NDA Syllabus 2012

1Algebra :
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 application.  Logarithms and their
applications.

2.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 - 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 a function at a point, geometrical and physical
interpreatation 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 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 equation, 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 vector,
 scalar product or dot product of two-vectors.  Vector product and cross
product of two vectors.  Applications-work 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.

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

(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