UPSC NDA Syllabus 2024 and Exam Pattern: GAT and Math

 Published On: 09-04-2024

UPSC NDA Syllabus 2024 and Exam Pattern: Mathematics

The Union Public Service Commission (UPSC) conducts the National Defence Academy (NDA) Exam annually, held twice a year. The NDA Syllabus 2024 PDF has been released via the official notification. Understanding the subject-wise topics covered in the UPSC NDA Syllabus and exam pattern is crucial for candidates aspiring to crack the NDA exam. Selection for eligible male and female candidates for the NDA exam is based on the written test followed by the Personality Test.

NDA Exam Pattern and Syllabus 2024

The NDA written examination comprises two papers: Mathematics and General Ability Test (GAT). The aspirants aiming for NDA 2024 must initiate their preparation by thoroughly understanding the detailed NDA Syllabus 2024 provided below. NDA 1 and NDA 2 Exams are set to be conducted offline on 21st April and 1st September 2024.

Key Points of NDA Syllabus 2024:

  • Name of the Exam: National Defence Academy (NDA)
  • Conducting Body: Union Public Service Commission (UPSC)
  • Frequency Of Exam: Twice in a Year (April & September 2024)
  • Selection Process:
    • Written Test consisting of Objective Type Questions
    • Intelligence & Personality Test (SSB)
  • Mode of Exam: Offline
  • Papers in NDA Exam:
    • Mathematics
    • General Ability Test
  • Marks Segregation:
    • Mathematics: 300 Marks
    • GAT: 600 Marks
  • Total No. of Questions:
    • Mathematics: 120
    • GAT: 150
  • Negative Marking:
    • Mathematics: -0.83
    • GAT: -1.33 marks
  • Exam Duration: 2.5 Hours For Each Paper (5 hours total)
  • Exam Date: 21st April 2024
  • Language of Question Paper: English & Hindi (English Language paper has to be attempted in English)

NDA Exam Pattern 2024

Before delving into the NDA Syllabus, its essential to understand the NDA Exam Pattern and marking scheme. The Mathematics paper comprises 120 questions carrying 300 marks, whereas the General Ability Test (GAT) includes English and GK Papers with 200 & 400 marks, respectively.

NDA Mathematics Syllabus

Here is the comprehensive syllabus for Mathematics covered in the NDA exam:


  • Sets, Venn diagrams, De Morgan laws
  • Cartesian product, relation, equivalence relation
  • Real numbers, Complex numbers, Modulus, Cube roots
  • Conversion of a number in Binary system to Decimals, and vice-versa
  • Arithmetic, Geometric and Harmonic progressions
  • Quadratic equations, Linear inequations
  • Permutation and Combination, Binomial theorem, and Logarithms


  • Concept of a real-valued function, domain, range, and graph of a function
  • Composite functions, one-to-one, onto, and inverse functions
  • The notion of limit, Standard limits, Continuity of functions
  • Algebraic operations on continuous functions
  • Derivative of function at a point, geometrical and physical interpretation of a derivative-application
  • Derivatives of sum, product, and quotient of functions
  • Second-order derivatives, Increasing and decreasing functions
  • Application of derivatives in problems of maxima and minima

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-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method

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
  • General and particular solution of differential equations
  • Solution of the first order, and first-degree differential equations of various types—examples
  • Application in problems of growth and decay


  • Angles and their measures in degrees and radians
  • Trigonometric ratios, Trigonometric identities
  • Sum and difference formulae, Multiple and Sub-multiple angles
  • Inverse trigonometric functions
  • Applications-Height and distance, properties of triangles

Vector Algebra:

  • Vectors in two and three dimensions, magnitude, and direction of a vector
  • Unit and null vectors, the addition of vectors, scalar multiplication of a vector
  • Scalar product, or dot product of two vectors, Vector product or cross product of two vectors
  • Applications—work done by a force and moment of a force and in geometrical problems

Analytical Geometry Of Two and Three Dimension:

  • Rectangular Cartesian Coordinate system, Distance formula
  • Equation of a line in various forms, The angle between two lines
  • Distance of a point from a line
  • Equation of a circle in standard and a general form
  • Standard forms of parabola, ellipse, and hyperbola
  • Eccentricity and axis of a conic
  • Point in a three-dimensional space, the distance between two points
  • Direction Cosines and direction ratios
  • Equation two points, Equation of a plane and a line in various forms
  • The angle between two lines and the angle between two planes
  • Equation of a sphere

Statistics and Probability:

  • Probability: Random experiment, outcomes, and associated sample space
  • Events, mutually exclusive and exhaustive events, impossible and certain events
  • Union and Intersection of events, Complementary, elementary, and composite events
  • Definition of probability—classical and statistical—examples
  • Elementary theorems on probability—simple problems
  • Conditional probability, Bayes’ theorem—simple problems
  • Random variable as function on a sample space
  • Binomial distribution, examples of random experiments giving rise to Binomial distribution

Topic-wise Question Distribution in Maths:

  • Calculus: 20-25 Questions
  • Quadratic equation: 20-15 Questions
  • Matrices & Determinants: 30 Questions
  • Probability: 10 Questions
  • Trigonometry: 30 Questions
  • Complex number: 10-15 Questions

NDA GAT Syllabus 2024

The NDA GAT (General Ability Test) consists of two papers: English and General Knowledge. The English paper carries 200 Marks, while the General Knowledge paper is worth 400 Marks.

NDA English Syllabus

The English paper aims to assess the candidate’s understanding of the English language. It covers various aspects as outlined below:

TopicNo. of QuestionsNo. of Marks
Spotting Errors520
Selecting Words1040
Ordering of Words in a Sentence936
Sentence Improvement1040

NDA General Knowledge Syllabus

The General Knowledge paper is structured as follows:

TopicNo. of QuestionsNo. of Marks
General Science1144
History & Freedom Movement1664
Current Affairs1768

NDA Physics Syllabus

The Physics syllabus for NDA covers the following topics:

  • Physical Properties and States of Matter
  • Modes of transference of Heat
  • Mass, Weight, Volume, Sound waves and their properties
  • Simple musical instruments
  • Rectilinear propagation of Light
  • Density and Specific Gravity
  • Reflection and refraction
  • Principle of Archimedes
  • Spherical mirrors and Lenses
  • Pressure Barometer
  • Human Eye
  • Motion of objects
  • Natural and Artificial Magnets
  • Velocity and Acceleration
  • Properties of a Magnet
  • Newton’s Laws of Motion
  • Earth as a Magnet
  • Force and Momentum
  • Static and Current Electricity
  • Parallelogram of Forces
  • Conductors and Non-conductors
  • Stability and Equilibrium of bodies
  • Ohm’s Law
  • Gravitation
  • Simple Electrical Circuits
  • Elementary ideas of work
  • Heating, Lighting, and Magnetic effects of Current
  • Power and Energy
  • Measurement of Electrical Power
  • Effects of Heat
  • Primary and Secondary Cells
  • Measurement of Temperature and Heat
  • Use of X-Rays
  • General Principles in the working of Simple Pendulum, Simple Pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner’s Compass; Lightning Conductors, Safety Fuses.

NDA Chemistry Syllabus

The NDA Chemistry syllabus includes the following topics:

  • Preparation and Properties of Hydrogen, Oxygen, Nitrogen, and Carbon Dioxide, Oxidation and Reduction.
  • Acids, bases, and salts.
  • Different forms of Carbon.
  • Physical and Chemical Changes.
  • Fertilizers—Natural and Artificial.
  • Elements.
  • Materials used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and Gunpowder.
  • Mixtures and Compounds.
  • Elementary ideas about the structure of Atom.
  • Symbols, Formulae, and simple Chemical Equations.
  • Atomic Equivalent and Molecular Weights.
  • Law of Chemical Combination (excluding problems).
  • Valency.
  • Properties of Air and Water.

NDA General Science Syllabus

The General Science syllabus for NDA covers the following areas:

  • Common Epidemics, their causes, and prevention.
  • Difference between the living and non-living.
  • Food—Source of Energy for man.
  • Basis of Life—Cells, Protoplasm, and Tissues.
  • Constituents of food.
  • Growth and Reproduction in Plants and Animals.
  • Balanced Diet.
  • Elementary knowledge of the Human Body and its important organs.
  • The Solar System—Meteors and Comets, Eclipses. Achievements of Eminent Scientists.

NDA Syllabus for History, Freedom Movement

The History syllabus for NDA includes:

  • Forces shaping the modern world.
  • Renaissance.
  • Exploration and Discovery.
  • A broad survey of Indian History, with emphasis on Culture and Civilization.
  • Freedom Movement in India.
  • French Revolution, Industrial Revolution, and Russian Revolution.
  • War of American Independence.
  • Impact of Science and Technology on Society.
  • Elementary study of Indian Constitution and Administration.
  • Concept of one World.
  • Elementary knowledge of Five Year Plans of India.
  • United Nations.
  • Panchsheel.
  • Panchayati Raj, Democracy, Socialism, and Communism.
  • Role of India in the present world.
  • Co-operatives and Community Development.
  • Bhoodan, Sarvodaya.
  • National Integration and Welfare State.
  • Basic Teachings of Mahatma Gandhi.

NDA Syllabus for Geography

The Geography syllabus for NDA covers:

  • The Earth, its shape, and size.
  • Ocean Currents and Tides, Atmosphere, and its composition.
  • Latitudes and Longitudes.
  • Temperature and Atmospheric Pressure, Planetary Winds, Cyclones, and Anticyclones; Humidity; Condensation, and Precipitation.
  • Concept of time.
  • Types of Climate.
  • International Date Line.
  • Major Natural Regions of the World.
  • Movements of Earth and their effects.
  • Regional Geography of India.
  • Climate, Natural vegetation. Mineral and Power resources.
  • Location and distribution of agricultural and Industrial activities.
  • Origin of Earth. Rocks and their classification.
  • Important Sea ports and main sea, land, and air routes of India.
  • Weathering—Mechanical and Chemical, Earthquakes, and Volcanoes.
  • Main items of Imports and Exports of India.

NDA Syllabus for Current Affairs

The Current Affairs syllabus includes:

  • Knowledge of Important events that have happened in India in recent years.
  • Prominent personalities of both Indian and International level.
  • Cultural activities and sports activities.
  • Current important world events.

NDA SSB Interview Process:

After successfully clearing the written exam of NDA, candidates are required to undergo the SSB (Services Selection Board) Interview rounds. The pattern of the NDA Interviews is structured as follows:

Stage 1: Screening Test

  • Verbal and non-verbal tests.
  • Picture Perception and Description Test (PPDT).

Stage 2: Psychological Test

  • Thematic Apperception Test (TAT)
  • Word Association Test (WAT)
  • Situation Reaction Test (SRT)
  • Self Description Test (SD)

Group Testing Officers Test