Скачать или смотреть What is NDA Exam? NDA Exam scheme | Benefits of NDA Cadets | NDA COACHING ONLINE | UPSC EXAM

Nda exam scheme and NDA EXAM Preparation
Join our Whats app 9995916183
Telegram Channel : https://t.me/VictorGrowthAcademyNDA
Website : https://victorgrowth.com/
NDA Syllabus

SYLLABUS OF THE EXAMINATION
PAPER-I
MATHEMATICS
(Code No. 01)
(Maximum Marks-300)
1. ALGEBRA
Concept of 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,
19
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 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.
20
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.
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.