Concept of a set, operation on set, Venn diagram. D. Morgan Law. Cartesian products, relations, equivalence relations. Representation of real numbers on a line. Complex numbers – Basic properties, modulus, logic, cubic roots of unity. Binary system of numbers. Converting a number into a binary system in the decimal system and vice versa. Arithmetic, Geometric and Harmonic Progress. Quadratic equations with real coefficients. Solve linear inequalities of two variables by graphing. Permutations and Combinations. Binomial Theorem and Its Applications. Logarithms and their applications.
Matrices and determinants:
Types of Matrix, Operations on Matrix, Determinants of a Matrix, Basic Properties of Determinants. Application of a square matrix and vice versa, application – solution of a system of linear equations in two or three unknowns by Cramer’s rule and matrix method.
Angles and their measures in degrees and radians. Trigonometric ratio. Trigonometric identity even and differential formulas. Multiple and sub-multiple angles. Invert trigonometric functions. Applications – Height and distance, properties of triangles.
Analytical geometry of two and three dimensions:
Rectangular Cartesian Coordinate System. Distance formula. Equation of a line in various forms. The angle between two lines. The distance of a point from a line. Equation of a circle in standard and general form. Standard forms of parabola, ellipse, and hyperbola. Eccentric and the axis of a cone.
The point in a three-dimensional space, the distance between two points. Direction cosine and direction ratio. Equation of a plane and a line in various forms. The angle between two lines and the angle between two planes. Equation of a sphere.
Concept of a real-valued function – domain, range, and graph of a function. Composite functions, one to one, onto and inverse functions. Boundary perception, standard boundaries – examples. Continuity of functions – Example, algebraic operations on continuous functions. Derivative, a derivative of a function at a point – geometric and physical interpretation of applications. Derivatives of sum, product, and quotient of functions, a derivative of one function, in relation to another function, a derivative of a composite function. Second-Order Derivatives. Increasing and decreasing functions. Application of derivatives in maxima and minima problems.
Integral Calculus and Differential Equations:
Standard integrals involving integration, algebraic expression, algebraic expressions, trigonometric, exponential, and hyperbolic functions as inverse of discrimination. Evaluation of fixed integrals – Determination of areas of plane fields imposed by curves – Application. Definition of order and degree of a differential equation, the formation of a differential equation by example. General and special solutions to a differential equation, solving first-order and first-degree differential equations of different types – examples. Applications in growth and decay problems.
Areas in two and three dimensions, magnitude, and direction of a vector. Unit and null vectors, in addition to vectors, scalar multiplication of a vector, scalar product, or dot product of two vectors. Vector product and cross product of two vectors. Application and work are done by forces and moments and geometric problems of a force.
Statistics and Probability:
Statistics: Classification of data, frequency distribution, cumulative frequency distribution – example graphical representation – histogram, pie chart, frequency polygon – example. Measures of central tendency – mean, mean, and mode. Variance and standard deviation – determination and comparison.
Correlation and Regression:
Probability: Random experiments, results, and associated sample locations, events, mutually exclusive and whole events, impossible and few events. Union of events and contradiction. Complementary, Primary, and Composite Events. Definition of probability – classical and statistical – examples. Elementary Theory on Probability – Simple Problems. Conditional Probability, Bayes Theorem – Simple Problems. Random variable as a function on the sample space. binomial distribution,
NDA Syllabus 2021 Paper-II
General aptitude test
(Maximum marks – 600)
Part ‘A’ – English (maximum marks 200). The question paper in English will be designed for the candidate’s understanding of English and working like words. The course covers various aspects: grammar and usage, vocabulary to test a candidate’s proficiency in English, concordance, and cohesiveness in a wide text.
Part ED B ‘- General Knowledge
The question paper on General Knowledge will broadly cover the topics: Physics, Chemistry, General Science, Social Studies, Geography, and Current Events. – The syllabus given below is designed to indicate the scope of these topics covered in this paper. The topics mentioned should not be considered in detail and questions of similar nature not specifically mentioned in the syllabus can also be asked. Candidate answers are expected to show their knowledge and understanding of the subject.
Section ‘A’ (Physics)
Physical properties and states, mass, weight, volume, density and specific gravity, Archimedes’ principle, pressure geometer. Speed, speed and acceleration, Newton’s laws of motion, force and momentum, parallel quadrilaterals of forces, stability and equilibrium bodies, gravity, elementary ideas of work, power, and energy. Effects of heat, measurement of temperature and heat, change of state and latent heat, modes of heat transition. Sound waves and their properties, Simple musical instruments. Rectangular propagation of light, reflection, and refraction. Spherical mirrors and lenses, the 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, Ordinary Electrical Circuits, Current Heating, Light and Magnetic Effects, Measurement of Electric Power, Primary and Secondary Cells, Use of X-rays. General principles in the work of the following: simple pendulum, simple pulses, siphon, lever, balloon, pumps, hydrometer, pressure cooker, thermos flask, gramophone, telegraph, telephone, periscope, telescope, microscope, mariner compass; Lightning conductor, safety fuses.
Section ‘B’ (Chemistry)
Physical and chemical changes. Elements, Mixtures and Compounds, Symbols, Formulas and Simple Chemical Equations, Law of Chemical Combinations (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 – various forms. Fertilizer – Natural and Artificial. Materials used in the preparation of substances such as soap, glass, ink, paper, cement, paint, safety mail, and gunpowder. Elementary ideas about the structure of atoms, atomic equivalents and molecular weights, validity.
Section C (General Science)
Differentiate between living and lifeless. Basis of Life- cells, protoplasm, and tissue. Growth and reproduction in plants and animals. A primary knowledge of the human body and its vital organs. Common Epidemics, their causes, and prevention. Food – A source of energy for humans. Food components, balanced diet. Solar System – Meteor and Comet, Eclipse. Achievements of eminent scientists.
Section ‘D’ (History, freedom movement, etc.)
A comprehensive survey of Indian history with an emphasis on culture and civilization. Independence movement in India. Preliminary Study of Indian Constitution and Administration. Early knowledge of Five Year Plans of India. Panchayati Raj, Cooperation and Community Development. Bhoodan, Sarvodaya, National Integration and Welfare State, Basic Education 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. India’s role in the current world.
Section ‘E’ (Geography)
Earth, its size and shape. Latitude and longitude, the concept of time. International Date Line. Earth’s Movements and Their Impact. Origin of Earth Rocks and their classification; Weathering-mechanical and chemical, earthquakes and volcanoes. Ocean currents and tidal atmospheres and their composition; Temperature and atmospheric pressure, planetary winds, cyclones, and anticipates; Humidity; Condensation and precipitation; Types of climate, major natural regions of the world. Regional geography-climate, natural vegetation of India. Mineral and Power Resources; Location and distribution of agricultural and industrial activities. Important seaports and main sea, land, and airways of India. Major items of import and export of India.
Section ‘F’ (Current Events)
Knowledge of important events in India in recent years. Current Important World Events. Key personalities – including those associated with cultural activities and sports, both Indian and international.
Note: Out of the maximum marks specified for Part ‘B’ of this paper, questions on Sections ‘A’, ‘B’, ‘C’, ‘D’, ‘E’ and ‘F’ are about 25%, up to 15% Will take. , 10%, 20%, 20% and 10% weight respectively.
Intelligence and personality test
The SSB process consists of a two-stage selection process – Phase I and Phase II. Only those candidates who clear Phase I are allowed to appear for Phase II. Details are:
(A) Stage I consists of Officer Intelligence Rating (OIR) tests, Picture perception * Description tests (PP and DT). Candidates will be shortlisted based on a combination of performance in the OIR Test and PP&DT.
(b) Compilation of stage II interviews, group test officer work, psychology tests, and conferences. These tests are conducted over 4 days. Details of these tests are given on the website joinindianarmy.nic.in. A candidate’s personality is assessed by three different evaluators. Interview Officer (IO), Group Testing Officer (GTO), and Psychologist. There is no separate weightage for each test.
Masks are allotted by the evaluators keeping in view the performance of the candidate in all the examinations. In addition, points are also allocated for the conference based on the candidate’s initial performance in the board’s three techniques and decisions. All these have equal weight. The various tests of IO, GTO, and Psych are designed to exclude the presence/absence of officer-like qualifications and their training ability in a candidate. Accordingly, candidates are not recommended or recommended in SSB.