NDA Exam Pattern

Paper  Subject Name Duration Containing Marks No. of Questions
I Mathematics 2.5 Hours (150 Min) 300 120
II General Ability Test 2.5 Hours (150 Min) 600 150
Total Marks 900 270

 Pattern of General Ability Test

Section  Subject Name Marks No. of Questions
I English  200 50
II General Knowledge 400  100
Total Marks 600 150

General Knowledge Marks distribution

Subject Name Marks
Physics 100
Chemistry 60
General Science 40
History, Freedom Movement 80
Geography 80
Current Events 40

NDA Maths Syllabus



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


  • Complex numbers
  • Basic properties
  • Modulus
  • Argument
  • Cube roots of unity
  • Conversion of a number in decimal system to binary system and vice-versa
  • Arithmetic
  • Geometric and Harmonic Progressions
  • Solution of linear inequations of two variables by graphs
  • Binomial theorem and its application
  • Representation of real numbers on a line
  • Binary system of numbers
  • Quadratic equations with real coefficients
  • Permutation and Combination
  • Logarithms and their applications.

Differential Calculus

  • Composite functions – one to one, onto and inverse functions
  • Continuity of functions
  • Algebraic operations on continuous functions
  • Geometrical and physical interpretation of a derivative – applications
  • Increasing and decreasing functions
  • Application of derivatives in problems of maxima and minima
  • Concept of a real valued function – domain, range, and graph of a function, Notion of limit,
  • Standard limits – Derivative of a function at a point.
  • Geometrical and Physical interpretation of a derivative – Applications, Derivatives of Sum, Product and quotient of functions.
  • Derivative of a function with respect to another function
  • The derivative of a composite function and Second order derivatives.

Vector Algebra:

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

Integral Calculus and Differential equations

  • Integration by substitution and by parts
  • Trigonometric
  • Exponential and hyperbolic functions
  • Definition of order and degree of a differential equation
  • Formation of a differential equation by examples
  • A solution of the first order and first-degree differential equations of various types – examples, Integration as the inverse of differentiation, Standard integrals involving algebraic expressions.
  • Evaluation of definite integrals
  • Determination of areas of plane regions bounded by curves – applications, General and particular solution of a differential equation, Application in problems of growth and decay.

Matrices and Determinants

  • Types of Matrices
  • Determinant of a matrix
  • Adjoint and inverse of a square matrix
  • Operations on matrices
  • Basic properties of determinant
  • Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.

Analytical Geometry of two and three dimensions:

  • Distance formula
  • Angle between two lines
  • Equation of a circle in standard and in general form
  • Ellipse and hyperbola
  • Rectangular Cartesian Coordinate system
  • Equation of a line in various forms
  • Distance of a point from a line
  • Standard forms of parabola
  • Eccentricity and axis of a conic.

Three dimensions:

  • Point in a three-dimensional space
  • Distance between two points
  • Equation of a plane and a line in various forms
  • Equation of a sphere
  • Direction Cosines and direction ratios
  • An angle between two lines and an angle between two planes.


  • Frequency distribution
  • Measures of Central tendency – mean, median and mode, Classification of data
  • Cumulative frequency distribution – examples
  • Graphical representation – Histogram, Pie Chart
  • Frequency Polygon – examples,
  • Variance and standard deviation – determination and comparison, Correlation and regression.



  • Outcomes and associated sample Space
  • Bayes’ theorem
    • Simple problems
    • Binomial distribution
    • Random experiment
    • Examples of random experiments giving rise to Binominal distribution
  • Events

    • Mutually exclusive and exhaustive events,
    • Impossible and certain events
    • Complementary
    • Elementary and composite events
    • Union and Intersection of events
  • Definition of probability
  • Classical and statistical – examples,
  • Elementary theorems on probability
    • Simple problems
    • Conditional probability
    • Random variable as function on a sample space
    • Binomial distribution
    • Examples of random experiments giving rise to Binomial distribution.

      General Ability Syllabus

    • Part A


      • Vocabulary
      • Grammar and usage
      • Comprehension and cohesion in extended text to test the candidate’s proficiency in English.

      Part B

      NDA Syllabus for General Knowledge

      The question paper comprises of general knowledge and covers the subjects that include Physics, Chemistry, General Science, Social Studies, Geography and Current Events.

      Section A – NDA Exam Syllabus – Physics

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

      Section B – UPSC NDA Syllabus of Chemistry

      • Preparation and Properties of Hydrogen
      • Oxygen
      • Nitrogen and Carbon-Di-oxide
      • Oxidation and Reduction
      • Carbon – different forms, Material used in the preparation of substances like soap, Ink, Glass, Cement, Paper,  Paints, Safety Matches, and Gun-Powder, Physical and Chemical changes.
      • Elements, Symbols, Mixtures and Compounds, Formulas and simple Chemical Equations, Law of Chemical Combination (excluding problems).
      • Properties of Air and Water, Acids, bases, and salts.
      • Fertilizers – Natural and Artificial, Elementary ideas about the Structure of Atom, Atomic, Equivalent and Molecular Weights, Valency.

      Section C – Syllabus of NDA – General Science

      • The basis of Life – Cells, Protoplasms and Tissues, Elementary knowledge of human Body and its important organs.
      • Food – Source of Energy for man, Balanced Diet, Constituents of food, Achievements of Eminent Scientists, Difference between the living and non-living, Common Epidemics, their causes, and prevention
      • The Solar System – Meteors and Comets, Eclipses.

      Section D – Syllabus for NDA Exam – History

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

      Section E – Syllabus for NDA Entrance Exam – Geography

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

      Section F – Current Events

      • Current important world events.
      • Knowledge of Important events that have happened in India in the recent years.
      • Prominent personalities – both Indian and International including those connected with cultural activities and sports.




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