Types of matrices
Operations on matrices
The determinant of a matrix, basic properties of determinants
Inverse and adjoint 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

Trigonometry:

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

Analytical Geometry of 2 and 3 Dimensions:

Equation of a line in various forms
Rectangular Cartesian Coordinate system
Distance formula
The angle between two lines
The angle between two planes
Direction Cosines and direction ratios
Equation of a plane and a line in various forms
The 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
Equation of a sphere
The angle between two lines
The point in a three-dimensional space, the distance between two points
Direction Cosines and direction ratios
Equation two points

Differential Calculus:

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

Integral and Differential Calculus:

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
Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential, and hyperbolic functions
Application in problems of growth and decay
General and particular solution of differential equations, solution of the first order, and first-degree differential equations of various types—examples

Vector Algebra:

Addition of vectors, Unit and null vectors, scalar multiplication of a vector, scalar product, or dot product of two vectors
Vectors in three and two magnitude, dimensions, and direction of a vector
Cross product or the Vector product of two vectors
Applications—work done by a force and moment of a force and in geometrical problems

Statistics and Probability:

Measures of Central tendency—Mean, median, and mode
Variance and standard deviation—determination and comparison
Correlation and regression
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
Probability: Random experiment, outcomes, and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events
Statistics: Classification of data, Frequency distribution, cumulative frequency distribution—examples
Graphical representation—Histogram, Pie Chart, frequency polygon—examples
Complementary, elementary, and composite events
Binomial distribution, examples of random experiments giving rise to Binomial distribution

The topic-wise distribution of questions in Maths

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

NDA Syllabus 2024 - Paper 2 (General Ability):

General Knowledge question paper will hold subjects - Chemistry, General Science, Social Studies, Geography, Physics, and Current Events.
The NDA Syllabus provided below is just to indicate the scope of these subjects included in this paper.
The topics mentioned are not to be regarded as exhaustive and questions on topics of similar nature not specifically mentioned in the syllabus may also be asked.
Candidates’ answers are expected to show their knowledge and intelligent understanding of the subject.

Section A (Physics):

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

Section B (Chemistry):

Physical and Chemical changes. Mixtures, Elements and Compounds, Formulae, Symbols, and simple Chemical Equations, Law of Chemical Combination
Properties of Air and Water. Properties and preparation of Oxygen, Nitrogen, Hydrogen, and Carbon dioxide, Reduction and Oxidation, Acids, bases, and salts.
Carbon— different forms
Fertilizers—Natural and Artificial
The material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and Gunpowder
Elementary ideas about the Atomic Equivalent, Structure of Atom, and Molecular Weights, Valency.

Section C (General Science):

Difference between the living and nonliving
The basis of Life—Cells, Protoplasms, and Tissues
Growth and Reproduction in Plants and Animals
Elementary knowledge of the 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

Section D (History, Freedom Movement, and the like):

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

Section E (Geography):

The Earth, its shape, and its size
Latitudes and Longitudes, Concept of time
International Date Line
Movements of Earth and their effects
Origin of Earth
Rocks with their classification; Weathering—Chemical and Mechanical, Earthquakes and Volcanoes
Regional Geography of India—Climate, Natural vegetation
Power and Mineral Resources: distribution and location of Industrial and agricultural activities
Important main sea and Seaports, land, and air routes of India
Main items of Imports and Exports of India
Ocean Currents and Tides; Atmosphere and its composition; Pressure, Planetary Winds, Cyclones, and Anticyclones; Humidity; Condensation and Precipitation; Temperature and Atmospheric Types of Climate, Major Natural Regions of the World’

Section F (Current Events):

Deep information of all the Important events that happened in India in recent years
Current important world events
Prominent personalities—including both Indian and International, those connected with cultural activities and sports.

NDA 2024 SSB Interview (Stage II)

Those candidates who qualify for stage I will only be permitted to appear for Stage II. The details are as follows:

Part I comprises of Officer Intelligence Rating (OIR) tests and the Picture Perception & Description Test (PP & DT). The candidates will be shortlisted based on the combination of their performance in their OIR Test and their PP & DT.
Part II Comprises the Interview session, Group Testing Officer Tasks, Psychology Tests, and the last is Conference. These tests are organized over a duration of 4 days.

The topic-wise distribution of questions in GAT

English

Topic	No. of Questions	No. of Marks
Spotting Errors	5	20
Comprehension	6	24
Selecting Words	10	40
Ordering of Words in a Sentence	9	36
Sentence Improvement	10	40
Antonyms	5	20
Synonyms	5	20
Total	50	200

General Knowledge

Topic	No. of Questions	No. of Marks
Physics	23	92
Chemistry	16	64
General Science	11	44
History & Freedom Movement	16	64
Geography	17	68
Current Events	17	68
Total	100	400

Books for NDA Exam

Subjects	Books
Mathematics	Mathematics for NDA and NA: National Defence Academy and Naval Academy by RS Aggarwal Quantitative aptitude for competitive examinations by RS Aggarwal
GAT	History Of Modern India (History) by Bipan Chandra Science and Technology in India (Science and Technology) by Kalpana Rajaram: Spectrum Objective General English for Competitive Exams by S.P. Bakshi Manorama Yearbook 2019 by Mammen Mathew

NOTE:

The personality of a candidate is assessed by 3 different assessors viz. The IO knew as Interviewing Officer, GTO is known as - Group Testing Officer, and the Psychologist.
There is no separate preference for any of the tests. The marks are allotted by the assessors only after taking into consideration the applicant's performance of the candidate holistically in all their tests.
Marks for the conference are also allotted based on the initial performance of the candidate in the 3 techniques and decisions of the Board. All the tests have equal preference.

How to prepare for NDA Exam 2024?

Fix your goal and make sure to start your preparation early for the exam.
Be thorough with the NDA Syllabus 2024 and follow a routine.
Clear all the basic concepts from the high school books.
The best way to improve English is by reading the newspaper daily and brush up the grammar skills.
Refer to the previous year’s NDA Exam question paper and solve as many questions as you can.
Attempt a mock test that will improve your speed and accuracy.
Look after your weak subjects and start working on them.