Exam Notification 2024

NDA 2020 Syllabus

NDA 2020 exam dates for NDA I and NDA II examinations have been released. Candidates can apply in online mode at upsconline.nic.in till 28th January, 2020.

NDA exam is conducted by UPSC as a gateway for the candidates who desire to make their career in Indian Defence (the Army, the Navy and the Air Force).


The NDA exam consists of two papers:

Mathematics: The syllabus of mathematics covers the following topic:-


  1. Trigonometric ratios
  2. Angles and their measures in degrees and in radians.
  3. Trigonometric identities sum and difference formula.
  4. Multiple And Sub-Multiple Angles
  5. Inverse Trigonometric Functions
  6. Applications – Height And Distance
  7. Properties of Triangles.


  1. Operations on sets
  2. Venn diagrams de Morgan laws
  3. Cartesian product relation
  4. Equivalence Relation
  5. Representation of real numbers on a-line
  6. Complex numbers – basic properties
  7. Modulus argument
  8. Cube roots of unity
  9. Binary system of numbers
  10. Conversion of a Number in Decimal System to Binary system and vice- versa
  11. Arithmetic
  12. Geometric and harmonic progressions
  13. Quadratic equations with real coefficients
  14. Solution Of Linear equations Of Two Variables By Graphs
  15. Permutation and combination
  16. Binomial theorem and its application
  17. Logarithms and Their Applications
  18. Concept of a set

Matrices and determinants:

  1. Types of matrices
  2. Operations on matrices determinant of a matrix
  3. Basic properties of determinant.
  4. Adjoint and inverse of a square matrix
  5. Applications – solution of a system of linear equations in two or three unknowns by Cramer’s rule and by matrix method.

Integral Calculus:

  1. Integration As Inverse Differentiation
  2. Integration By Parts And Substitution
  3. Standard Integrals Involving Expression Of Algebraic,
  4. Trigonometric,
  5. Evaluation of Definite Integrals – Determination of Areas of Plane Regions
  6. Bounded By Curves – Applications.

Analytics Geometry Of Two And Three Dimensions:

  1. Rectangular Cartesian coordinate system
  2. Distance formula
  3. Equation of a line in various forms
  4. Angle between two lines
  5. Distance of a point from a line
  6. Equation of a circle in standard and in general, form
  7. Standard forms of parabola
  8. Ellipse and hyperbola
  9. Eccentricity and axis of a conic
  10. Point in a three-dimensional space, distance between two points.
  11. Direction cosines and direction ratios.
  12. The equation of a plane and a line in various forms.
  13. The angle between two lines and angle between two planes.
  14. The equation of a sphere.

Differential Calculus:

  1. Concept of a real-valued function – domain
  2. Range and graph of a function
  3. composite functions
  4. Derivative of function at a point
  5. Derivatives of sum
  6. Product and quotient of functions
  7. Derivative of a function with respect of another function
  8. Derivative of a composite function
  9. second-order derivatives
  10. Increasing and decreasing functions
  11. Application of derivatives in problems of maxima and minima.

Differential Equations:

  1. Definition of order and degree of a differential equation
  2. Formation of a differential equation
  3. General and particular solution of a differential equation
  4. Solution of first order and first degree differential equations of various types
  5. Application in problems of growth and decay.


  1. Random experiment
  2. Outcomes and associated sample space
  3. Events
  4. Mutually exclusive and exhaustive events
  5. Impossible and certain events
  6. Union and intersection of events
  7. Complementary
  8. Elementary and composite events
  9. Conditional probability
  10. Bayes’ theorem – simple problems
  11. Random variable as function on a sample space
  12. Binomial distribution
  13. Examples of random experiments giving rise to binominal distribution.

Vector Algebra:

  1. Vectors In Two And Three Dimensions
  2. Magnitude And Direction Of A Vector
  3. Unit And Null Vectors Addition Of Vectors
  4. Scalar Multiplication Of Vector


  1. Classification Of Data
  2. Frequency Distribution
  3. Cumulative Frequency Distribution – Examples
  4. Graphical Representation – Histogram
  5. Pie Chart
  6. Frequency Polygon – Examples
  7. Measures Of Central Tendency – Mean Median And Mode
  8. Variance And Standard Deviation – Determination And Comparison
  9. Correlation And Regression

General Ability Test:

English: The syllabus of mathematics covers the following topic:-

  1. Grammar and usage.
  2. Vocabulary.
  • Comprehension and cohesion in extended text.
  1. Use of words.

General Knowledge:

  1. Knowledge of important events that have happened in India in recent years
  2. Current important world events
  • Prominent personalities—both Indian and International
  1. Sports affairs.
  2. Current important economy related events.

General Science: The question paper on General science will cover questions from Physics, Chemistry, Biology, History, Polity and Geography.


  • Physical properties and states of matter
  • Mass
  • Weight
  • Volume
  • Density
  • Specific gravity
  • Principle of Archimedes
  • Pressure barometer.
  • 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.
  • Effects of heat
  • Measurement of temperature and heat
  • Change of state and latent heat
  • Modes of transference of heat.
  • Sound waves and their properties
  • Simple musical instruments.
  • Rectilinear propagation of light
  • Reflection and refraction.


  • Difference between the living and non-living
  • Basis of life – cells, protoplasm’s and tissues
  • Growth and reproduction in plants and animals
  • Elementary knowledge of human body and its important organs
  • Common epidemics, their causes and prevention
  • Food – source of energy for man. Constituents of food, balanced diet
  • the solar system – meteors and comets, eclipses.
  • Achievements of eminent (important) scientists.


  • Physical and Chemical Changes.
  • Elements Mixtures And Compounds Symbols Formulae
  • Simple Chemical Equations Law Of Chemical Combination (Excluding Problems).
  • Properties of Air and Water.
  • Preparation and Properties Of    Hydrogen, Oxygen, Nitrogen, Carbon Dioxide, Oxidation, And Reduction.
  • Acids Bases and Salts.
  • Carbon – Different Forms.
  • Fertilizers – Natural And Artificial
  • Material Used in the Preparation Of Substances Like Soap Glass Ink Paper Cement Paints Safety Matches And Gun-Powder.
  • Elementary Ideas about the Structure Of Atom Atomic Equivalent And Molecular Weights Valency.

NDA Coaching In Allahabad

Social Studies:

  • A Broad Survey Of Indian History, With Emphasis On Culture And Civilization
  • Freedom Movement In India
  • Elementary Study Of Indian Constitution And Administration
  • Elementary Knowledge Of Five Year Plans Of India
  • Panchayati Raj, Co-Operatives And Community Development
  • Bhoodan, Sarvodaya, National Integration And Welfare State, Basic Teachings Of Mahatma Gandhi
  • Forces Shaping The Modern World; Renaissance, Exploration, And Discovery; War Of American Independence. French Revolution, Industrial Revolution and Russian
  • 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


  • Earth Its 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
  • Mechanical and Chemical Earthquakes and Volcanoes.
  • Ocean Currents And Tides
  • Atmosphere And Its Composition;
  • Temperature And Atmospheric Pressure Planetary Winds Cyclones And Anti-Cyclones;
  • Humidity
  • Condensation And Precipitation
  • Types of Climate.
  • Major Natural Regions of the World.
  • Regional Geography Of 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 of India.
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