UPSC Exam Syllabus – National Defense Academy (NDA) & Naval

Are you looking for UPSC NDA Syllabus? If Yes! than we sarkari Naukri has launched our syllabus pattern for UPSC’s Official website. If you are preparing for this exam then you can read this syllabus and prepare yourself for this Government Exam.

Academy Exam:

Pattern of the Examination for UPSC National Defense Academy (NDA)

This examination will be conducted in just Two Phase which are following

Phase – I

Written Examination (Objective Type)

Phase – II

SSB Test/Interview


RBI UPSC NDA Exam Pattern


Total Marks




2½ Hours

General Ability Test


2½ Hours




SSB Test/Interview


The SSB procedure consists of two main selection stages process – Stage I and Stage II. And one important thing is those candidates who clear the stage I, they are permitted to appear for stage II.


Syllabus For UPSC NDA Examination






Matrices & Determinants


Analytical Geometry

Differential Calculus

Integral Calculus

Vector Algebra

Statistics and Probability




PART B (General Knowledge)

SECTION A (Physics)

SECTION B (Chemistry)

SECTION C (General Science)

SECTION D (History)

SECTION E (Geography)

SECTION F (Current Event)


Eligibility Criteria

12th Class pass of the 10+2 pattern of School Education or equivalent examination.


Mathematics (300 Marks)

Algebra: Complex numbers – basic properties, Conversion of a number in decimal system to binary system and vice-versa, modulus, argument, Arithmetic, Permutation and Combination, Geometric and Harmonic progressions,  Representation of real numbers on a line, Quadratic equations with real coefficients, Logarithms and their applications, Solution of the linear equations of two variables by the graphs, cube roots of unity, Binary system of numbers, Binomial theorem and its application.

Trigonometry: Properties of triangles, Trigonometrical ratios, An Inverse trigonometric function, Trigonometric identities Sum and difference formulae, Applications – Height and distance chapter, Multiple and Sub-multiple angles, Angles and their measures in the degrees and in the radians.

Differential Calculus: Composite functions, onto and inverse functions, one to one, physical and the geometrical interpretation of the derivative – it’s applications, increasing and decreasing functions also, Continuity of the functions – examples, algebraic operations on continuous functions, Application of derivatives,  Problems of maxima and minima, Concept of a real valued function – domain, Notion of limit, range and graph of a function, Standard limits – examples, geometrical and physical interpretation of a derivative – applications,  derivative of a function with respect of another function, Derivatives of sum, product and quotient of functions,  derivative of a composite function and Second order derivatives, Derivative of a function at one point.

Vector Algebra: Scalar multiplication of vector, Vectors in two and three dimensions, scalar product or dot product of two-vectors, addition of vectors, magnitude and direction of a vector, Unit and null vectors, Vector product and cross product of two vectors. Applications-work is done by the force and moment by the force, and in geometrical problems.

Integral Calculus and Differential equations: Formation of a differential equation by examples, Integration by substitution and by the parts, exponential and hyperbolic functions, trigonometric, Definition of order and degree of a differential equation, solution of first order and first degree of the differential equations of various types – examples, standard integrals involving algebraic expressions. Evaluation of the definite integrals – determination of areas of plane regions bounded by curves – General and particular solution of a differential equation, applications, Integration as inverse of differentiation, And application in problems of the growth and the decay.

Matrices and Determinants: Determinant of the matrix, all types of the matrix, adjoin of the matrix and inverse of a square matrix, operation of the matrix, Application – Solution of the system of linear equation in two or more unknown by Cramer’s rule and by the Matrix method, And in the last the basic property of the determinant.

Analytical Geometry of two and three dimensions: The first you have to study about Distance formula, equation of a circle in general form or in a standard form, hyperbola and ellipse, the angle between two lines, rectangular cartesian coordinate system, equation of the line in a various form, Standard formula of the parabola, distance of a point from a line, and eccentricity and the axis of a conic.