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# upsc.gov.in NDA Exam Syllabus National Defence Academy : Union Public Service Commission

** Organisation **: Union Public Service Commission

**: NDA Exam National Defence Academy**

__Name Of The Exam__**: Syllabus**

__Announcement__** Website **: http://www.upsc.gov.in/

**: http://www.syllabus.gen.in/uploads/1000-NDA-Exam.pdf**

__Download Syllabus__## NDA Exam Syllabus :

** Mathematics **:

**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.

Related / Similar Syllabus: UPSC Combined Geo-Scientist Exam Syllabus 2020

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. 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. 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