The National Defense Academy (NDA) admits students to the Army, Navy and Air Force wings through an entrance examination held twice a year, generally in the months of April and September. This examination is conducted by the Union Public Service Commission (UPSC).

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For appearing in examination, a candidate must be an unmarried male, at least 161/2 years old but below the age of 19 as of January 1, or July 1, of the year succeeding the examination year.

Educational Qualifications:

(1)

For Army Wing of National Defence Academy: Must have successfully completed Class XII in the 10 + 2 pattern of school education or equivalent examination conducted by a State education board or a university.

(2)

For Air Force and Naval Wings of National Defence Academy and for the 10 + 2(Executive Branch) Course at the Naval Academy: Must have passed Class 12 of the 10 + 2 pattern of school education or equivalent with Physics and Mathematics conducted by a State education board or a university. Candidates currently in Class XII in the 10 + 2 pattern of school education, or equivalent examination, can also apply.

Examination

Plan of the Examination: The examination comprises (i) a written examination and (ii) intelligence, obstacles and group tests of the candidates who qualify in the written examination.

Examination Subjects: The subjects of the written examination, the time allowed and the maximum marks allotted to each subject are as follows :

S.No SubjectDuration Max. Marks
1Mathematics21/2 hours300
2General Ability Test (English, GK and Science)21/2 hours600
Total900

Notes
• The papers in all subjects will consist only of objective-type questions.
• The question papers (test booklets) will be set in English.

Syllabus for Mathematics

Trigonometry – Angles and their measures in degree and in radians. Trigonometrical ratios. Trigonometry identities. Sum and difference formulae. Multiple and sub-multiple angles trigonometric functions. Applications – height and distance, properties of triangles.

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.

Algebra – Concept of a set, operations on sets, Venn diagrams. De Morgan laws. Cartesian product, relation equivalence relation.

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 plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

Differential Calculus – Concept of a real valued function – domain, range and graph of a 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, derivatives 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, 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 type – examples. Application in problems of growth and decay.

Vector Algebra – Vectors in two and three dimensions, magnitude and direction of 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.

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 or 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 binomial distribution.