# NDA Syllabus 2021 PDF

## NDA Syllabus 2021 PDF Summary

NDA syllabus is broadly divided into two sections – Mathematics and General Ability Test (GAT). The question paper of GAT will have total 150 questions while the Mathematics section will have 120 questions. To solve each section, candidates will be given 2 ½ hours. In this article we have also provided the download link for UPSC NDA Syllabus 2021 PDF in English language.

### NDA Syllabus for Mathematics

NDA syllabus for Mathematics comprises the topics which candidates have studied in Class 12. Total marks allotted for this section is 300. This section basically test a candidates calculative skills. NDA syllabus for Mathematics is given below –

Topics Sub-Topics
Algebra 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.
Calculus Concept of a real valued function, domain, range and graph of a function. Composite functions, one to one, onto and inverse functions. 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, derivative of a function with respect to another function, derivative of a composite function. 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—applications.

Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of differential equations, solution of first order and first-degree differential equations of various types—examples. Application in problems of growth and decay.

Trigonometry Angles and their measures in degrees and in 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 in 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. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and 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 Distribution of Questions in Mathematics

Topic Questions
Calculus 20-25
Matrices & Determinants 30
Probability 10
Trigonometry 30
Complex number 10-15

### NDA Syllabus 2021 for GAT (General Ability Test)

Physics
Physical Properties and States of Matter Modes of transference of Heat
Mass Sound waves and their properties
Weight Simple musical instruments
Volume 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 the following: 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.
Chemistry
Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon Dioxide, Oxidation and Reduction. Acids, bases and salts. Carbon— different forms Physical and Chemical Changes
Fertilizers—Natural and Artificial Elements
Material 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 Equation
Atomic Equivalent and Molecular Weights Law of Chemical Combination (excluding problems)
Valency Properties of Air and Water
General Science
Common Epidemics, their causes and prevention Difference between the living and non-living
Food—Source of Energy for man Basis of Life—Cells, Protoplasms and Tissues
Constituents of food Growth and Reproduction in Plants and Animals
Balanced Diet Elementary knowledge of Human Body and its important organs
The Solar System—Meteors and Comets, Eclipses. Achievements of Eminent Scientists
History
Forces shaping the modern world; Renaissance A broad survey of Indian History, with emphasis on Culture and Civilisation
Exploration and Discovery; War of American Independence, French Revolution, Industrial Revolution and Russian Revolution Freedom Movement in India
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, Democracy, Socialism and Communism Panchayati Raj
Role of India in the present world Co-operatives and Community Development
A broad survey of Indian History, with emphasis on Culture and Civilisation Bhoodan, Sarvodaya, National Integration and Welfare State
Basic Teachings of Mahatma Gandhi
Geography
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
Current Affairs
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
Current important world events 