NDA Syllabus 2019

Topics

Sub-Topics

Algebra

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 17 equations with real coefficients.

A solution of linear inequations of two variables by graphs.

Permutation and Combination.

Binomial theorem and its applications.

Logarithms and their applications.

Concept of set

Operations on sets

Venn diagrams.

De Morgan laws, Cartesian product, relation, equivalence relation.

Matrices and Determinant

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.

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 of two and three dimensions

Rectangular Cartesian Coordinate system. Distance formula.

Distance formula.

The equation of a line in various forms.

The angle between two lines.

The distance of a point from a line.

The equation of a circle in standard and in general form. Standard forms of

Standard forms of a parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a

Eccentricity and axis of a conic. Point in a three-dimensional space, the distance between two points.

Direction Cosines and direction ratios.

Equation two points. Direction Cosines and direction ratios.

Direction Cosines and direction ratios.

Equation two points. Direction Cosines and direction ratios. The equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

Direction Cosines and direction ratios. The equation of a plane and a line in various forms. The angle between two lines and angle between two planes. The equation of a sphere.

The equation of a plane and a line in various forms. The angle between two lines and angle between two planes. The equation of a sphere.

The angle between two lines and angle between two planes. The equation of a sphere.

Differential Calculus

The concept of a real-valued function–domain, range and graph of a function.

Composite functions, one to one, onto and inverse functions.

The notion of limit, Standard limits—examples.

Continuity of functions—examples, algebraic operations on continuous functions.

Derivative of the function at a point, geometrical and physical interpretation of a derivative—applications.

Derivatives of the sum, product, and quotient of functions, the 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.

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.

18 Definition of order and degree of a differential equation, formation of a differential equation by examples.

General and particular solution of differential equations, the solution of first order and first-degree differential equations of various types—examples.

Application in problems of growth and decay.

Vector Algebra

Vectors in two and three dimensions, magnitude and direction of a vector.

Unit and null vectors, the addition of vectors, scalar multiplication of a vector, scalar product or dot product of two vectors.

Vector product or cross product of two vectors. Applications—work was done by a force and moment of a force and in geometrical problems.

Statistics and Probability

Statistics: Classification of data, Frequency distribution, cumulative frequency distribution, Graphical representation Histogram, Pie Chart, frequency polygon, 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.