Rational vs irrational numbers, decimal expansions, locating √x on the number line, surds & rationalising denominators, and the laws of exponents for real bases.

The particle nature of matter, the three states and their properties, change of state, latent heat of fusion & vaporisation, sublimation, and evaporation as a cooling process.

Isaac Asimov's 'The Fun They Had' — a 2157 schoolroom, telebooks versus the attic paper book, and the irony of children envying the old kind of school. (+ Frost's 'The Road Not Taken'.)

प्रेमचंद की 'दो बैलों की कथा' — हीरा-मोती की मित्रता, स्वतंत्रता की चाह, अहिंसक विद्रोह, और बैल = पराधीन किसान का प्रतीक।

The French Revolution (1789): the three estates, Enlightenment thinkers, the storming of the Bastille, the Republic and execution of Louis XVI, the Reign of Terror, and the rise of Napoleon.

Fundamental Theorem of Arithmetic, irrationality proofs, decimal expansions. Topper templates show the exact step-by-step structure CBSE markers reward with full marks.

Balancing, the 4 reaction types, redox, corrosion, rancidity. Highest-yield Chemistry chapter — 3 topper-answer templates with mark-by-mark structure.

G. L. Fuentes's 'A Letter to God' — Lencho's unshakeable faith, the irony of blaming the post office, and the goodness of ordinary people. (+ Frost's 'Dust of Snow' & 'Fire and Ice'.)

सूरदास के पद (भ्रमरगीत प्रसंग) — उद्धव-गोपी संवाद, निर्गुण-योग की अस्वीकृति, गोपियों का वाक्-चातुर्य और सगुण भक्ति की विजय।

The Rise of Nationalism in Europe — the French Revolution's legacy, liberal nationalism, the Zollverein, and the unification of Germany (Bismarck) and Italy (Cavour, Garibaldi).

Mesopotamia (c.3200 BCE) — the rise of the city, the temple economy, and the invention of cuneiform writing on clay tablets. (Themes in World History)

What a constitution is and why we need one — the Constituent Assembly, the adoption on 26 Nov 1949, and the core ideals of the Indian Constitution.

Geography as an integrating discipline — systematic vs regional approaches (Humboldt & Ritter), the physical–human dualism, and the branches of the subject.

The sociological imagination (C. W. Mills) — private troubles vs public issues, society beyond the individual, and how sociology differs from common sense.

Psychology as the science of mind and behaviour — from Wundt's 1879 Leipzig lab through behaviourism and psychoanalysis to the cognitive revolution.

What accounting is and why it matters — the accounting process, book-keeping vs accountancy, users of accounts, and the basic terms (capital, assets, liabilities, debtors/creditors).

Business, trade and commerce — economic vs non-economic activity, the industry/commerce classification, the aids to trade, and the objectives and risks of business.

Statistics for Economics — the singular (method/science) vs plural (data) senses of statistics, its functions in economics, scope, and limitations.

Numbers & numerical applications — modulo arithmetic, indices & logarithms, and word-problems (averages, alligation & mixture, boats-streams, pipes-cisterns).

Units & measurement — the SI base units, accuracy vs precision, error propagation, significant figures, and dimensional analysis (and its limits).

The mole concept, the laws of chemical combination, atomic & molecular masses, empirical vs molecular formula, stoichiometry & limiting reagent, and concentration terms.

Sets — representation, subsets & power sets (2ⁿ), Venn diagrams, union/intersection/complement, De Morgan's laws, and the n(A∪B) cardinality formula.

What 'living' means, biodiversity & the need for classification, binomial nomenclature, the taxonomic hierarchy (Kingdom→Species), and taxonomical aids.

Khushwant Singh's 'The Portrait of a Lady' — the three phases of the bond with the grandmother, her serene faith, and the sparrows' silent mourning. (+ the poem 'A Photograph'.)

कबीर के पद एवं सबद (आरोह भाग-1) — 'हम तौ एक एक करि जांनां' का अद्वैत-भाव और 'संतों देखत जग बौराना' का बाह्याडंबर-खंडन एवं हिन्दू-मुस्लिम समन्वय।

Computer System — functional units (CPU/ALU/CU, memory, I/O), the von Neumann model, hardware vs software, the memory hierarchy, RAM vs ROM, the boot process, and encoding (ASCII/Unicode).

Introduction to Computer System — components & CPU, memory hierarchy and units, system vs application software, FOSS vs proprietary, the OS's role, booting, and mobile vs desktop.

Physical education — meaning, aims & objectives, the development of PE in India (HVPM, YMCA, LNIPE, NSNIS), changing trends (Khelo India, Fit India), and career options.

Entrepreneur vs entrepreneurship vs enterprise; characteristics & functions (innovation + risk-bearing); the entrepreneurial process; Danhof's types; and the role of entrepreneurship in the economy.

Theory and Sources of Law — the nature & functions of law, the five schools of jurisprudence (natural/positivist/historical/sociological/realist), the sources of law, and the classifications of law.

Home Science as an interdisciplinary applied science — the name evolution (Home Economics → HEFS), the five areas (Food & Nutrition, Human Development, Fabric & Apparel, Resource Management, Communication & Extension), and careers.

Rome across three continents — Republic to Principate (Augustus, 27 BCE), the army & Senate, the third-century crisis, slavery and manumission, and the rise of Christianity.

Rights in the Indian Constitution — the six Fundamental Rights (Articles 14–32), the five writs, the Directive Principles, and the Fundamental Duties.

How the Earth formed — early theories (nebular, planetesimal, tidal), the Big Bang, the solar system, and the Earth's differentiation into core, mantle and crust.

The sociologist's toolkit — social groups, status & role, community vs society (Tönnies), the four systems of stratification, and social control.

How psychologists find things out — the goals of enquiry, observation and the experimental method (IV vs DV), correlation vs causation, and research ethics.

The theory base — GAAP, the accounting concepts and assumptions (going concern, accrual, matching, prudence), and the dual-aspect equation Assets = Liabilities + Capital.

Forms of business organisation — sole proprietorship, Joint Hindu Family, partnership, cooperative society and the joint-stock company, compared on liability, control and continuity.

Collecting data — primary vs secondary sources, the collection methods, census vs sample, sampling & non-sampling errors, and India's sources (Census of India, NSSO).

Algebra — sets and Venn diagrams, relations & functions (domain/range, types), and arithmetic & geometric progressions (nth term and sums).

Nomadic Empires — the Central Asian steppe, Chinggis Khan's rise (1206) and his decimal army, the Mongol campaigns and administration (yam, Yasa), and the empire after him.

Election and Representation — First-Past-The-Post vs proportional representation, reserved constituencies, universal adult franchise, and the Election Commission of India.

Interior of the Earth — direct and indirect sources, earthquakes and seismic waves (P vs S waves and the shadow zones), the layered structure (crust/mantle/core), and volcanoes.

Understanding social institutions — the functionalist and conflict views, and the family/marriage/kinship, work, political, religious and educational institutions.

The bases of human behaviour — the nervous system, the brain, the endocrine system, heredity (nature vs nurture), and the cultural bases of behaviour.

Recording of transactions — the accounting equation, the rules of debit and credit, source documents and vouchers, and journalising (with fully worked entries).

Private, public and global enterprises — the three forms of public-sector enterprise, the changing role of the public sector, MNCs, joint ventures and PPP.

Organisation of data — classification, variables (discrete vs continuous), and building a frequency distribution (inclusive vs exclusive, class limits vs boundaries).

Mathematical reasoning — statements and truth values, negation, AND/OR, the quantifiers, implications, and the converse / inverse / contrapositive.

The Three Orders — medieval Western European feudalism: those who pray, those who fight and those who work; the manor, the role of the Church, and the 14th-century crisis.

Executive — parliamentary vs presidential systems, the President of India (the nominal head), the Prime Minister and Council of Ministers (the real executive), and the bureaucracy.

Distribution of Oceans and Continents — Wegener's continental drift and its evidence, sea-floor spreading, and the theory of plate tectonics.

Culture and Socialisation — material vs non-material culture, ethnocentrism and cultural relativism, cultural lag, and the agencies of socialisation.

Human Development — the life-span perspective, heredity and environment, Bronfenbrenner's ecological model, and the stages from infancy to old age.

Recording of Transactions II — posting to the ledger and balancing accounts, the special purpose books, and the cash book (with contra entries).

Business Services — the goods-vs-services distinction and the key services: banking, insurance (and its principles), transport, warehousing and communication.

Presentation of Data — tabular presentation, bar and pie diagrams, and the graphic presentation of frequency distributions (histogram, polygon, ogive).

Calculus — functions and limits, the rules of differentiation, and applications: rate of change, marginal cost & revenue, and maxima–minima.

Coulomb's law, electric field, Gauss's law, dipole — the launchpad of all electromagnetism.

Concentration units, Raoult's law, colligative properties, van't Hoff factor.

Equivalence relations, bijective functions, composition, inverse functions.

Embryo sac (8-nucleate), double fertilisation, post-fertilisation seed and fruit.

NPO accounting: R&P, I&E, Balance Sheet, capital fund, subscriptions, donations.

Management: characteristics, objectives, levels, functions, coordination as essence.

Macro vs micro, central problems, stock vs flow, circular flow of income.

British rule's impact: deindustrialisation, drain of wealth, stagnant agriculture.

Harappan civilisation (2600-1900 BCE): urban planning, script, decline. Source-based + map work.

Three schools of thought: environmental determinism, possibilism, neo-determinism. Scope of human geography.

Cold War (1945-1991): origins, Cuban Missile Crisis, NAM with Nehru-Nasser-Tito, end of bipolarity.

Sociological imagination (Mills), Indian diversity, colonialism's comprehensive impact, key sociologists.

Theories of intelligence: Spearman g-factor, Gardner MI, Sternberg triarchic, Indian integral, Goleman EI.

Alphonse Daudet's 'The Last Lesson' — Alsace, 1870, the Franco-Prussian War, M. Hamel's last French lesson + linguistic chauvinism.

बच्चन की दो कविताएँ — 'आत्म-परिचय' का विरोधाभास-दर्शन एवं 'दिन जल्दी-जल्दी ढलता है' की प्रत्याशा-त्रिकोण।

Modulo arithmetic + allegation + boats-streams + pipes-cisterns + numerical inequalities — the four headline formulas of practical maths.

Python revision — tokens, mutable/immutable types, operators (/ vs //), range() endpoint, control flow with break/continue.

Pandas Series + DataFrame, .loc/.iloc, head/tail, add/delete/rename columns, Boolean indexing, CSV import/export.

Five POSDC functions of event management, knock-out and league fixtures, intramural vs extramural, committees.

Idea vs opportunity, PESTEL framework, sources of opportunities, four-dimension feasibility, opportunity assessment.

Indian court hierarchy, Collegium for SC/HC appointments, judicial review + Kesavananda Bharati basic-structure doctrine, tribunals.

Work / livelihood / career definitions, paid vs unpaid work, five Home Science sub-disciplines, 4-step career planning framework.

National Income aggregates (GDP/GNP/NDP/NNP at MP/FC), three calculation methods (Value-Added, Income, Expenditure), depreciation + NIT + NFIA conversions, Real vs Nominal GDP + Deflator, GDP welfare limitations.

Partnership Act 1932 (Section 4 essentials, Section 13 defaults), Partnership Deed, P&L Appropriation A/c, Fixed vs Fluctuating Capital, Interest on Drawings (Average Period method), guarantee of profit.

Fayol's 14 principles + Taylor's 4 principles + 5 techniques of Scientific Management, Functional Foremanship, Mental Revolution, Bethlehem Steel pig-iron experiment, Gang Plank exception to Scalar Chain.

Planning Era 1950-1990: Five-Year Plans + Mahalanobis Model, Four goals of planning, Land Reforms (Zamindari + Tenancy + Ceiling), Green Revolution (HYV seeds + MSP + Punjab/Haryana), IPR 1956 + IDR Act 1951 + Import Substitution.

Electric potential V, equipotential surfaces, V due to point/multiple charges + dipole, capacitance C = Q/V, parallel-plate capacitor with dielectric C = Kε₀A/d, series/parallel combinations, energy stored ½CV² + redistribution.

Galvanic + electrolytic cells, SHE reference, standard electrode potentials, Nernst equation E = E° − (0.0591/n)log Q, Faraday's two laws (m = ZIt), molar conductivity + Kohlrausch's law, batteries + fuel cells + corrosion.

Kings, Farmers and Towns (c.600 BCE–600 CE) — the Mahajanapadas, the Mauryas (Ashoka, Arthashastra, Megasthenes), agrarian change, the evolution of coinage, and how inscriptions are read.

The world's people — patterns of population distribution and density, the components of growth (birth/death/migration), the demographic transition theory, and doubling time.

The end of bipolarity — Gorbachev's perestroika & glasnost, the fall of the Berlin Wall (1989), the disintegration of the USSR (1991), shock therapy, and US unipolarity.

India's demographic structure — formal vs social demography, the demographic transition, sex ratio and the dependency ratio, the demographic dividend, and population policy.

Self and personality — self-concept and self-esteem, and the type, trait (the Big Five), psychodynamic (Freud) and humanistic approaches, plus personality assessment.

Algebra — matrices and their operations, types of matrices, determinants, minors & cofactors, the adjoint and inverse, and solving linear systems (matrix method & Cramer's rule).

Kinship, Caste and Class (c.600 BCE–600 CE) — the Mahabharata as a source, the rules of kinship and marriage, the varna order and the Manusmriti, and life beyond the four varnas.

Human Development — the concept (Mahbub-ul-Haq & Amartya Sen), the four pillars, and how the Human Development Index measures it (health, education, income).

US Hegemony in World Politics — the post-1991 unipolar moment, the Gulf War, 9/11 and the War on Terror, the three senses of hegemony, and its constraints.

Social Institutions: Continuity and Change — caste and its colonial reshaping, tribal communities, and the changing forms of the family.

Meeting Life Challenges — the nature and sources of stress, Selye's General Adaptation Syndrome, appraisal and coping (problem- vs emotion-focused), and stress management.

Admission of a Partner — the new and sacrificing ratios, the treatment of goodwill, revaluation of assets and liabilities, and adjustment of capitals (fully worked numericals).

Business Environment — its meaning and five dimensions (economic, social, technological, political, legal) and the impact of the 1991 LPG reforms on business.

Money and Banking — the functions of money, the measures of money supply, credit creation (the money multiplier), and the RBI's monetary-policy tools.

Liberalisation, Privatisation and Globalisation — the 1991 crisis and reforms, the LPG measures (including the WTO, 1995), and an appraisal of their impact.

Calculus — higher-order derivatives, increasing/decreasing functions and maxima–minima, marginal cost & revenue, integration, and consumer/producer surplus.

Thinkers, Beliefs and Buildings (c. 600 BCE–600 CE) — Buddhism, Jainism, the Sangha, stupas at Sanchi and Amaravati, jataka tales, and the rise of Bhakti.

Human Settlements — rural vs urban, settlement types and patterns, urban functions and hierarchy (town → conurbation → megalopolis), and problems of urbanisation.

Alternative Centres of Power — the rise of the European Union, ASEAN's three pillars, China's post-1978 transformation, and shifting India–China relations.

The Market as a Social Institution — weekly haats, caste-embedded markets, Nakarattar trade networks, commodification, and globalised consumption.

Psychological Disorders — the 4 Ds of abnormality, ICD-11 + DSM-5 classification, anxiety / mood / dissociative / schizophrenia / childhood disorders, and substance dependence.

Retirement and Death of a Partner — gaining ratio, treatment of goodwill, revaluation A/c, accumulated reserves, executor's account, and settlement (lump sum / instalments).

Planning — its features, importance, limitations, the 7-step planning process, and types of plans (objective, strategy, policy, procedure, method, rule, budget, programme).

Determination of Income and Employment — Keynesian AD = C + I equilibrium, the consumption function, the investment multiplier k = 1/(1−MPC), and deflationary / inflationary gaps.

Poverty — who the poor are, the Tendulkar poverty line, head-count ratio, causes of poverty, and the three-pronged policy response (growth, anti-poverty schemes, basic needs).

Probability Distributions — random variables and PMF, E(X) and Var(X), the binomial and Poisson distributions, and the standard normal distribution with z-scores.