UPSC NDA Syllabus and Exam Pattern 2022

• Distance formula
• Distance of a point from a line
• Point in a three-dimensional space, the distance between two points
• Rectangular Cartesian Coordinate system
• 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
• Equation two points
• Angle between two lines and angle between two planes
• Direction Cosines and direction ratios
• Standard forms of parabola, ellipse and hyperbola
• Eccentricity and axis of a conic

• 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 matrix method
• Types of matrices, operations on matrices
• Determinant of a matrix

• Sets and Venn diagrams
• Cartesian product
• De Morgan laws
• Equivalence relation
• Complex numbers
• Arithmetic, Geometric and Harmonic progressions
• Representation of real numbers on a line
• Real numbers and complex numbers
• Cube roots of unity
• Conversion of a number in Binary system to Decimals and vice-versa
• Quadratic equations with real coefficients
• Permutation and Combination
• Binomial theorem
• Modulus
• Linear inequations

• Vectors in two and three dimensions
• Vector product or cross product of two vector
• Applications—work done by a force and moment of a force      and geometrical problems
• Addition of vectors, scalar
• Multiplication of a vector
• Unit and null vectors
• Scalar product or dot product of two vectors
• Magnitude and direction of a vector

• Statistics
• Variance and standard deviation
• Union and Intersection of events
• Complementary, elementary and composite events
• Random variable as function on a sample space
• Graphical representation
• Measures of Central tendency – Mean, median and mode
• Binomial distribution, examples of random experiment    giving rise to Binomial distribution
• Probability: Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events
•  Definition of probability – classical and statistical – examples. Elementary theorems on probability – simple problems
• Conditional probability, Bayes’ theorem – simple problems

• Concept of a real valued function–domain, range and graph of a function
• Increasing and decreasing functions
• Derivative 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, derivative of a composite function
• Continuity of functions— algebraic operations on            continuous functions
• Composite functions, one to one, onto and inverse           functions.  Notion of limit, Standard limits
• Second order derivatives
• Application of derivatives in problems of maxima and minima

• 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 the first order and first-degree differential equations of various types—examples
• Application in problems of growth and decay

Fill in the blanks

Complete the sentences

Idioms and phrases

Synonym and antonym

Active and passive voice

Finding errors

Modes of transference of Heat

Mass, Weight, Volume, Sound waves and their properties

Simple musical instruments

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 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.

Mixtures and Compounds, Symbols, Formulae and simple Chemical Equations, Law of Chemical Combination

Properties of Air and Water

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

Preparation and Properties of Hydrogen

Growth and Reproduction in Plants and Animals.

Achievements of Eminent Scientists.

Common Epidemics, their causes and prevention.

Basis of Life—Cells, Protoplasm and Tissues.

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 and 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

Bhoodan, Sarvodaya, National Integration and Welfare State, Basic Teachings of Mahatma Gandhi

India’s freedom struggle

Panchayati Raj, Co-operatives and Community Development

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

Forces shaping the modern world; Renaissance, Exploration and Discovery

Important personalities in the national and International level

Cultural activities and sports activities

Current important world events