynes's IS-LM, the neo-classical synthesis and New Classical. (The notification prints this unit as 'Advance Macro-Economics'; we have kept its spelling.)
Advance Macro- Economics — Theories of Interest Rate determination and Interest Rate Structure	Theories of interest rate determination and the structure of interest rates — practically useful ground for a treasury post.
Money-Banking and Finance — (a) Demand for and Supply of Money: Money Multiplier Quantity Theory of Money (Fisher, Pique and Friedman) and Keynes's Theory on Demand for Money	The demand for and supply of money — the money multiplier, the quantity theory of money (Fisher, Pigou and Friedman) and Keynes's theory of the demand for money.
Money-Banking and Finance — (a) Goals and Instruments of Monetary Management in Closed and Open Economies; Relation between the Central Bank and the Treasury; Proposal for ceiling on growth rate of money	What a central bank is trying to achieve, the levers it has, and how it must deal with the government's own purse. That last part touches the job you are applying for directly.
Money-Banking and Finance — (b) Public Finance and its Role in market Economy: In stabilisation of supply, allocation of resources and in distribution and envelopment	Public finance and its role in a market economy — stabilising supply, allocating resources, and distribution and development.
Money-Banking and Finance — (b) Sources of Government revenue, forms of Taxes and Subsidies, their incidence and effects; Limits to taxation, loans, crowding-out effects and limits to borrowing; Public expenditure and its effects	Sources of government revenue, the forms of taxes and subsidies and where their burden falls; the limits of taxation and borrowing and crowding-out effects; and public expenditure and its effects.

Economics, Paper-I — units 4 and 5: international economics, growth and development ↑

These two units are the largest part of Paper-I, and the notification breaks them into lettered and roman-numbered sub-items in fine detail. Every sub-item is set out below in the notification's own order and numbering, so you can match it against the real paper.

Topic as the notification prints it	What it means and how to prepare it
International Economics — (a) Old and New theories of International Trade: (i) Comparative advantage	Comparative advantage — the oldest and most basic argument in trade: each country should make what it gives up least to make.
International Economics — (a) (ii) Terms of Trade and Offer Curve	Terms of trade and the offer curve — the ratio between export and import prices, and how that rate settles.
International Economics — (a) (iii) Product Cycle and Strategic Trade Theories	Product cycle and strategic trade theories — where a new product is first made, and how its making later migrates elsewhere.
International Economics — (a) (iv) Trade as an engine of growth and theories of underdevelopment in an open economy	The oldest argument in development economics, and the case against it. Prepare both sides — this item is written to invite a discussion, not a definition.
International Economics — (b) Empirical Models of International Trade: Gravity Model of trade, Outsourcing and International Trade, Time zone differences and International Trade, Inter-industry Trade- Lloyd-Grubel Index	Empirical models of international trade — the gravity model, outsourcing, time-zone differences, and the Lloyd-Grubel index of inter-industry trade.
International Economics — (c) Forms of Protection: Tariff and quota	Forms of protection — tariff and quota. Both hold back imports, but only the tariff brings the government revenue.
International Economics — (d) Balance of Payments Adjustment: (i) Price versus income, income adjustments under fixed exchange rates	Balance of payments adjustment — price versus income, and income adjustment under fixed exchange rates.
International Economics — (d) (ii) Theories of Policy Mix	Theories of the policy mix — how fiscal and monetary policy are run together.
International Economics — (d) (iii) Exchange rate adjustments under capital mobility	Exchange rate adjustment under capital mobility — what free movement of capital does to the rate.
International Economics — (d) (iv) Floating Rates and their Implications for Developing Countries: Currency Boards	Floating rates and what they mean for developing countries, and currency boards.
International Economics — (d) (v) Trade Policy and Developing Countries	Trade policy and developing countries — the choice between protection and openness.
International Economics — (d) (vi) BOP adjustments and Policy Coordination in open economy macro model	Balance of payments adjustment and policy coordination inside an open-economy macro model.
International Economics — (d) (vii) Speculative attacks	Speculative attacks — the sudden pressure on a currency that breaks a pegged exchange rate.
International Economics — (d) (viii) Trade Blocks and Monetary Unions	Trade blocs and monetary unions — the ladder from a regional agreement up to a shared currency.
International Economics — (d) (ix) WTO: TRIMS, TRIPS, Domestic Measures, Different Rounds of WTO talks	The WTO — TRIMS, TRIPS, domestic measures and the different rounds of talks. This item connects directly to current affairs.
Growth and Development — (a) (i) Theories of growth: Harrod's model	Theories of growth — Harrod's model, in which the savings rate and the capital-output ratio fix the growth rate.
Growth and Development — (a) (ii) Lewis model of development with surplus labour	Lewis's model of development with surplus labour — the countryside's spare labour moving into industry and driving growth.
Growth and Development — (a) (iii) Balanced Unbalanced Growth	Balanced versus unbalanced growth — invest across all sectors at once, or in a few chosen ones. An old and clean debate.
Growth and Development — (a) (iv) Human Capitals and Economic Growth	Human capital and economic growth — spending on education and health is investment, not consumption.
Growth and Development — (a) (v) Research and Development and Economic Growth	Research and development and economic growth — how new technology becomes the real source of long-run growth.
Growth and Development — (b) Process of Economic Development of less developed countries: Myrdal and Kuznets' on economic development and structural change; Role of Agriculture in Economic Development of less developed countries	Why poor countries stay poor, answered by two economists who did not agree about it, and the place farming holds in climbing out. Attach one clear idea to each name.
Growth and Development — (c) Economic Development and International Trade and Investment, Role of Multinationals	Economic development in relation to international trade and investment, and the role of multinationals.
Growth and Development — (d) Planning and Economic Development: changing role of Markets and Planning, Private-Public Partnership	Planning and economic development — the changing roles of markets and planning, and public-private partnership.
Growth and Development — (e) Welfare indicators and measures of growth—Human Development Indices; The basic needs approach	The case that a country's income and its people's wellbeing are not the same thing, and the yardsticks built to measure the gap between them.
Growth and Development — (f) Development and Environmental Sustainability— Renewable and Non-renewable Resources, Environmental Degradation, Intergenerational equity development	What growth costs the environment, and the argument that the generation after this one has a claim on what this one uses up.

Economics, Paper-II — the Indian economy, in two eras ↑

All of Paper-II is the Indian economy, and the notification splits it cleanly in two: the era before liberalization and the era after. Let that split be the shape of your preparation too — take each subject (agriculture, industry, trade, finance) through both eras separately.

Topic as the notification prints it	What it means and how to prepare it
Indian Economy in Post-Independence Era — Land System and its changes, Commercialization of agriculture	The land system and how it changed, and the commercialisation of agriculture — the colonial root from which today's farm problems grow.
Indian Economy in Post-Independence Era — Drain theory, Laissez faire theory and its critique	The drain theory, and laissez faire theory with the critique of it — Dadabhai Naoroji's argument sits here.
Indian Economy in Post-Independence Era — Manufacture and Transport: Industry - Jute, Cotton, Railways, Money and Credit	Manufacture and transport — jute, cotton, the railways, and money and credit.
The Pre-Liberalization Era — (i) Contribution of Mahalanobis, Vakil, Gadgil and V.K.R.V. Rao	The contribution of four Indian economists. This is asked by name, so attach one idea to each name.
The Pre-Liberalization Era — (ii) Agriculture: Land Reforms and land tenure system, Green Revolution and capital formation in agriculture	Agriculture — land reform and the tenure system, the Green Revolution, and capital formation in farming.
The Pre-Liberalization Era — (iii) Industry Trends in composition and growth, Role of public and private sector, small scale and cottage industries	Trends in industrial composition and growth, the role of the public and private sectors, and small-scale and cottage industry.
The Pre-Liberalization Era — (iv) National and Per capita income: Patterns, trends, aggregate and sectoral composition and changes therein	How much the country earned, how that was split between farming, industry and services, and which way the split moved across the decades. Carry the actual figures here, not just the concepts.
The Pre-Liberalization Era — (v) Broad factors determining National income and distribution, Measures of poverty, Trends in poverty and inequality	The broad factors that determine national income and its distribution, the measures of poverty, and trends in poverty and inequality.
The Post-Liberalization Era — (i) New Economic Reform and Agriculture: Agriculture and WTO, Food processing, subsidies, Agricultural prices and public distribution system, Impact of credit policy and public expenditure on agricultural growth	What opening the economy did to the farmer — to prices, to subsidy, and to what reaches the ration shop. This is a live political question, so read it with current affairs beside you.
The Post-Liberalization Era — (ii) New Economic Policy and Industry: Strategy of industrialization, Privatization, Disinvestments, Role of foreign direct investment and multinationals	The state stepping back from running factories, and foreign money stepping into the space. Read it as one continuous story from 1991 onwards rather than as separate headings.
The Post-Liberalization Era — (iii) New Economic Policy and Trade: Intellectual property rights: Implications of TRIPS, TRIMS, GATS and new EXIM policy	What India signed up to on joining the world trading system, and what those agreements oblige it to do at home.
The Post-Liberalization Era — (iv) New Exchange Rate Regime: Partial and full convertibility, Capital account convertibility	How freely the rupee may be exchanged, and why the government has so far opened that door only part of the way.
The Post-Liberalization Era — (v) New Economic Policy and Public Finance: Fiscal Responsibility and Budget Management (FRBM) Act, Twelfth Finance Commission and Fiscal Federalism and Fiscal Consolidation	The new economic policy and public finance — the FRBM Act, the Twelfth Finance Commission, fiscal federalism and fiscal consolidation. For a treasury post this is the single most job-relevant item here.
The Post-Liberalization Era — (vi) New Economic Policy and Monetary System; Role of RBI under the new regime	The new economic policy and the monetary system, and the RBI's role under the new regime.
The Post-Liberalization Era — (vii) Planning: From central Planning to indicative planning, Relation between planning and markets for growth and decentralized planning: 73rd and 74th Constitutional amendments	Planning — from central to indicative planning, the relation between planning and markets, and decentralised planning through the 73rd and 74th constitutional amendments.
The Post-Liberalization Era — (viii) New Economic Policy and Employment: Employment and poverty, Rural wages, Employment Generation, Poverty alleviation schemes, New Rural Employment Guarantee Scheme	Whether growth actually produced jobs, and the schemes that had to be built because it did not produce enough. The employment guarantee scheme is the item asked most often.

Mathematics, Paper-I — six units, topic by topic ↑

Mathematics Paper-I runs in six units: linear algebra, calculus, analytic geometry, ordinary differential equations, dynamics and statics, and vector analysis. This is degree-level pure and applied mathematics, so take it only if your own degree is in the subject.

Topic as the notification prints it	What it means and how to prepare it
Linear Algebra — Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimensions, Linear transformations, rank and nullity, matrix of a linear transformation	Vector spaces and their foundations — dependence, subspaces, bases and dimension; then linear transformations, rank and nullity. Fix the definitions first, the theorems later.
Linear Algebra — Algebra of Matrices; Row and column reduction, Echelon form, congruence and similarity, Rank of a matrix, Inverse of a matrix, Solution of system of linear equations, Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew- symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues	Matrix algebra — row and column reduction, echelon form, rank, inverse and the solution of linear systems; eigenvalues and eigenvectors, the characteristic polynomial, the Cayley-Hamilton theorem; and the eigenvalues of six special matrix types.
Calculus — Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor's theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing	One-variable calculus at degree standard. The theorems here have to be stated precisely, not merely used — this unit rewards clean definitions more than practice sums.
Calculus — Functions of two or three variables; Limits, continuity, partial derivatives, maxima and minima, Lagrange's method of multipliers, Jacobian	The same calculus carried into two and three dimensions. If you are rusty this is where it shows, because every later unit assumes partial derivatives come easily to you.
Calculus — Riemann's definition of definite integrals; Indefinite integrals; Infinite and improper integral; Double and triple integrals (evaluation techniques only); Areas, surface and volumes	Integration — Riemann's definition of the definite integral, indefinite, infinite and improper integrals, double and triple integrals, and areas, surfaces and volumes. Note that for double and triple integrals the notification asks only for evaluation techniques, not the theory.
Analytic Geometry — Cartesian and polar coordinates in three dimensions, second degree equations in three variables, reduction to canonical forms; straight lines, shortest distance between two skew lines, Plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties	Three-dimensional analytic geometry — cartesian and polar coordinates, reducing second-degree equations to canonical form; straight lines, the shortest distance between skew lines, and the properties of the plane, sphere, cone, cylinder, paraboloid, ellipsoid and hyperboloids.
Ordinary Differential Equations — Formulation of differential equations; Equations of first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut's equation, singular solution	Forming differential equations; first-order first-degree equations and the integrating factor; orthogonal trajectories; first-order higher-degree equations, Clairaut's equation and singular solutions.
Ordinary Differential Equations — Second and higher order linear equations with constant coefficients, complementary function, particular integral and general solution	The workhorse of the unit — nearly every applied problem comes back to this one standard routine. Practise it until it needs no thought.
Ordinary Differential Equations — Second order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using method of variation of parameters	Second order equations with variable coefficients, the Euler-Cauchy equation, and finding the complete solution from one known solution by variation of parameters.
Ordinary Differential Equations — Laplace and Inverse Laplace transforms and their properties, Laplace transforms of elementary functions; Application to initial value problems for 2nd order linear equations with constant coefficients	Laplace and inverse Laplace transforms, their properties, and their application to initial value problems.
Dynamics and Statics — Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; Constrained motion; Work and energy, conservation of energy; Kepler's laws, orbits under central forces	Motion, from a straight line up to planetary orbits. It is shaped like physics rather than algebra, which is why candidates from a pure-maths background usually find this the hardest unit here.
Dynamics and Statics — Equilibrium of a system of particles; Work and potential energy, friction, Common catenary; Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions	Bodies that are not moving, and the conditions holding them still. Smaller than dynamics and far more scoring, so do not leave it until last.
Vector Analysis — Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in cartesian and cylindrical coordinates; Higher order derivatives; Vector identities and vector equation	The language every later physics-facing topic is written in. Get fluent with the three operators in both coordinate systems, because questions move between them without warning.
Vector Analysis — Application to Geometry: Curves in space, curvature and torsion; Serret-Frenet's formulae	How a curve bends and twists through space, said in numbers. A short, self-contained block, and one of the easiest places on this paper to bank full marks.
Vector Analysis — Gauss and Stokes' theorems, Green's identities	The Gauss and Stokes theorems and Green's identities — three tools that convert one kind of integral into another.

Mathematics, Paper-II — seven units, topic by topic ↑

Paper-II has seven units — algebra, real analysis, complex analysis, linear programming, partial differential equations, numerical analysis and computer programming, and mechanics and fluid dynamics. Note that the sixth unit carries computer programming as well, which mathematics candidates routinely leave until last.

Topic as the notification prints it	What it means and how to prepare it
Algebra — Groups, subgroups, cyclic groups, cosets, Lagrange's Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley's theorem	Abstract algebra from the ground up. Here you write proofs rather than calculate, and it is where candidates who only ever practised sums come unstuck.
Algebra — Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains and unique factorization domains; Fields, quotient fields	The second structure of abstract algebra, built the same way as the first. Take it straight after groups, while the definition-example-theorem pattern is still fresh.
Real Analysis — Real number system as an ordered field with least upper bound property; Sequences, limit of a sequence, Cauchy sequence, completeness of real line	Why the calculus you already use is actually valid. The whole unit rests on one property of the real line, so put your first hours there.
Real Analysis — Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series	Series and convergence — absolute and conditional convergence of real and complex series, and rearrangement of series.
Real Analysis — Continuity and uniform continuity of functions, properties of continuous functions on compact sets	The distinction between the two kinds of continuity is the entire item, and it is asked almost every time. Carry a counter-example for it, not just a definition.
Real Analysis — Riemann integral, improper integrals; Fundamental theorems of integral calculus; Partial derivatives of functions of several (two or three) variables, maxima and minima	The Riemann integral and improper integrals, the fundamental theorems of integral calculus; and partial derivatives of functions of two or three variables with their maxima and minima.
Complex Analysis — Analytic function, Cauchy-Riemann equations, Cauchy's theorem, Cauchy's integral formula, power series, representation of an analytic function, Taylor's series; Singularities; Laurent's series; Cauchy's residue theorem; Contour integration	Complex analysis — analytic functions, the Cauchy-Riemann equations, Cauchy's theorem and integral formula, power series, Taylor series, singularities, Laurent series, the residue theorem and contour integration.
Linear Programming — Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality	Linear programming — basic solutions, basic feasible solutions and the optimal solution; the graphical and simplex methods; and duality.
Partial Differential Equations — Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasilinear partial differential equations of the first order, Cauchy's method of characteristics	Families of surfaces in three dimensions and forming partial differential equations; solving first-order quasilinear equations and Cauchy's method of characteristics.
Partial Differential Equations — Linear partial differential equations of the second order with constant coefficients, canonical form; Equation of a vibrating string, heat equation, Laplace equation and their solutions	Second-order linear partial differential equations with constant coefficients and their canonical form; the vibrating string, heat and Laplace equations and their solutions.
Numerical Analysis and Computer Programming — Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton- Raphson methods, solution of system of linear equations by Gaussian Elimination and Gauss-Jorden (direct), Gauss-Seidel (iterative) methods	Arriving at an approximate answer by repeating one step until it settles. Marks here come from setting the iterations out neatly, so practise the table as well as the formula.
Numerical Analysis and Computer Programming — Newton's (forward and backward) and interpolation, Lagrange's interpolation	Interpolation — Newton's forward and backward interpolation, and Lagrange's interpolation.
Numerical Analysis and Computer Programming — Numerical integration: Trapezoidal rule, Simpson's rule, Gaussian quadrature formula	Numerical integration — the trapezoidal rule, Simpson's rule and the Gaussian quadrature formula.
Numerical Analysis and Computer Programming — Numerical solution of ordinary differential equations: Euler and Runga Kutta methods	The numerical solution of ordinary differential equations — the Euler and Runge-Kutta methods.
Numerical Analysis and Computer Programming — Computer Programming: Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal Systems; Conversion to and from decimal Systems; Algebra of binary numbers	Number systems and how a machine handles them. The notification names no programming language anywhere, so this is arithmetic in other bases rather than coding as such.
Numerical Analysis and Computer Programming — Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms; Representation of unsigned integers, signed integers and reals, double precision reals and long integers; Algorithms and flow charts for solving numerical analysis problems	How a machine stores a number and settles a yes-or-no. Short and definition-heavy — the kind of block you revise near the end rather than study for weeks.
Mechanics and Fluid Dynamics — Generalised coordinates; D'Alembert's principle and Lagrange's equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions	Classical mechanics rewritten the way a mathematician writes it. If you met this as physics the ideas will feel familiar, but the machinery will not.
Mechanics and Fluid Dynamics — Equation of continuity; Euler's equation of motion for inviscid flow; Stream-lines, path of a particle; Potential flow; Two-dimensional and axisymmetric motion	How a moving fluid is described mathematically. The unit builds from the frictionless ideal towards the real, sticky one — follow it in that order.
Mechanics and Fluid Dynamics — Sources and sinks, vortex motion; Navier- Stokes equation for a viscous fluid	Sources and sinks, vortex motion, and the Navier-Stokes equation for a viscous fluid — the last item in this paper.

Statistics, Paper-I — probability, inference, linear models and sampling ↑

Statistics Paper-I has four units. The thing to notice is that the probability unit is written at measure-theoretic level — that is a post-graduate demand, not a degree-level one.

Topic as the notification prints it	What it means and how to prepare it
Probability — Sample space and events, probability measure and probability space, random variable as a measurable function, distribution function of a random variable, discrete and continuous-type random variable, probability mass function, probability density function, vector-valued random variable, marginal and conditional distributions, stochastic independence of events and of random variables	Probability rebuilt on measure theory instead of on counting. That is a post-graduate demand, and it is the biggest single reason candidates find this paper harder than they expected.
Probability — expectation and moments of a random variable, conditional expectation, convergence of a sequence of random variable in distribution, in probability, in path mean and almost everywhere, their criteria and inter-relations, Chebyshev's inequality and Khintchine's weak law of large numbers, strong law of large numbers and Kolmogoroff's theorems	What a random quantity settles down to over the long run, and the precise senses in which it settles. The four modes of convergence and the order between them are the examinable core.
Probability — probability generating function, moment generating function, characteristic function, inversion theorem, Linderberg and Levy forms of central limit theorem, standard discrete and continuous probability distributions	Generating functions — probability generating, moment generating and characteristic functions; the inversion theorem; the Lindeberg and Levy forms of the central limit theorem; and the standard discrete and continuous distributions.
Statistical Inference — Consistency, unbiasedness, efficiency, sufficiency, completeness, ancillary statistics, factorization theorem, exponential family of distribution and its properties, uniformly minimum variance unbiased (UMVU) estimation, Rao Blackwell and Lehmann-Scheffe theorems, Cramer-Rao inequality for single Parameter	What makes one estimate better than another. Every named theorem here answers the same question — how close an unbiased estimate can possibly get — so learn them as one argument, not five.
Statistical Inference — Estimation by methods of moments, maximum likelihood, least squares, minimum chi square and modified minimum chi square, properties of maximum likelihood and other estimators, asymptotic efficiency, prior and posterior distributions, loss function, risk function, and minimax estimator; Bayes estimators	Four ways of squeezing an estimate out of data, and then the Bayesian route that carries a prior belief along. Knowing when each is preferred matters more than deriving all of them.
Statistical Inference — Non-randomised and randomised tests, critical function, MP tests, Neyman-Pearson lemma, UMP tests, monotone likelihood ratio; similar and unbiased tests; UMPU tests for single parameter, likelihood ratio test and its asymptotic distribution; Confidence bounds and its relation with tests	How a statistical claim is put on trial. One lemma sits under this entire block; get that right and the other named tests fall out of it.
Statistical Inference — Kolmogorov's test for goodness of fit and its consistency, sign test and its optimality, Wilcoxon signed ranks test and its consistency, Kolmogorov-Smirnov two sample test, run test, Wilcoxon-Mann-Whitney test and median test, their consistency and asymptotic normality; Wald's SPRT and its properties, OC and functions for tests regarding parameters for Bernoulli, Poisson, normal and exponential distributions; Wald's fundamental identity	Non-parametric tests — Kolmogorov's goodness-of-fit test, the sign test, the Wilcoxon signed-ranks test, the Kolmogorov-Smirnov two-sample test, the run test, the Wilcoxon-Mann-Whitney and median tests; and Wald's SPRT with its properties, OC functions and Wald's fundamental identity.
Linear Inference and Multivariate Analysis — Linear statistical models, theory of least squares and analysis of variance, Gauss-Markoff theory, normal equations, least squares estimates and their precision, test of significance and interval estimates based on least squares theory in one way, two-way and three-way classified data	Fitting a straight-line model to data, then asking whether the fit means anything at all. This is the machinery under analysis of variance, the most usable skill in the whole paper.
Linear Inference and Multivariate Analysis — regression analysis, linear regression, curvilinear regression and orthogonal polynomials, multiple regression, multiple and partial correlations, estimation of variance and covariance components, multivariate normal distribution, Mahalanobis D2 and Hotelling's T2 statistics and their applications and properties	Tying one quantity to several others, and then handling several at once. The multivariate half is heavier than it looks, and is usually where preparation runs out of time.
Sampling Theory and Design of Experiments — An outline of fixed-population and super-population approaches, distinctive features of finite population sampling, probability sampling designs, simple random sampling with and without replacement, stratified random sampling, systematic sampling and its efficacy, cluster sampling, two-stage and multi-stage sampling, ratio and regression methods of estimation involving one or more auxiliary variables, two-phase sampling	Learning about a whole population by measuring only a part of it, and being able to say how wrong you might be. For a government post this is the most directly useful thing in Paper-I.
Sampling Theory and Design of Experiments — Fixed effects model (two-way classification) random and mixed effects models (two-way classification with equal observation per cell), CRD, RBD, LSD and their analyses, incomplete block designs, concepts of orthogonality and balance, BIBD, missing plot technique, factorial experiments and 2⁴ and 3², confounding in factorial experiments, split- plot and simple lattice designs, transformation of data Duncan's multiple range test	Design of experiments — fixed, random and mixed effects models; CRD, RBD, LSD and their analysis; incomplete block designs, orthogonality and balance, BIBD, the missing plot technique; factorial experiments and confounding; split-plot and simple lattice designs; data transformation and Duncan's multiple range test.

Statistics, Paper-II — industrial, optimization, quantitative and official statistics ↑

Paper-II runs in four units and is more applied than Paper-I — quality control, operations research, econometrics and India's official statistical system. That last unit is the most job-relevant of all for a government post, so do not treat it as an afterthought.

Topic as the notification prints it	What it means and how to prepare it
Industrial Statistics — Process and product control, general theory of control charts, different types of control charts for variables and attributes, X, R, s, p, np and c charts, cumulative sum chart	Process and product control — the general theory of control charts, the chart types for variables and for attributes, and the cumulative sum chart.
Industrial Statistics — Single, double, multiple and sequential sampling plans for attributes, OC, ASN, AOQ and ATI curves, concepts of producer's and consumer's risks, AQL, LTPD and AOQL, Sampling plans for variables, Use of Dodge-Romin tables	Deciding whether to take a whole consignment after inspecting a handful of it, and the curves that show whose risk it is when you get that wrong. (The notification prints 'Dodge-Romin'; we kept its spelling rather than correcting the commission.)
Industrial Statistics — Concept of reliability, failure rate and reliability functions, reliability of series and parallel systems and other simple configurations, renewal density and renewal function; Failure models: exponential, Weibull, normal, lognormal; Problems in life testing, censored and truncated experiments for exponential models	How long a thing runs before it breaks, and how that changes when parts are wired one behind another instead of side by side. Applied and formula-driven rather than theoretical.
Optimization Techniques — Different types of models in Operations Research, their construction and general methods of solution, simulation and Monte- Carlo methods	Operations research models — their types, construction and general methods of solution; and simulation and Monte-Carlo methods.
Optimization Techniques — formulation of Linear Programming (LP) problem, simple LP model and its graphical solution, the simplex procedure, the two-phase method and the M-technique with artificial variables, the duality theory of LP and its economic interpretation, sensitivity analysis, transportation and assignment problems, rectangular games, two-person zero-sum games, methods of solution (graphical and algebraic)	Getting the best answer available when resources are short and rules tie your hands. It is a procedure to be drilled, not a theory to be read — work the iterations by hand.
Optimization Techniques — Replacement of failing or deteriorating items, group and individual replacement policies, concept of scientific inventory management and analytical structure of inventory problems, simple models with deterministic and stochastic demand with and without lead time, storage models with particular reference to dam type	Replacement — group and individual replacement policies for deteriorating items; scientific inventory management and the analytical structure of inventory problems; models with deterministic and stochastic demand; and storage models of the dam type.
Optimization Techniques — Homogeneous discrete-time Markov chains, transition probability matrix, classification of states and ergodic theorems, homogeneous continuous-time Markov chains, Poisson process, elements of queuing theory, M/M/1, M/M/K, G/M/1 and M/G/1 queues; Solution of statistical problems on computers using well known statistical software packages like SPSS	Markov chains — discrete and continuous time, the transition probability matrix, classification of states, ergodic theorems; the Poisson process; queuing theory and the four standard queue models; and solving problems on computers with statistical packages such as SPSS.
Quantitative Economics and Official Statistics — Determination of trend, seasonal and cyclical components, Box- Jenkins method, tests for stationary series, ARIMA models and determination of orders of autoregressive and moving average components, forecasting	Time series analysis — trend, seasonal and cyclical components; the Box-Jenkins method; tests for stationarity; ARIMA models and fixing their orders; and forecasting.
Quantitative Economics and Official Statistics — Commonly used index numbers — Laspeyre's, Paasche's and Fisher's ideal index numbers, chain-base index number, uses and limitations of index numbers, index number of wholesale prices, consumer price, agricultural production and industrial production, test for index numbers — proportionality, time-reversal, factor-reversal and circular	Index numbers — the Laspeyres, Paasche and Fisher ideal indices and the chain-base index; their uses and limits; the wholesale price, consumer price, agricultural and industrial production indices; and the four tests for index numbers.
Quantitative Economics and Official Statistics — General linear model, ordinary least square and generalized least squares methods of estimation, problem of multi-collinearity, consequences and solutions of multi-collinearity, autocorrelation and its consequences, heteroscedasticity of disturbances and its testing, test for independence of disturbances	The general linear model — ordinary and generalised least squares estimation; the problem of multicollinearity, its consequences and its remedies; autocorrelation and its consequences; and heteroscedasticity and how it is tested.
Quantitative Economics and Official Statistics — concept of structure and model for simultaneous equations, problem of identification-rank and order conditions of identifiability, two-stage least square method of estimation	Simultaneous equations — the concept of structure and model; the identification problem with its rank and order conditions; and two-stage least squares estimation.
Quantitative Economics and Official Statistics — Present official statistical system in India relating to population, agriculture, industrial production, trade and prices, methods of collection of official statistics, their reliability and limitations, principal publications containing such statistics, various official agencies responsible for data collection and their main functions	Where the government's own numbers come from, who produces them, and how far each can be trusted. For a treasury post this is the item you are likeliest to use after selection, not just in the exam.
Demography and Psychometry — Demographic data from census, registration, NSS other surveys, their limitations and uses, definition, construction and uses of vital rates and ratios, measures of fertility, reproduction rates, morbidity rate, standardized death rate, complete and abridged life tables, construction of life tables from vital statistics and census returns, uses of life tables, logistic and other population growth curves, fitting a logistic curve, population projection, stable population, quasi-stable population, techniques in estimation of demographic parameters, standard classification by cause of death, health surveys and use of hospital statistics	Measuring births, deaths and the shape of a population, and projecting it forward. The life table is the central tool — if you learn one thing here, learn to build one and read one.
Demography and Psychometry — Methods of standardisation of scales and tests, Z-scores, standard scores, T-scores, percentile scores, intelligence quotient and its measurement and uses, validity and reliability of test scores and its determination, methods of factor analysis and path analysis in psychometry	Putting a number on something as slippery as ability, then asking whether that number measures what it claims to. A small block, and the only place in the paper where statistics meets psychology.

What the notification does not state — and we will not invent ↑

Every line below is absent from these 20 pages. The list exists because several websites present these figures in a tidy table when the official document simply does not carry them. An invented figure harms the candidate who plans a year around it.

Not stated in the notification	What the document actually says
How the optional subject is chosen	The notification gives the syllabus for four optional subjects. It nowhere states how many a candidate offers, how the choice is made, or what qualification it requires. That belongs to the recruitment advertisement — do not act on any website's guess, including a guess set in a table.
Marks for the optional papers	Marks appear in exactly one place — 200 for Commercial Mathematics in the Recruitment Test. This document gives no marks for any optional paper.
Duration of any paper	No time limit for any paper appears anywhere in these 20 pages.
Number of questions	The notification does not say how many questions will be asked.
Whether questions are objective or descriptive	The form of the questions — multiple choice or written — is never stated. Guessing it from the depth of the syllabus is not a safe basis for preparation.
Negative marking	There is no mention of whether marks are deducted for a wrong answer.
Qualifying marks	The marks needed to qualify are not given.
Stages of the exam and interview	The notification names only the 'Recruitment Test (RT)'. How many stages there are, and whether there is an interview, is not described.
Vacancies, eligibility, age and application dates	This is a syllabus notification only. The number of posts, the educational qualification, the age limit, the fee and the application dates are not in it — they come in the recruitment advertisement.
Exam date	The exam date is not part of this document; it comes in a separate announcement.
Medium of the examination	The notification does not say what language the question paper will be in.

How to actually use this syllabus ↑

The tables above are the syllabus. The eight points below are our own advice, drawn from reading this same document and from what it does and does not contain.

Do Commercial Mathematics first. It is the only place in the whole notification where marks are stated — 200 in the Recruitment Test — so it is the first claim on your time.
Copy the twelve-unit list above into your notebook and mark each unit 'good / average / none'. Start with the ones marked none.
Give unit 5 (Banker's Discount and Bills of Exchange) its own slot. It rarely appears in general competitive preparation, which is exactly why marks are lost there.
Read unit 11's sub-list. The notification files arithmetic mean, average speed and average age under 'Time and Work' — skip the unit on the strength of its name and you lose a whole topic.
Pick your optional subject by the strength of your own degree — Commerce, Economics, Mathematics or Statistics. Both papers of each are set out above, unit by unit.
But how the optional subject is chosen is not stated in this notification. Wait for the recruitment advertisement to learn that; do not start preparing on an assumption.
Marks, duration, question count and negative marking are all absent from this document. Any website showing you those figures in a neat table has filled them in itself.
Finally, open the official PDF once and check this page against it. Every word here comes from that document, but the paper your year is planned around is worth seeing with your own eyes.

Important Links

View Syllabus / Notification

APPSC Notification No. PSC-R/10/2026 (FAO/TO & STO), read in full and restated here in our own words. The original: APPSC FAO/TO & STO syllabus (PDF) ↗