### NDA 2015 Syllabus:

The following article stated below is the NDA 2015 Syllabus:

### Paper 1 Mathematics:

**Algebra:**

Concept of Set, operations on sets, Venn Diagrams. De Morgans 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 equation with real coefficients. Solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its application. Logarithms and their applications.

**Matrices and Determinants:**

Types of matrices, operations on matrices Determinant of a matrix, basic properties of determinant. Adjoint and inverse of a square matrix, Applications-Solutions of a system of linear equation in two or three unknowns by Cramers rule and by Matrix Method.

**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.

**Analytical Geometry and 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 of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

**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 continous 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 of another function, derivative of a composite function. Second order derivative. Increasing and decreasing functions. Applications of derivatives in problem of maxima and minima.

**Integral Calculus and Differential equations:**

Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbole 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 equation, solution of first order and first degree differential equation of various types-examples. Applications in problem of growth and decay.

**Vector Algebra:**

Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, additional of vectors, scalar multiplication of vector, scalar product or dot product of two vectors. Vectors product and cross product of two vectors. Applications-work done by a force and moment of force, and in geometrical problems

**Statistics and Probability:**

Statistics Classification of data, Frequency distribution, cumulative frequency distribution- examples Graphical representation-Histogram, PieChart, 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 Binomial distribution.

### Paper 2 General Ability:

**Part A-English:**

The question paper is designed and crafted in such a manner so as to thoroughly test the Candidates understanding of the Language of English. This Section covers several aspects of the Language such as the Grammar, Composition, Comprehension and Cohesion.

**Part B-General Knowledge:**

This section of the paper will exclusively covers subjects of Physics, Chemistry, General Studies, Social Studies, Current Events, Geography Etc.

**(i)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 laws of Motion, Force and Momentum, Parallelogram of Forces, Stability and Equilibrim 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, Ohms 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, Gramaphone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariners Compass; Lightening Conductors, Safety Fuses.

**(ii)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 an salts.

Carbon-different forms

Fertilizers-Natural and Artifical

Material used in the preparation of substances like soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, Gun Powder.

Elementary ideas about the structure of atom, Atomic, Equivalent and Molecular Weights, Valency.

**(iii)General Studies:**

Difference between the living and the non-living

Basics 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, balance diet

The solar system-Meteors and comets, Eclipses.

Achievements of Eminent Scientists.

**(iv)Social Studies:**

A broad survey of Indian History, with emphasis on Culture and civilization.

Freedom Movement of India

Elementary study of Indian Constitution and Administration

Elementary knowledge of Five year plans in India

Panchayat 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 America 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.

**(v)Current Events:**

All the important events that have taken place in India in the last recent years. Current important world events. Prominent personalities-both Indian and international including those connected with cultural activities and sports.

**(vi)Geography:**

The Earth, its shape and size. Lattitudes and Longitudes, Concept of Time. International Date Line. Movements of Earth and their effects.

Origins of the Earth. Rocks and their classification; weathering-mechanical and chemical, Earthquakes and Volcanoes.

Ocean Current and Tides.

Atmosphere and its composition; Temperature and Atmosphere Pressure, Planetary Winds, Cyclones and Anti-Cyclone; 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 Export and Import of India.

**NDA 2015 Paper Pattern:**

The following given below is the NDA 2015 Paper Pattern:

- The NDA Entrance Examination will be of the Written Nature and not of the Online or the Computer Test Mode.
- The Entrance Examination shall consist of 2 Subjects or Papers, namely (i) Mathematics and (ii) General Ability.
- The Duration for each of the above mentioned Papers (i.e. Mathematics & General Ability) will be of 2.5 Hrs.
- The Mathematics Paper shall comprise of 300 Marks and
- The General Ability Paper shall consist of 600 Marks
- Thus the Total Marks for the Entrance Examination shall be 900 Marks.
- All the Questions Asked in the Entrance Examination shall be in the nature of the Multiple Choice Questions (MCQs)

### The General Ability Test shall comprise of 2 Parts:

- (a)English (Maximum 200 Marks)
- (b)General Knowledge (Maximum 400 Marks) which is divided into the following Sections, given below:

- Physics Section- 100 Marks
- Chemistry Section- 60 Marks
- General Science Section-40 Marks
- History & Freedom Movement Section-80 Marks
- Geography Section-80 Marks
- Current Events Section- 40 Marks.