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NDA Examination pattern

In this examinaton , there are two papers. Paper I is 'Mathematics' and Paper II is 'General Ability Test'. Each paper duration is 2.5 hours. But paper I is 300 marks and Paper II is 600 marks.

Subject	Duration	Maximum Marks
Mathematics (Paper I)	2.5 hr	300
General Ability Test (Paper II)	2.5 hr	600

Note : 1. The Papers in all the subjects will consist of objective type qustions only .It means all the questions will be multiple choice question
2. There is also a minimum qualifying marks for each paper.
3.The Question papers(test booklets) of mathematics and part “B” of general ability test wil be set BILINGUALLY in Hindi as well as english

NDA Examination Syllabus

Paper I (Mathematics)

1. Algebra

a) SET ( Concept of set, operations on sets, Venn diagrams. De Morgan laws, Cartesian product, relation, equivalence relation.)
b) Complex number ( Representation of real numbers on a line. Complex numbers—basic properties, modulus, argument, cube roots of unity.)
c) Boolean Algebra ( Binary system of numbers. Conversion of a number in decimal system to binary system and vice-versa.)
d) Progression ( Arithmetic, Geometric and Harmonic progressions.)
e) Equation ( Quadratic equations with real coefficients. Solution of linear inequations of two variables by graphs.)
f) Permutation and Combination.
g) Binomial theorem and its applications.
h). Logarithms and their applications.

2. MATRICES AND DETERMINANTS

a) Matrices (Types of matrices, operations on matrices.)
b)Determinant ( Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix)
c) Linear equation ( Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method).

3. Trigonometrtry

a)Trigonometry ( Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles)
b) Inverse trigonometry
c) Applications-Height and distance
d) Properties of triangles

4. ANALYTICAL GEOMETRY OF TWO AND THREE DIMENSIONS

a) 2D Geometry (Rectangular Cartesian Coordinate system. Distance formula.)
b)Straight line ( Equation of a line in various forms. Angle between two lines. Distance of a point from a line. )
c)Circle ( Equation of a circle in standard and in general form. )
d) Conic section ( Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic. )
e) 3D geometry ( 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

a)Function(Concept of a real valued function–domain, range and graph of a function. Composite functions, one to one, onto and inverse functions)
b) Limit Notion of limit, Standard limits—examples
c)Continuity (Continuity of functions—examples, algebraic operations on continuous functions)
d)Derivative (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.)
e)Application of derivative (Second order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima)

6. INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS

a) Indefinite Integration(Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions)
b) Definite Integrals(Evaluation of definite integrals—determination of areas of plane regions bounded by curves—applications)
c) Differential Equation(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

a)Vector(Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, addition of vectors, scalar multiplication of a vector)
b) Dot Vector (scalar product or dot product of two vectors.)
c)Cross product ( Vector product or cross product of two vectors.)
d) Application ( Appliciations—work done by a force and moment of a force and in geometrical problems )

7. STATISTICS AND PROBABILITY

a)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)
b)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

Part 'A' - ENGLISH

Grammar and usage, vocabulary, comprehension and cohesion in extended text.

Part 'B' - General Studies

The question paper on General Knowledge will broadly cover the subjects :

• Physics
• Chemistry
• General Science
• Social Studies
• Geography
• Current Events

Syllabus for Part B

Section 'A'- PHYSICS

• Kinematics and laws of motion :
  • Motion of objects, Velocity and Acceleration
  • Newton’s Laws of Motion
  • Force and Momentum
  • Parallelogram of Force
  • Stability and Equilibrium of bodies
• Gravitation
• Work, Power and Energy
• Properties of Bulk Material
  • Physical Properties and States of Matter
  • Mass, Weight, Volume, Density and Specific Gravity, Principle of Archimedes, Pressure Barometer
• Thermodynamics
  • Effects of Heat
  • Measurement of Temperature and Heat
  • change of State and Latent Heat
  • Modes of transference of Heat
• Sound Waves
  • Sound waves and their properties
  • Simple musical instruments
• Optics
  • Rectilinear propagation of Light
  • Reflection and refraction
  • Reflection and refraction
  • Human Eye
• Magnet
  • Natural and Artificial Magnets
  • Properties of a Magnet
  • Earth as a Magnet
• Electricity
  • Static Electricity
  • Current Electricity
  • Conductors and Non conductors
  • Ohm's laws , Simple Electrical Circuits
  • Heating, Lighting
  • 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
• 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 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.

• Indian History :
  • 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
• World History :
  • 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

• Physical geography :
  • 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
• Indian geography :
  • 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.