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 28^{th} 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).

**NDA 2020: SYLLABUS**

The NDA exam consists of two papers:

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

**Trigonometry**:

- Trigonometric ratios
- Angles and their measures in degrees and in radians.
- Trigonometric identities sum and difference formula.
- Multiple And Sub-Multiple Angles
- Inverse Trigonometric Functions
- Applications – Height And Distance
- Properties of Triangles.

**Algebra**:

- Operations on sets
- Venn diagrams de Morgan laws
- Cartesian product relation
- Equivalence Relation
- Representation of real numbers on a-line
- Complex numbers – basic properties
- Modulus argument
- Cube roots of unity
- Binary system of numbers
- Conversion of a Number in Decimal System to Binary system and vice- versa
- Arithmetic
- Geometric and harmonic progressions
- Quadratic equations with real coefficients
- Solution Of Linear equations Of Two Variables By Graphs
- Permutation and combination
- Binomial theorem and its application
- Logarithms and Their Applications
- Concept of a set

**Matrices and determinants:**

- Types of matrices
- Operations on matrices determinant of a matrix
- Basic properties of determinant.
- 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:**

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

**Analytics Geometry Of Two And Three Dimensions:**

- 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 in general, form
- Standard forms of parabola
- Ellipse and hyperbola
- Eccentricity and axis of a conic
- Point in a three-dimensional space, distance between two points.
- Direction cosines and direction ratios.
- The equation of a plane and a line in various forms.
- The angle between two lines and angle between two planes.
- The equation of a sphere.

**Differential Calculus:**

- Concept of a real-valued function – domain
- Range and graph of a function
- composite functions
- Derivative of function at a point
- Derivatives of sum
- Product and quotient of functions
- Derivative of a function with respect of another function
- Derivative of a composite function
- second-order derivatives
- Increasing and decreasing functions
- Application of derivatives in problems of maxima and minima.

**Differential Equations:**

- Definition of order and degree of a differential equation
- Formation of a differential equation
- General and particular solution of a differential equation
- Solution of first order and first degree differential equations of various types
- Application in problems of growth and decay.

**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
- Conditional probability
- Bayes’ theorem – simple problems
- Random variable as function on a sample space
- Binomial distribution
- Examples of random experiments giving rise to binominal distribution.

**Vector Algebra:**

- Vectors In Two And Three Dimensions
- Magnitude And Direction Of A Vector
- Unit And Null Vectors Addition Of Vectors
- Scalar Multiplication Of Vector

**Statistics:**

- Classification Of Data
- Frequency Distribution
- Cumulative Frequency Distribution – Examples
- Graphical Representation – Histogram
- Pie Chart
- Frequency Polygon – Examples
- Measures Of Central Tendency – Mean Median And Mode
- Variance And Standard Deviation – Determination And Comparison
- Correlation And Regression

**General Ability Test**:

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

- Grammar and usage.
- Vocabulary.

- Comprehension and cohesion in extended text.

- Use of words.

**General Knowledge:**

- Knowledge of important events that have happened in India in recent years
- Current important world events

- Prominent personalities—both Indian and International

- Sports affairs.
- Current important economy related events.

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

**Physics:**

- 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.

**Biology: **

- 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.

**Chemistry: **

- 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.

**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

**Geography:**

- 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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