• Concept of a set
• 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 inequations of two variables by graphs
• Permutation and Combination
• Binomial theorem and its application
• Logarithms and their applications

• 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.

• 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.

• 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.

• 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.

NDA Syllabus for Trigonometry 2025:

Angles and their measures in degrees and in radians Trigonometrical ratios Trigonometric identities Sum and difference formulae Multiple and Sub-multiple angles Inverse trigonometric functions Applications – Height and distance Properties of triangles.

NDA 2025 Syllabus Analytical 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

UPSC 2025 NDA Syllabus Analytical 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

Read – Top 10 Toughest Exams in India 2025

• 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.
• NDA Eligibility Criteria

• 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.
• NDA Eligibility Criteria

• Integration as inverse of differentiation
• Integration by substitution and by parts
• Standard integrals involving algebraic expressions
• Trigonometric
• Exponential and hyperbolic functions
• General and particular solution of a differential equation

• Vectors in two and three dimensions
• Magnitude and direction of a vector
• Unit and null vectors addition of vectors
• Scalar multiplication of a vector

NDA 2025 Syllabus Analytical Geometry of two and three dimensions:

Rectangular Cartesian Coordinate system Distance formula. Equation of a line in various forms Angle between two line. 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 Equation of a plane and a line in various forms Angle between two lines and angle between two planes Equation of a Sphere

• NDA Exam 2025 question paper in English is designed to test the candidate’s understanding of the English language and workman like use of words. The UPSC NDA Syllabus 2025 Pdf covers various broad topics, like
• Grammar and Application
• Vocabulary
• Comprehension and Cohesion

• The question paper on General Knowledge broadly covers the following subjects like Physics, Chemistry, General Science, Social Studies, Geography and Current Events. So, for your benefit we have indicated below-

• 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
• Spherical mirrors and Lenses
• Human Eye
• Natural and Artificial Magnets
• Properties of a Magnet
• Earth as a Magnet
• Static and Current Electricity
• conductors and Non-conductors
• Ohm’s Law Simple Electrical Circuits
• Heating
• Lighting and Magnetic effects of Current
• Measurement of Electrical Power
• Primary and Secondary Cells
• Use of X-Rays

• 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 and Carbondioxide 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

• Difference between the living and non-living
• Basis of Life – Cells Protoplasms 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 Scientists
• General Science Quiz

Section D: UPSC NDA History Freedom Movement Syllabus 2025

A broad survey of Indian History with an emphasis on Culture and Civilisation. 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 Revolution 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

Section E: UPSC 2025 NDA Geography Syllabus 2025

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. World Geography Questions and Answers

Section F: UPSC 2025 NDA Current Events Syllabus 2025

Knowledge of Important events that have happened in India in recent years. Current important world events. Prominent personalities – both Indian and International including those connected with cultural activities and sports.