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[QUOTE=muthukalee;177158][CENTER][B]The scheme and syllabus of examination[/B]
[/CENTER]

1. The subjects of the written examination, the time allowed and the maximum marks allotted to each subject will be as follows :– 
Subject Code Duration Maximum Marks
Mathematics 01 2-½ Hours 300
General 02 2-½ Hours 600
Ability Test Total 900
SSB Test/Interview : 900

[URL]http://upsc.gov.in/[/URL]
[URL]http://upsc.gov.in/exams/notifications/2012/nda1/upsc%20nda-na-I%202012.pdf[/URL]
[B]
PAPER-I
MATHEMATICS[/B] (Code No. 01) (Maximum Marks- 300)
1. ALGEBRA : Concept of a 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 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. Applicationswork 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.

[B]PAPER-II
GENERAL ABILITY TEST[/B] (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.
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.
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.
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.
Section ‘E’ (Geography) The Earth, its shape and size. Lattitudes and Longitudes, Concept of time. International Date Line. Movements of Earth and their effects.[/QUOTE]

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