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NATIONAL DEFENCE ACADEMY AND NAVAL ACADEMY EXAMINATION (I), 2026

Kartikey Singh Kartikey Singh
Updated: 13 days ago
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APPENDIX-I (The Scheme and Syllabus of Examination)

The Scheme and Syllabus of Examination

A. SCHEME OF EXAMINATION

Mathematics (Code 01, 2½ Hours, 300 Marks)
General Ability Test (Code 02, 2½ Hours, 600 Marks)
Total Written Examination Marks: 900
SSB Test/Interview: 900
Papers will consist of Objective Type Questions only
Mathematics and Part B of General Ability Test will be set bilingually in Hindi and English
Questions will involve metric system of Weights and Measures
Candidates must write papers in their own hand, no scribes allowed
Commission may fix qualifying marks
Use of calculator, mathematical or logarithmic tables is not permitted

PAPER-I: MATHEMATICS (Code 01, Max Marks 300)

Algebra
Matrices and Determinants
Trigonometry
Analytical Geometry of Two and Three Dimensions
Differential Calculus
Integral Calculus and Differential Equations
Vector Algebra
Statistics and Probability

Algebra

Concept of set, operations on sets, Venn diagrams, De Morgan laws
Cartesian product, relation, equivalence relation
Complex numbers, modulus, argument, cube roots of unity
Binary system of numbers, decimal-binary conversions
Arithmetic, Geometric, Harmonic progressions
Quadratic equations with real coefficients
Solution of linear inequations of two variables by graphs
Permutation and Combination, Binomial theorem, Logarithms

Matrices and Determinants

Types and operations of matrices
Determinant properties
Adjoint and inverse of square matrix
Solution of linear equations by Cramer’s rule and Matrix Method

Trigonometry

Angles in degrees and radians
Trigonometrical ratios, identities
Sum and difference, multiple and sub-multiple angles
Inverse trigonometric functions
Applications: Heights, distances, triangle properties

Analytical Geometry of Two and Three Dimensions

Cartesian system, distance formula
Equation of line, angle between lines, distance from a point
Circle, parabola, ellipse, hyperbola equations
Eccentricity and axes
3D geometry: points, direction cosines/ratios
Plane and line equations, angles between lines/planes
Equation of sphere

Differential Calculus

Functions, domain, range, graphs
Composite, one-to-one, onto, inverse functions
Limits and continuity
Derivatives: definitions, interpretations, rules
Second order derivatives
Increasing/decreasing functions
Applications: maxima, minima

Integral Calculus and Differential Equations

Integration basics and methods (substitution, parts)
Standard integrals (algebraic, trig, exponential, hyperbolic)
Definite integrals and area applications
Differential equations: order, degree, formation
General/particular solutions
First order and first degree equations
Applications: growth and decay

Vector Algebra

2D/3D vectors, magnitude, direction, unit/null vectors
Addition, scalar multiplication
Dot and cross product
Applications: work, moment, geometry

Statistics and Probability

Data classification, frequency distribution
Histogram, pie chart, frequency polygon
Mean, median, mode, variance, standard deviation
Correlation and regression
Probability concepts, events, theorems
Conditional probability, Bayes’ theorem
Random variable, Binomial distribution

PAPER-II: GENERAL ABILITY TEST (Code 02, Max Marks 600)

Part A - English (Max Marks 200)
Part B - General Knowledge (Max Marks 400)

Part A - English

Grammar and usage
Vocabulary
Comprehension
Cohesion in extended text

Part B - General Knowledge

Physics
Chemistry
General Science
History, Freedom Movement etc.
Geography
Current Events

Physics

Properties of matter, mass, weight, volume, density, Archimedes principle
Motion, velocity, acceleration, Newton’s laws, momentum, forces, gravitation
Work, power, energy
Heat, temperature, latent heat, heat transfer
Sound waves, musical instruments
Light: reflection, refraction, mirrors, lenses, human eye
Magnetism and electricity, Ohm’s law, circuits, cells, X-rays
General working principles: pendulum, pulleys, siphon, levers, pumps, hydrometer, pressure cooker, thermos flask, gramophone, telegraphs, telephone, periscope, telescope, microscope, compass, lightning conductor, safety fuses

Chemistry

Physical and chemical changes
Elements, mixtures, compounds, equations
Laws of chemical combination
Air and water properties
Hydrogen, oxygen, nitrogen, CO2: preparation and properties
Oxidation and reduction
Acids, bases, salts
Carbon forms
Fertilizers
Preparation of substances: soap, glass, ink, paper, cement, paints, matches, gunpowder
Atomic structure basics, atomic weight, valency

General Science

Living vs non-living
Cells, protoplasm, tissues
Growth and reproduction in plants/animals
Human body and organs
Common epidemics and prevention
Food and nutrition, balanced diet
Solar system, meteors, comets, eclipses
Achievements of scientists

History, Freedom Movement etc.

Survey of Indian history, culture and civilisation
Indian freedom movement
Indian Constitution and Administration basics
Five Year Plans
Panchayati Raj, Co-operatives, Community Development
Bhoodan, Sarvodaya, National Integration, Welfare State, Teachings of Mahatma Gandhi
World events: Renaissance, Discovery, American Independence, French, Industrial and Russian Revolutions
Impact of science and technology on society
Concept of one World, UN, Panchsheel, Democracy, Socialism, Communism
India’s role in world affairs

Geography

Earth: shape, size, latitudes, longitudes, time, International Date Line
Earth movements and effects
Origin of Earth, rocks, weathering, earthquakes, volcanoes
Ocean currents, tides
Atmosphere: composition, temperature, pressure, winds, cyclones, humidity, rainfall, climates, natural regions
Regional geography of India: climate, vegetation, resources, industries
Sea ports, routes, imports and exports

Current Events

Important national and international events
Prominent personalities: cultural, sports, politics

Note

Part B weightage distribution: Physics 25%, Chemistry 15%, General Science 10%, History 20%, Geography 20%, Current Events 10%

Study Tips

Preparation Strategy:

  • Create a study schedule
  • Focus on high-weightage topics
  • Practice previous year papers
  • Take regular mock tests

Important Resources:

  • NCERT books for basics
  • Current affairs magazines
  • Online practice platforms
  • Join study groups