National Defence Academy NDA Exam Pattern & Syllabus

· De Morgan laws

· Cartesian product, relation, equivalence relation

· Representation of real numbers on a line

· Complex numbers – basic properties, modulus, argument and 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 in equations of two variables by graphs

· Permutation and Combination

· Binomial theorem and its application

· Logarithms and their applications.

· 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

· 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.

· 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

· 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 of another function, derivative of a composite function

· Second order derivatives. Increasing and decreasing functions

· Application of derivatives in problems of maxima and minima

· 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

· Trigonometrical ratios

· Trigonometric identities Sum and difference formulae

· Multiple and Sub-multiple angles

· Inverse trigonometric functions. Applications – Height and distance, properties of triangles

· 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