# NDA Syllabus

### SYLLABUS OF THE EXAMINATION

PAPER SUBJECT TOPICS MAXIMUM MARKS DURATION

PAPER-I

MATHEMATICS

1. Algebra,
2. Matrices & Determinants,
3. Trigonometry,
4. The geometry of 2 & 3 dimensions,
5. Differential Calculus,
6. Integral Calculus,
7. Vector Algebra &
8. Statistics & Probability
.

300

2 hours 30 minutes

PAPER-II

GENERAL ABILITY TEST

PART A- ENGLISH
PART B- GENERAL KNOWLEDGE
1. Physics,
2. Chemistry,
3. General Science,
4. History Freedom Movement,
5. Geography &
6. Current Events
.

600

2 hours 30 minutes

### PAPER-I MATHEMATICS (Code No. 01) (Maximum Marks-300)

1. ALGEBRA:
Concept of 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 applications. Logarithms and their applications.

2. 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.

3. TRIGONOMETRY:
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.

4. 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. Point in a three dimensional space, 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.

5. DIFFERENTIAL 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-examples. Continuity of functions-examples, algebraic operations on continuous functions. Derivative of 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. Second order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.

6. 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 a differential equations, solution of first order and first degree differential equations of various types-examples. Application in problems of growth and decay.

7. VECTOR ALGEBRA :
Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, 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.

8. STATISTICS AND PROBABILITY :

Statistics: Classification of data, Frequency distribution, cumulative frequency distribution-examples. Graphical representation-Histogram, Pie Chart, frequency polygon- examples. Measures of Central tendency-Mean, median and mode. Variance and standard deviation-determination and comparison. Correlation and regression.

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, Baye's theorem-simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution.

### Part 'A'-ENGLISH (Maximum Marks-200)

The question paper in English will be designed to test the candidate's understanding of English and workman like use of words. The syllabus covers various aspects like: Grammar and usage, vocabulary, comprehension and cohesion in extended text to test the candidate's proficiency in English.

### Part 'B'-GENERAL KNOWLEDGE (Maximum Marks-400)

The question paper on General Knowledge will broadly cover the subjects: Physics, Chemistry, General Science, Social Studies, Geography and Current Events.

The syllabus given below is designed 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. Candidate's answers are expected to show their knowledge and intelligent understanding of the subject.

Section 'A' (Physics)

Physical Properties and States of Matter, Mass, Weight, Volume, Density and 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. 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; Lightening Conductors, Safety Fuses.

Section 'B' (Chemistry)

Physical and Chemical changes. Elements, Mixtures and Compounds, Symbols, Formulae and simple Chemical Equations, Law of Chemical Combination (excluding problems). Properties of Air and Water.

Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon dioxide, 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 GunPowder. Elementary ideas about the structure of Atom, Atomic Equivalent and Molecular Weights, Valency.

Section 'C' (General Science)

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.

Section 'D' (History, Freedom Movement etc.)

A broad survey of Indian History, with 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' (Geography)

The 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.

Section 'F' (Current Events)

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

### SECTION WISE DISTRIBUTION OF MARKS:

SECTION SUBJECT MAXIMUM MARKS

Sections A

Physics

25%

Sections B

Chemistry

15%

Sections C

General Science

10%

Sections D

History, Freedom Movement etc.

20%

Sections E

Geography

20%

Sections F

Current Events

10%

### Why NDA?

National defence academy is a dream destination for all aspiring military boys, where cadets of 3 services - the Army, the Navy and the Air force are equipped with mental, moral, and physical characteristics aimed at leading soldiers.

### Who conducts the NDA exam?

NDA exam is conducted by UNION PUBLIC SERVICE COMMISSION (UPSC).

### From where one can enroll for NDA?

Candidates have to go to https://upsconline.nic.in/ to enroll for NDA and NA exams.

### What is the procedure to fill the online application form?

Online application form is filled in 2 parts:-
Part 1:
1. Registration
2. Preferred branch selection
3. Details verification
4. Withdrawal/Cancellation of application
Part 2:
2. Payment
3. Select the exam centre
5. Agree to terms and conditions
6. Submit

### When can candidates get their admit cards?

Candidates get their admit cards almost three weeks before the exam begins.

### What is the age criteria to appear in NDA & NA exam?

The age criteria to appear in NDA & NA exam are as follows:
1. NDA I- 16.5 years to 19.5 years.
2. NDA II- 16.5 years to 19.5 years.

### Who can apply for NDA Exam?

The below candidates are eligible to appear in NDA exam:
(a) A citizen of India, or
(b) A subject of Nepal, or
(c) A subject of Bhutan, or
(d) A Tibetan refugee who came over to India before 1st January 1962
(e) Persons of Indian Origin
(f) Overseas Citizens of India

### Can married aspirant apply for NDA exams?

No, only unmarried male aspirants can apply for this post.

### What is the educational qualification required to appear in the NDA exam?

12th class or appearing candidates are eligible to appear in the exam

### Can females apply for NDA exams?

The Supreme Court of India passed an order in August 2021 to allow female candidates to appear in all upcoming NDA entrance examination with respect to the age and qualification requirements. The interested female candidates age should be between 16.5 to 19.5 years and they should have passed Class 12th exam from a recognised education board.

### What are the citizenship rules for female candidates applying to NDA?

NDA Nationality for Girls. A candidate applying for NDA must be either unmarried, as well as: an Indian national, or a Nepali subject, or a person of Indian descent from Burma, Pakistan, Sri Lanka, the East African nations of Zambia, Uganda, the United Republic of Tanzania, Malawi, Kenya, Zaire, and Ethiopia, or Vietnam who are permanently settled here.

### Which candidates are not eligible to appear in the NDA exam?

Candidates who are not eligible:
. Candidates of class 11th are not eligible to appear in the exam.
. Candidates who are deprived of any commission by the Ministry of defence are not eligible to give the examination.
. A candidate who has resigned from any of the training academies of Armed forces is not eligible to apply.

### How often does the NDA exam conduct?

The NDA and NA exam is conducted twice a year, and it includes a written test and SSB Interview.

### Will NDA exam has descriptive questions?

NDA has only objective type questions.

### Is the calculator allowed in NDA exam?

NO, the calculator is not allowed in the NDA exam.

### Can we use any colour pen for giving NDA exam?

Only black ball pen is allowed to give the exam.

### What is the duration of NDA exam?

Duration of exam: 2 hours 30 minutes for each paper (Paper I - Maths and Paper II - General Ability Test).

### How is the NDA exam conducted?

NDA exam is conducted in 2 phases:
Phase 1- Written-test
1. Mathematics (300 marks)
2. General Ability Test (600 marks)
Phase 2- SSB Interview
1. Screening
2. Psychology Test
3. Group Exercise
4. Personal Interview
5. Conference

### How is the NDA exam selection process done?

NDA selection process: Registration/ LoginApply online Admit card Exam Call Letter SSB Interview Medical Test Result/Merit List NDA/NA

### Does height matters in NDA exam?

Yes, height matters a lot in NDA exams. The minimum acceptable height is 157 cm for the Army, 152 cm for the Navy and 162.5 cm for the Air Force.

### What happens in NDA medical test?

In NDA medical test, it includes- Urine test, blood test, sugar test, Blood pressure (BP) test, ECG. There should be no hydrocele, varicocele or piles, pyorrhea.