# NDA Syllabus 2021 April: Mathematics & General Ability Test Syllabus

NDA Syllabus 2021 April & September: Union Public Service Commission (UPSC) Conducts NDA Exam 2021 twice a year (once in April and in September) for admission to the Army, Navy, and Air Force of the NDA and Indian Naval Academy Course (INAC). Every year a large number of students apply for the National Defense Academy (NDA) Exam. All the candidates who want to apply for NDA Exam 2021 need to fill the Online Application form with Required Information.

Candidates who have completed their education in Physics, Chemistry, and Maths can choose from all three services – The Air Force, Navy, and Army. The NDA April & September Syllabus 2021 and Exam pattern is given in this article. Students must-read Complete details to know about NDA 2021 exam Syllabus.

**NDA 2021 Exam Pattern**

Code | Subject | Marks | Time |

01 | Mathematics | 300 Marks | 2 hrs 30 mints |

02 | General Ability Test | 600 Marks | 2 hrs 30 mints |

Total | 900 Marks |

**NDA Syllabus 2021 April **

National Defense Academy / Naval Academy entrance exam conducted twice a year by UPSC. There are two papers in the NDA Exam – Mathematics and General Aptitude Test. Paper 1 in NDA includes Mathematics. The Syllabus of the NDA exam is the same as last year. In the Exam Question, 10 + 2 level questions will only be asked. General Ability Test (GTA) is the 2nd paper of the NDA Exam, which is divided into two parts- English and General Knowledge. The GAT is meant to evaluate a Students’ basic awareness and English proficiency. Now check the Detailed Syllabus of the NDA exam 2021.

**NDA Mathematics Syllabus 2021**

**The Mathematics Complete Topics are given below:**

**Trigonometry:**

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

**Algebra**

- Argument
- Binary system of numbers
- Binomial theorem and its application
- Complex numbers
- cube roots of unity
- Geometric and Harmonic progressions
- Logarithms and their applications.
- Permutation and Combination
- Quadratic equations with real coefficients
- Representation of real numbers on a line
- Solution of linear in equations of two variables by graphs

**Differential Calculus**

- Application of derivatives in problems of maxima and minima
- Composite functions
- Concept of a real valued function – domain, range and graph of a function
- Continuity of functions – examples, algebraic operations on continuous functions,
- Derivative of a composite function and second order derivatives.
- Derivative of a function at a point, Derivatives of sum
- derivative of a function with respect of another function
- geometrical and physical interpretation of a derivative – applications, increasing and decreasing functions
- Notion of limit, Standard limits – examples
- one to one
- onto and inverse functions
- product and quotient of functions,

**Vector Algebra**

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

**Integral Calculus and Differential equations**

- Application in problems of growth and decay
- Definition of order and degree of a differential equation
- Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications
- exponential and hyperbolic functions
- formation of a differential equation by examples
- General and particular solution of a differential equation
- Integration as inverse of differentiation
- Integration by substitution and by parts
- solution of first order and first degree differential equations of various types – examples
- standard integrals involving algebraic expressions
- Trigonometric

**Matrices and Determinants**

- Types of Matrices
- adjoin and inverse of a square matrix
- basic properties of determinant
- Determinant of a matrix
- Operations on matrices, 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**

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

**Statistics**

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

**Probability:**

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

**General Ability Test (GAT) Syllabus 2021**

**NDA Physics Syllabus 2021**

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

**Chemistry** Syllabus For NDA 2021 April Exam

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

**UPSC NDA Syllabus 2021 for Geography**

- Concept of time
- Condensation and Precipitation
- Humidity
- Important Sea ports
- Imports and Exports of India.
- International Date Line
- Lattitudes and Longitudes
- Location and distribution of agricultural and Industrial activities.
- Mineral and Power resources;
- Ocean Currents and Tides
- Origin of Earth, its Movements and their effects
- Planetary Winds, Cyclones and Anti-cyclones
- Regional Geography of India—Climate, Natural vegetation.
- Rocks and their classification
- Temperature and Atmospheric Pressure
- Types of Climate, Major Natural regions of the World.
- Weathering— Mechanical and Chemical, Earthquakes and Volcanoes

**General Science** Syllabus For NDA Exam 2021

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

**History Syllabus for NDA Exam 2021**

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

**Current Events**

- Current important world events
- Knowledge of Important events– both Indian and International cultural
- sports

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