# Syllabus for National Defence Academy 2018 (UPSC NDA) – Maths, GAT, PT

## NDA Syllabus 2018 National Defence Academy Mathematics, General Ability Test, Intelligence and Personality Test Marks

National Defence Academy Exam consists of Mathematics paper of 300 marks & General Ability Test of 600 marks & Intelligence and Personality Test, Detailed NDA Syllabus 2018 is given below:

### PAPER 1 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.

1. 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.

1. 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.

1. 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.

1. 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.

1. 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.

1. 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.

1. 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, Bayes’ theorem—simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution.

### PAPER-II GENERAL ABILITY TEST  (Code No. 02) (Maximum Marks—600)

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 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.

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. Lattitudes 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.

NOTE : Out of maximum marks assigned to part ‘B’ of this paper, questions on Sections ‘A’, ‘B’, ‘C’, ‘D’, ‘E’ and ‘F’ will carry approximately 25%, 15%, 10%, 20%, 20% and 10% weightages respectively.

### Intelligence and Personality Test

The SSB procedure consists of two stage Selection process – stage I and stage II. Only those candidates who clear the stage I are permitted to appear for stage II. The details are :

• Stage I comprises of Officer Intelligence Rating (OIR) tests are Picture Perception * Description Test (PP&DT). The candidates will be shortlisted based on combination of performance in OIR Test and PP&DT.
• Stage II Comprises of Interview, Group Testing Officer Tasks, Psychology Tests and the Conference. These tests are conducted over 4 days. The details of these tests are given on the website joinindianarmy.nic.in.

The personality of a candidate is assessed by three different assessors viz. The Interviewing Officer (IO), Group Testing Officer (GTO) and the Psychologist. There are no separate weightage for each test. The mks are allotted by assessors only after taking into consideration the performance of the candidate holistically in all the test. In addition, marks for Conference are also allotted based on the initial performance of the Candidate in the three techniques and decision of the Board. All these have equal weightage.

The various tests of IO, GTO and Psych are designed to bring out the presence/absence of Officer Like Qualities and their trainability in a candidate. Accordingly candidates are Recommended or Not Recommended at the SSB.

## NDA 2018 HEIGHT/WEIGHT STANDARDS FOR NAVY

TABLE-II

 Height in Weight in Kgs. Centimetres (Without 16 18 20 shoes) years years years

1_________________2___________3___________4________________________

 152 44 45 46 155 45 46 47 157 46 47 49 160 47 48 50 162 48 50 52 165 50 52 53 168 52 53 55 170 53 55 57 173 55 57 59 175 57 59 61 178 59 61 62 180 61 63 64 183 63 65 67

“Individual’s weight is considered normal if it is within ±10% departure from average weight given in the table I and II”. However, in individuals with heavy bones and broad build as well as individuals wiin build but otherwise healthy this may be relaxed to some extent on merit.

NOTE 1 : To meet special requirement as a pilot in the Air Force the acceptable measurements of leg length, thigh length and sitting height will be as under :

 Minimum Maximum Leg Length 99.00 cms. 120.00 cms. Thigh Length — 64.00 cms. Sitting Height 81.50 cms. 96.00 cms.
• Chest should be well developed. Fully expanded chest should not be less than 81 cms. The minimum range of expansion after full inspiration should be 5 cms. The measurement will be taken with a tape so adjusted that its lower edge should touch the nipple in front and the upper part of the tape should touch the lower angle of the shoulder blades behind. X-Ray of the chest is compulsory and will be taken to rule out any disease of the chest.
• There should be no maldevelopment or impairment of function of the bones or joint.

Spinal Conditions

• Past medical history of diseases or injury of the spine or sacro iliac joints, either with or without objective signs which have prevented the candidate from successfully following a physically active life, is a cause for rejection for commissioning in IAF. History of spinal fracture/prolapsed intervertebral disc and surgical treatment for these conditions will entail rejection. The following conditions detected radiologically during medical exam will disqualify a candidate for Air Force service:
• Granulomatous disease of spine
• Arthritidies/spondylosis

— Rheumatoid arthritis and allied disorders

— Ankylosing spondylitis

— Osteoarthrosis, spondylosis and degenerative joint disease

— Non articular rheumatism (e.g. lesions of the rotator cuff, tennis elbow, recurrent lumbago etc.)

— Miscellaneous disorders including SLE, , polymyositis, vasculitis.

• Spondylolisthesis/spondylolysis.
• Compression fracture of vertebrae.
• Loss of cervical lordosis when associated with clinically restricted movements of cervical spine.
• Unilateral/Bilateral cervical ribs with demonstrable neurological or circulatory deficit.
• Scoliosis more than 10 degree as measured by Cobb’s method.
• Degenerative Disc. Disease.
• Presence of schmorl’s nodes at more than one level.
• Atlanto-occipital and atlantoaxial anomalies.
• Hemi vertebrae and/or incomplete block (fused) vertebrae at any level in cervical, dorsal or lumbar spine and complete block (fused) vertebrae at more than one level in cervical or dorsal spine.
• Unilateral Sacralisation or lumbarisation (Complete or incomplete) at all levels and bilateral incomplete sacralisation or lumbarisation.
• Any other abnormality if so considered by the specialist.
• Mild Kyphosis or Lordosis where deformity is barely noticeable and there is no pain or restriction of movement will not preclude acceptance.
• In case of noticeable Scoliosis or suspicion of any other abnormality or spinal deformity, more than mild, appropriate X-rays of the spine are to be taken and the Examinee referred for specialist’s advice.
• The following conditions detected on X-ray examination will be disqualifying for entry to Armed Forces :
• Granulomatius disease of spine.
• Arthritidies/spondylosis
• Scoliosis more than 15 degree as measured by Cobb’s Method (10 degree for Army and Navy).
• More than mild Kyphosis/Lordosis
• Spondylolisthesis/Spondylosis/Spondylolysis
• Herniated nucleus pulposes.
• Compression fracture of Vertebra.
• Sacaralisation Disease
• Cervical ribs with demonstrable neurological or Circulatory deficit.
• Presence of Schmorl’s node at more than one level.
• Atlanto-occipital and atlanto-axial anomalies.
• Incomplete Sacaralisation Unilateral or Bilateral
• Spina Bifida other than SV 1 and LV 5 if completely Sacralised
• Any other abnormality, if so considered by specialist.

(j) A candidate should have no past history of mental breakdown or fits.

• The hearing should be normal. A candidate should be able to hear a forced whisper with each ear at a distance of 610 cms. in a quiet room. There should be no evidence of present or past disease of the ear, nose and throat. Audiometric test will be done for AF. Audiometric hearing loss should not be greater than 20 db in frequencies between 250 and 8000 Hz. There is no impediment of speech.
• There should be no signs of functional or organic disease of the heart and blood vessels. Blood pressure should be normal.
• There should be no enlargement of liver or spleen. Any evidence of disease of internal organs of the abdomen will be a cause for rejection.
• Un-operated hernias will make a candidate unfit. In case of Hernia which has been operated, a minimum of one year must have passed prior to final medical examination before commencement of the course.
• There should be no hydrocele, varicocele or piles.
• Urine examination will be done and any abnormality if detected will be a cause for rejection.
• Any disease of skin which is likely to cause disability or disfigurement will also be a cause for rejection.
• Distance Vision (Corrected): Better Eye 6/6; Worse Eye 6/9. Myopia should not be more than -2.5D including astigmatism and manifest hypermetropia not more than +3.5D including Astigmatism. Internal examination of the eye will be done by means of ophthalmoscope to rule out any disease of the eye. A candidate must have good binocular vision. The Colour vision standard will be CP-II (DEFECTIVE SAFE). Candidates should be able to recognize white, signal red and signal green colours correctly as shown by Martin’s Lantern at a distance of 1.5 metre or read the requisite plate of Ishihara Book / Tokyo Medical College Book. Candidates who have undergone or have evidence for having undergone Radial Keratotomy, to improve the visual acuity will be permanently rejected for all the services. Candidates who have undergone Laser Surgery for correction of refractive error are also not acceptable to defence services.
 Vision standard for Naval candidates Uncorrected without glass 6/6, 6/9 Corrected with glass 6/6, 6/6 Limits of Myopia –0.75 Limits of Hypermetropia +1.5 Binocular vision III Limits of colour perception I

Visual Standards for Air Force

Candidates who habitually wear spectacles are not eligible for Air Force, Minimum distant vision 6/6 in one eye and 6/9 in other, correctable to 6/6 only for Hypermetropia. Colour vision CP-I Hypermetropia : +2.0 D Sph Manifest Myopia : Nil Retinoscopic Myopia : 0.5 in any Meridian permitted Astigmatism : + 0.75 D Cyl (within + 2.0 D.Max) Maddox Rod Test

(i) at 6 meters

• Exo-6 prism D
• Eso-6 prism D
• Hyper-1 prism D
• Hypro-1 prism D

(ii) at 33 cms

• Exo-16 prism D
• Eso-6 prism D
• Hyper-1 prism D
• Hypo-1 prism D

Hand held Stereoscope–All of BSV grades Convergence–Up to 10 cm Cover test for distant and near–Latent divergence/convergence recovery rapid and complete.

“Candidates who have undergone PRK (Photo Refractive Keratotomy / Lasik (Laser in Situ Keratomileusis) may be considered fit for commissioning in the Air

Force in all branches”. Candidates having undergone cataract surgery with or without IOL implants will also be declared unfit. Binocular vision must possess good binocular vision (fusion and stereopsis with good amplitude and depth).

• “Post PRK/Lasik candidates must meet the visual requirements required for the branch”.
• The following criteria must be satisfied prior to selecting post-PRK/LASIK at the time of Air Force Medical Examination:-
• LASIK surgery should not have been carried out before the age of 20 years.
• The axial length of the eye should not be more than 25.5 mm as measured by IOL master.

(iii)At least 12 months should have elapsed post uncomplicated stable LASIK with no history or evidence of any complication.

• The post LASIK corneal thickness as measured by a corneal pachymeter should not be less than 450 microns.
• Individual with high refractive errors (> 6D) prior to LASIK are to be excluded.
• Radial Keratotomy (RK) surgery for correction of refractive errors is not permitted for any Air Force duties. Candidates having undergone cataract surgery with or without IOL implants will also be declared unfit.
• USG abdomen examination will be carried out and any congential structural anomaly or disease of the abdominal organs will be a cause for rejection in Armed Forces.
• The candidates should have sufficient number of natural and sound teeth. A minimum of 14 dental points will be acceptable. When 32 teeth are present, the total dental points are 22. A candidate should not be suffering from severe pyorrhoea.
• Routine ECG for Air Force candidates must be within normal limits.
• Physical conditioning : Prospective candidates are advised to keep themselves in good physical condition, by following the under mentioned routine :—
• Running 2.4 km in 15 minutes
• Skipping
• Pushups and sit ups (minimum 20 each)
• Chin ups (minimum 08)
• Rope climbing 3-4 metres.

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