UPSC National Defence Academy

Mathematics syllabus (8 sections)

• Algebra — sets, De Morgan laws, Cartesian product/relations, complex numbers, binary numbers, AP/GP/HP, quadratic equations, linear inequations, permutations & combinations, binomial theorem, logarithms
• Matrices and Determinants — types and operations on matrices, determinants, adjoint and inverse of a square matrix, Cramer's rule, applications of the matrix method
• Trigonometry — trigonometric ratios and identities, sum/difference formulae, multiple and sub-multiple angles, inverse trigonometric functions, applications to heights and distances, properties of triangles
• Analytical Geometry of Two and Three Dimensions — Cartesian coordinate systems, straight lines, circles, conic sections (parabola, ellipse, hyperbola), points/planes/spheres in three dimensions
• Differential Calculus — functions, limits, continuity, derivatives, applications to maxima and minima
• Integral Calculus and Differential Equations — techniques of integration, definite integrals and areas, ordinary differential equations
• Vector Algebra — vectors in two and three dimensions, dot and cross products, applications of vectors
• Statistics and Probability — classification and graphical representation of data, measures of central tendency and variance, correlation and regression, probability theory, Bayes' theorem, binomial distribution

Part A · English (200 marks)

• English (200 marks) — grammar, vocabulary, comprehension and cohesion, skill-based

Part B · General Knowledge (400 marks, six sections)

• Section A · Physics (25% weightage) — properties and states of matter, mechanics (motion, Newton's laws, force and momentum, gravitation, work/power/energy), heat, sound, light and optics, magnetism, electricity, general working principles of common devices (pendulum, pulleys, siphon, levers, pressure cooker, telescope, etc.)
• Section B · Chemistry (15% weightage) — physical and chemical changes, elements/mixtures/compounds, chemical equations, properties of air and water, preparation of hydrogen/oxygen/nitrogen/carbon dioxide, oxidation and reduction, acids/bases/salts, forms of carbon, fertilizers, materials (soap, glass, ink, paper, cement), elementary atomic structure, valency
• Section C · General Science (10% weightage) — living vs non-living, cells and protoplasm and tissues, growth and reproduction, elementary human body knowledge, epidemics and their prevention, food and nutrition, the solar system, eminent scientists and their discoveries
• Section D · History, Freedom Movement etc. (20% weightage) — broad survey of Indian history with emphasis on culture and civilisation, the freedom movement, the Indian Constitution and administration, the Five Year Plans, Panchayati Raj/cooperatives/community development, Bhoodan/Sarvodaya/national integration/Gandhi's teachings, forces shaping world history (Renaissance, and the American/French/Russian/Industrial revolutions), the UN/Panchsheel/democracy/socialism/communism, India's role in the contemporary world
  1. 1.Decline of the Mughal Empire
  2. 2.Rise of Regional States
  3. 3.Advent of Europeans in India — From Vasco da Gama to British Supremacy
  4. 4.British Conquest of Bengal
  5. 5.Anglo-Mysore Wars (1767-1799)
  6. 6.Anglo-Maratha Wars (1775-1818)
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  1. 7.Subsidiary Alliance, Doctrine of Lapse & the Anglo-Sikh Wars
  2. 8.Drain of Wealth, Deindustrialisation, and Land Revenue Systems
  3. 9.Civil Rebellions and Tribal Uprisings Before 1857
  4. 10.The Revolt of 1857
  5. 11.Post-1857 Administration and Crown Rule (1858-1900)
  6. 12.Socio-Religious Reform Movements of 19th Century India
  7. 13.Early Nationalism and the Formation of the Indian National Congress (1858-1905)
  8. 14.Partition of Bengal and the Swadeshi Movement (1905-1911)
  9. 15.The Three Infrastructures of Nationalism: Press, Education and the Peasant Movements (1780-1947)
  10. 16.World War I, Ghadar, Home Rule and the Lucknow Pact (1914-1918)
  11. 17.Gandhi's Emergence: From the South African Laboratory to Jallianwala Bagh (1915-1920)
  12. 18.Non-Cooperation Movement and Khilafat Aandolan (1920-1922)
  13. 19.The Years of Stagnation: Swarajists, the New Forces and the Revolutionaries (1922-1931)
  14. 20.The Gathering Storm: Simon Commission, the Nehru Report and Purna Swaraj (1927-1930)
  15. 21.Civil Disobedience Movement and Round Table Conferences (1930-34)
  16. 22.The Constitution They Despised and the Office They Took: GoI Act 1935, Congress Ministries and the Rise of the Left (1935-1939)
  17. 23.The Inclined Plane: Communalism from Syed Ahmad Khan to the Two-Nation Theory (1880s-1947)
  18. 24.Wartime Politics: From the Crisis at Tripuri to the Cripps Mission (1939-1942)
  19. 25.The Two Frontiers: Princely India and the Indian Capitalists in the Freedom Struggle (1920s-1947)
  20. 26.Quit India Movement and the INA (1942-1945)
  21. 27.Post-War National Scenario and the Transfer of Power (1945–47)
  22. 28.Independence with Partition — the Freedom and the Fracture
  23. 29.Post-Independence Consolidation (1947-1964)
  24. 30.Making of the Constitution — The Constituent Assembly and the Birth of the Republic
  25. 31.Salient Features of the Constitution — The Design Choices That Define India's Founding Charter
  26. 32.The Preamble — Identity, Authority and the Conscience of the Constitution
  27. 33.Union and its Territory — The Indestructible Union and the Reorganisation of States
  28. 34.Citizenship — Membership, the Single-Citizenship Design and the Democratic Project
  29. 35.Fundamental Rights — The Magna Carta of India
  30. 36.Directive Principles of State Policy — The Conscience of the Constitution
  31. 37.Fundamental Duties — The Code the Constitution Forgot and the Courts Revived
  32. 38.Basic Structure Doctrine — The Unamendable Core of the Constitution
  33. 39.Amendment of the Constitution — The Power to Mend, Not to Destroy
  34. 40.Federal System — 'Union of States', the Quasi-Federal Debate, and Cooperative Federalism
  35. 41.Centre-State Relations — The Three-Dimensional Machinery of Divided Power
  36. 42.Inter-State Relations — The Horizontal Machinery of a Single Nation
  37. 43.Emergency Provisions — A Constitution That Can Suspend Itself
  38. 44.Panchayati Raj — From Article 40 to the 73rd Amendment and PESA
  39. 45.Municipalities — Urban Local Self-Government Under the 74th Amendment
  40. 46.Union Territories — A Deliberate Unitary Exception in a Federal Constitution
  41. 47.Parliament — The Union Legislature and the Heart of Indian Democracy
  42. 48.State Legislature -- Organisation, Composition and Legislative Procedure of the Vidhan Sabha and Vidhan Parishad
  43. 49.The President — Head of the Indian State and Nominal Executive of the Union
  44. 50.The Vice-President — India's Second-Highest Office and the Guarantee of Continuity
  45. 51.The Prime Minister and Council of Ministers — India's Real Executive
  46. 52.The Governor — Nominal Head of the State Executive and the Centre's Constitutional Link
  47. 53.Chief Minister and State Council of Ministers — The Real Executive Behind the Governor
  48. 54.The Supreme Court of India — Composition, Independence and Jurisdiction
  49. 55.High Court and Subordinate Courts — The State Judiciary Beneath the Supreme Court
  50. 56.The Attorney-General of India — Chief Law Officer Held at the President's Pleasure
  51. 57.Advocate General of the State — The Governor's Law Officer, Not the State's
  52. 58.The Election Commission — Guardian of Free and Fair Elections Under Article 324
  53. 59.The Union Public Service Commission — Recruiting the Civil Services Under Articles 315-323
  54. 60.The State Public Service Commission — A Calibrated Mirror of the UPSC Under Articles 315-323
  55. 61.The Finance Commission — Article 280 and the Balancing Wheel of Fiscal Federalism
  56. 62.The Comptroller and Auditor-General — Guardian of the Public Purse Under Articles 148-151
  57. 63.The National Commission for Scheduled Castes — A Constitutional Template Extended Three Times
  58. 64.The National Commission for Scheduled Tribes — A Constitutional Safeguard Born of Bifurcation
  59. 65.The National Commission for Backward Classes — Completing a Constitutional Template
  60. 66.The Special Officer for Linguistic Minorities — the Half of Part XVII That Protects, Not Promotes
• Section E · Geography (20% weightage) — the Earth's shape and size, latitudes and longitudes, time and the international date line, the Earth's movements, origin of the Earth, rocks and weathering, earthquakes and volcanoes, ocean currents and tides, atmosphere and its composition, regional geography of India (climate, natural vegetation, minerals, location of agricultural and industrial activity), India's seaports and trade routes and imports/exports
  1. 1.Geomorphology — The Two Forces That Build the Land and Wear It Down
  2. 2.World Regional Physiography — Where the Earth's Relief Actually Is
  3. 3.Climatology — What the Air Does, and Why Water Is the Reason
  4. 4.World Climatic Regions — The Types, and Two Ways of Sorting Them
  5. 5.Oceanography — The Relief, the Salt, the Heat and the Currents of the Water Half of the Earth
  6. 6.Biogeography and the Natural Vegetation of the World — How an Ecosystem Works, and Why the Living Cover of the Earth Lies in Belts
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  1. 7.India: Physiography — A Shield, a Rising Wall, a Filled Trough, and Two Kinds of Island
  2. 8.Drainage Systems of India — How the Rivers Are Arranged, and Why They Behave As They Do
  3. 9.India: Climate and the Monsoon — One Rhythm, and the Variety Inside It
  4. 10.Soils of India — Formation, the Profile, the Groups, and the Erosion That Takes Them
  5. 11.India's Natural Vegetation and Wildlife — The Forest Types, the Belts Up the Himalaya, and What Has Been Done to Them
  6. 12.Water Resources of India — Four Per Cent of the World's Water for Seventeen Per Cent of Its People
  7. 13.World Resources and Industry — Where the Minerals Lie and Where the Factories Went
  8. 14.Minerals and Energy Resources of India — What the Rock Decides, and How Old Every Number Here Is
  9. 15.Industries of India — Why a Factory Stands Where It Does, and Which of These Sentences Has Expired
  10. 16.Economic Geography and Human Activities — Why an Activity Is Where It Is
  11. 17.India's Agriculture — Where the Crops Are, in Which Season, and Why the Yields Divide
  12. 18.Transport, Communication and Trade in India — The Network That Carries the Economy, and the Date on Every Number
• Section F · Current Events (10% weightage) — important events in India and the world, prominent personalities including those in cultural activities and sports