UPSC NDA Syllabus 2026: Topic-Wise Maths & GAT Breakdown

1. NDA Exam Pattern 2026 — Start Here

UPSC conducts both written exam papers on the same day. Here is what UPSC has specified in the official notification:

SSB Interview: 900 marks | Grand Total: 1800 marks

Based on NDA 1 2026 exam data, Paper I has 120 questions (2.5 marks each) and Paper II has 150 questions (4 marks each). UPSC does not specify the number of questions in the official notification — confirm from your admit card before the exam.

2. Negative Marking — The Practical Math

Every wrong answer costs you one-third of the marks for that question. Leaving it blank costs nothing. You can use our interactive Negative Marking Calculator to simulate your scores and see how incorrect attempts impact your total marks.

Based on NDA 1 2026 exam data:

• Mathematics (2.5 marks per question):
  • Correct answer → +2.5 marks
  • Wrong answer → −0.83 marks
  • Blank → 0 marks
• GAT (4 marks per question):
  • Correct answer → +4 marks
  • Wrong answer → −1.33 marks
  • Blank → 0 marks

Real example for Maths — attempt 10 questions, get 7 right and 3 wrong:

• Right: 7 × 2.5 = +17.50
• Wrong: 3 × (2.5 / 3) = −2.50
• Net: 15.00 marks

The rule is simple. If you can confidently knock out 2 wrong options, attempt it. If you have to guess — skip it.

3. NDA Maths Syllabus — Paper I (300 Marks)

The NDA maths syllabus is at the Class 11 and 12 level. The following topics are as specified in the official UPSC NDA-II 2026 notification:

1. Algebra

Concept of set, operations on sets, Venn diagrams, De Morgan's laws, Cartesian product, relations and equivalence relations. Representation of real numbers on a line. Complex numbers — basic properties, modulus, argument, cube roots of unity. Binary number system — conversion between decimal and binary. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequalities of two variables by graphs. Permutation and combination. Binomial theorem and its applications. Logarithms and their applications.

2. Matrices and Determinants

Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix. Applications — solving a system of linear equations in two or three unknowns by Cramer's rule and by the matrix method.

3. Trigonometry

Angles in degrees and radians. Trigonometric ratios. Trigonometric identities. Sum and difference formulae. Multiple and sub-multiple angles. Inverse trigonometric functions. Applications — heights and distances, properties of triangles.

4. Analytical Geometry — 2D and 3D

2D: Rectangular Cartesian coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic.

3D: Points in 3D space, distance between two points. Direction cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

5. Differential Calculus

Concept of a real-valued function — domain, range and graph. Composite functions, one-to-one, onto and inverse functions. Limits — notion and standard limits. Continuity of functions. Derivative of a function at a point — geometrical and physical interpretation. Derivatives of sum, product and quotient of functions, derivative of a composite function, derivative of a function with respect to another function. Second-order derivatives. Increasing and decreasing functions. Applications — maxima and minima.

6. Integral Calculus and Differential Equations

Integration as inverse of differentiation. Integration by substitution and by parts. Standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals — determination of areas of plane regions bounded by curves.

Definition of order and degree of a differential equation. Formation of differential equations. General and particular solutions. Solution of first-order and first-degree differential equations. Applications — problems of growth and decay.

7. Vector Algebra

Vectors in 2D and 3D. Magnitude and direction of a vector. Unit and null vectors. Addition of vectors. Scalar multiplication of a vector. Dot product (scalar product) of two vectors. Cross product (vector product) of two vectors. Applications — work done by a force, moment of a force, geometrical problems.

8. Statistics and Probability

Statistics: Classification of data, frequency distribution, cumulative frequency distribution. Graphical representation — histogram, pie chart, frequency polygon. Measures of central tendency: mean, median, mode. Variance and standard deviation. Correlation and regression.

Probability: Random experiment, outcomes and sample space. Events — mutually exclusive, exhaustive, impossible and certain. Union and intersection of events. Complementary, elementary and composite events. Classical and statistical definitions of probability. Elementary theorems on probability. Conditional probability. Bayes' theorem. Random variable as a function on a sample space. Binomial distribution.

4. Which Maths Topics Are Asked Most?

Based on previous year papers, the most frequently tested topics are:

Algebra and Calculus together make up roughly 40-45% of the Maths paper. Do not skip either.

5. NDA GAT Syllabus — Paper II (600 Marks)

The General Ability Test has two parts:

• Part A — English: 200 marks
• Part B — General Knowledge: 400 marks

Part A — English (200 Marks)

The English paper tests whether you can use the language correctly, not literary knowledge. Four areas as specified in the notification:

• Grammar and usage
• Vocabulary
• Comprehension
• Cohesion in extended text

Class 10-12 level English is sufficient. This is the most scoring section in the entire exam for a well-prepared candidate.

6. GK Subject-Wise Detailed Syllabus

Six subjects. Here is the official weightage as specified in the UPSC notification:

Physics and History together = 45% of the GK paper. Most candidates spread their time equally across all subjects. That is a preparation mistake this table should fix.

Physics (~100 marks)

Physical properties and states of matter, mass, weight, volume, density and specific gravity, Archimedes' principle, pressure, barometer. Motion — velocity, acceleration, Newton's laws of motion, force and momentum, parallelogram of forces, stability and equilibrium, gravitation, work, power and energy. Heat — measurement of temperature, change of state, latent heat, modes of heat transfer. Sound waves and properties, simple musical instruments. Light — rectilinear propagation, reflection and refraction, spherical mirrors and lenses, human eye. Magnetism — natural and artificial magnets, properties of a magnet, Earth as a magnet. Electricity — static and current, conductors and non-conductors, Ohm's law, simple circuits, heating, lighting and magnetic effects of current, electrical power, primary and secondary cells, X-rays. Working principles of: simple pendulum, pulleys, siphon, levers, balloon, pumps, hydrometer, pressure cooker, thermos flask, gramophone, telegraphs, telephone, periscope, telescope, microscope, mariner's compass, lightning conductors, safety fuses.

Chemistry (~60 marks)

Physical and chemical changes. Elements, mixtures and compounds, symbols, formulae, simple chemical equations, law of chemical combination. Properties of air and water. Preparation and properties of hydrogen, oxygen, nitrogen and carbon dioxide. Oxidation and reduction. Acids, bases and salts. Carbon — different forms. Natural and artificial fertilisers. Materials used in soap, glass, ink, paper, cement, paints, safety matches and gunpowder. Structure of atom, atomic and molecular weights, valency.

General Science (~40 marks)

Living vs non-living. Cells, protoplasm and tissues. Growth and reproduction in plants and animals. Elementary knowledge of the human body and its important organs. Common epidemics — causes and prevention. Food as a source of energy, constituents of food, balanced diet. Solar system — meteors, comets, eclipses. Achievements of eminent scientists.

History (~80 marks)

Indian history with emphasis on culture and civilisation. The Freedom Movement in India. Elementary study of the Indian Constitution and administration. Five-Year Plans. Panchayati Raj, cooperatives, and community development. Bhoodan, Sarvodaya, national integration, welfare state, Gandhi's basic teachings. World history — Renaissance, exploration and discovery, American War of Independence, French Revolution, Industrial Revolution, Russian Revolution. Impact of science and technology on society. United Nations, Panchsheel, democracy, socialism, communism. Role of India in the present world.

Geography (~80 marks)

Earth — shape and size, latitudes and longitudes, concept of time, International Date Line, movements of Earth and their effects. Origin of Earth, rocks and their classification, weathering, earthquakes and volcanoes. Ocean currents and tides. Atmosphere — composition, temperature, atmospheric pressure, planetary winds, cyclones and anti-cyclones, humidity, condensation and precipitation, types of climate, major natural regions of the world. India — climate, natural vegetation, mineral and power resources, location and distribution of agricultural and industrial activities. Important sea ports and main sea, land and air routes of India. Main items of imports and exports.

Current Events (~40 marks)

Important recent events in India and across the world. Prominent personalities, Indian and international, connected with cultural activities and sports.

7. NDA Ka Syllabus — Same for Army, Navy, Air Force?

Yes. The NDA ka syllabus is identical for all three wings. Every candidate writes the same two papers. Wing allocation is based on merit and preference — not on which subjects you scored in.

8. Commerce and Arts Students — What to Focus On

You can apply only for the Army wing. Here is your situation:

• Maths — Needs serious work. Start with NCERT Class 11 and 12 before any NDA book. Give it at least 60% of your study time.
• History and Geography — Leverage these sections as your natural strengths. Together, they make up a massive 40% of the GK paper.
• Physics — Highest single-subject weightage at 25% of GK. Give it dedicated time, even without a prior background.
• English — Straightforward for most Commerce and Arts students. Do not neglect it.

9. Best Books for NDA Preparation

Mathematics Books

English Books

General Knowledge Books

Arihant NDA Book vs Mission NDA Book

Arihant Pathfinder NDA/NA: Covers the full syllabus with chapter-wise theory, solved examples, and 10+ years of previous year papers. Best used as a single revision and practice resource after covering the basics from the NCERT.

Mission NDA: Covers all subjects, including Maths, English, General Science, History, Geography, and mock tests. Good for candidates who want one book that touches everything.

Neither replaces NCERT. That comes first.

10. How to Prepare for NDA

• Maths needs daily practice — not daily reading. 120 questions in 150 minutes is the target pace. Speed only comes from solving questions every day. Minimum 50 questions daily.
• Physics is 25% of GK — treat it like a separate subject. Most candidates lump it into general GK revision. It carries ~100 marks out of 400. Give it dedicated daily time.
• Current affairs — start exactly 3 months before the exam. NDA-II 2026 exam is on 13 September 2026. Start current affairs from June 2026. Questions come from recent months — not the past year. Earlier preparation for current affairs is wasted time.
• English is 200 marks — do not treat it as easy. Easy to score in, easy to ignore. 30 minutes daily on grammar and vocabulary makes it your highest-scoring section.
• Solve at least 5 years of previous year papers. Nothing else tells you what actually comes in the exam. Pattern, difficulty, topic distribution — all of it becomes clear from past papers.

11. Check Your Attempts Before You Start Preparing

Before putting in months of preparation, confirm you are actually eligible for NDA-II 2026 or upcoming cycles. Your eligibility depends entirely on your date of birth.

Use our NDA Attempt Calculator — enter your date of birth, and it shows every cycle you are eligible for instantly.

Quick Reference

Syllabus verified against the official UPSC NDA & NA Examination-II, 2026 notification (Examination Notice No. 10/2026-NDA-II) dated 20 May 2026. Question counts and marks per question are based on NDA 1 2026 exam data and are not specified in the official notification.