In this guide
Most candidates read the NDA syllabus once, decide it is "Class 11–12 maths plus GK", and never open it again. That is a mistake. The official syllabus is short, specific and full of small signals: topics that are not in your school course, a GK section that includes the working of a pressure cooker and a thermos flask, and a note that tells you almost exactly how the 400 GK marks are split. Read closely, it is the best study plan you will get for free.
This guide goes through each paper, points out what candidates usually miss, and ends with priorities and a tracker.
Paper I: Mathematics (300 marks)
The syllabus has eight units. The table lists each, with the topics that school courses sometimes leave out.
| Unit | Main topics | Easy to miss |
|---|---|---|
| Algebra | Sets, Venn diagrams, relations; complex numbers; AP, GP and HP; quadratic equations; permutations and combinations; binomial theorem; logarithms | Binary numbers and decimal–binary conversion; cube roots of unity; linear inequations in two variables solved by graphs; harmonic progression |
| Matrices and determinants | Types and operations, determinants and their properties, adjoint and inverse | Solving two or three equations by Cramer's rule and by the matrix method |
| Trigonometry | Degrees and radians, ratios, identities, sum and difference, multiple and sub-multiple angles | Inverse trigonometric functions; heights and distances; properties of triangles |
| Analytical geometry (2D and 3D) | Distance formula, lines, angle between lines, distance of a point from a line, circles, parabola, ellipse, hyperbola | Direction cosines and ratios; equations of a plane and a line; angle between planes; equation of a sphere |
| Differential calculus | Functions, domain and range, limits, continuity, derivatives, second derivatives | One-one, onto and inverse functions; increasing and decreasing functions; maxima and minima |
| Integral calculus and differential equations | Substitution, by parts, standard integrals, definite integrals, area under curves | Integrals involving hyperbolic functions; order and degree; growth and decay problems |
| Vector algebra | Magnitude and direction, unit and null vectors, dot and cross products | Work done by a force; moment of a force |
| Statistics and probability | Frequency distributions, histograms, pie charts, mean, median, mode, variance, standard deviation | Correlation and regression; conditional probability; Bayes' theorem; binomial distribution |
The level is broadly Class 11 and 12, but the paper rewards speed. With 120 questions in two and a half hours, standard results — such as properties of definite integrals, sums of series and trigonometric values — need to be instant.
Paper II, Part A: English (200 marks)
The notification describes the English section in one sentence: it tests "grammar and usage, vocabulary, comprehension and cohesion in extended text". In practice, papers have used these question types:
- spotting errors in a sentence;
- sentence improvement;
- synonyms and antonyms, often in context;
- ordering of words in a sentence or sentences in a paragraph;
- fill in the blanks;
- reading comprehension passages.
The mix of types can shift between papers, so practise all of them. There is no fixed book syllabus; what is being tested is a habit of reading correct English. Our English plan for NDA turns this into a daily routine.
Paper II, Part B: General Knowledge (400 marks)
This is the part candidates underestimate most, and the one the notification is most precise about. It says questions from the six sections will carry approximately these weightages:
| Section | Weightage | Approx. marks | Approx. questions (at 4 marks) |
|---|---|---|---|
| A. Physics | 25% | 100 | 25 |
| B. Chemistry | 15% | 60 | 15 |
| C. General Science | 10% | 40 | 10 |
| D. History, Freedom Movement, etc. | 20% | 80 | 20 |
| E. Geography | 20% | 80 | 20 |
| F. Current Events | 10% | 40 | 10 |
What each section actually covers
Physics covers properties of matter (density, Archimedes' principle, pressure and the barometer), motion and Newton's laws, equilibrium, gravitation, work, energy and power, heat and latent heat, sound, light (mirrors, lenses, the human eye), magnetism, static and current electricity, and uses of X-rays. It also lists the working principles of everyday devices: the simple pendulum, pulleys, siphon, levers, balloon, pumps, hydrometer, pressure cooker, thermos flask, periscope, telescope, microscope, mariner's compass, lightning conductors and safety fuses.
Chemistry covers physical and chemical changes, elements, mixtures and compounds, equations, properties of air and water, hydrogen, oxygen, nitrogen and carbon dioxide, oxidation and reduction, acids, bases and salts, forms of carbon, fertilisers, and the materials used to make soap, glass, ink, paper, cement, paints, safety matches and gunpowder. Atomic structure, valency and equivalent and molecular weights come in at an elementary level.
General Science is mostly biology: living and non-living, cells and tissues, growth and reproduction, the human body, common epidemics, food and balanced diet. It also includes the solar system, eclipses and the achievements of eminent scientists.
Section D is broader than its name. Beyond Indian history and the freedom movement, it includes the Constitution and administration, Five Year Plans, Panchayati Raj, co-operatives, Bhoodan and Sarvodaya, Gandhi's basic teachings, and world history: the Renaissance, the American War of Independence, and the French, Industrial and Russian Revolutions, as well as the United Nations and Panchsheel.
Geography runs from the Earth's shape, latitudes, longitudes and time zones, through rocks, earthquakes, ocean currents, winds and climate, to India's resources, industries, ports, trade routes and main imports and exports.
Current Events covers important recent national and world events and prominent personalities, including those in culture and sports.
How to set priorities
- Mathematics, every day. It is the largest single paper, and speed only comes from volume.
- Physics and chemistry for GK. About 160 marks between them, mostly from school textbooks.
- History, polity and geography. About 160 marks together; science students must build these from scratch, so start early.
- English, daily and short. Twenty minutes of reading and a few objective questions beat a weekend marathon.
- General science and current affairs. Steady weekly coverage, with defence news and a monthly revision.
For a paper-wise plan, see the maths plan and the GK plan.
Try the syllabus: five quick questions
- Convert 45 (decimal) to binary.
- Find the value of log₂ 8 + log₃ 9.
- A periscope works mainly on which property of light?
- Name the three ingredients of traditional gunpowder.
- Panchsheel is associated with an agreement between India and which country?
Answers:
- 101101. 45 = 32 + 8 + 4 + 1, so the 32, 8, 4 and 1 places are 1 and the 16 and 2 places are 0.
- 5. log₂ 8 = 3 because 2³ = 8, and log₃ 9 = 2 because 3² = 9.
- Reflection, using two plane mirrors (or prisms) set at 45°.
- Potassium nitrate, charcoal and sulphur.
- China (the 1954 agreement).
Each of these comes from a line of the syllabus that many candidates skip.
A tracker
Copy this into a notebook and extend it to every topic in the tables above. Tick each column only when it is really done.
| Paper | Topic | Studied | Practised (timed) | Revised once | Revised twice |
|---|---|---|---|---|---|
| Maths | Binary numbers and logarithms | ||||
| Maths | Trigonometry and inverse functions | ||||
| Maths | 3D geometry and the sphere | ||||
| Maths | Probability and Bayes' theorem | ||||
| GK | Physics — everyday devices | ||||
| GK | Chemistry — soap, glass, cement and others | ||||
| GK | World history — revolutions | ||||
| English | Spotting errors |
Review the tracker every Sunday. Topics with an empty "Practised" column are the ones most likely to cost you marks on exam day.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Union Public Service Commission website .
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