 National Defense Academy and Naval Academy examination are conducted twice in a year for the Indian Armed Forces (Army, Navy & Air- Force) as per the notifications issued by UPSC (Union Public Service Commission).

Generally, the notification for the first exam comes in the month of December for which the exam takes place in the month of April. Similarly, the second notification is published in the month of May and the exam takes place in the month of August.

Candidates surpassing the written exam are mobilized for testing their personality traits in the 5 days SSB round. Those clearing the SSB are sent for their medical examination done. Eventually, the all India Merit list is revealed by the commission. Candidates falling under the merit list join National Defense Academy.

ELIGIBILITY CRITERIA
Age - 16½ - 19½ Years.

EDUCATIONAL QUALIFICATIONS -
For Army - 12th Class pass on 10+2 pattern, or equivalent.
For Air Force and Naval- 12th Class pass on 10+2 pattern with Physics and Mathematics, or equivalent.

EXAMINATION SCHEME
The paper consists of objective type questions only. There will be four options available for each question. Candidates are expected to tick the correct answer in the provided answer sheet.

 SUBJECT PAPER CODE MARKS DURATION PAPER-I MATHEMATICS 01 120 QUESTIONS-300 MARKS 2 ½ Hrs. PAPER-II GENERAL ABILITY 02 150 QUESTIONS-600 MARKS 2 ½ Hrs.

SYLLABUS-

PAPER-I MATHEMATICS (01)

There is a negative (-) marking of (0.825) for each WRONG Answer

The question in Mathematics paper will be based on

• 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.  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 and its application.  Logarithms and their applications.
• Matrices &Determinants-Types of matrices, operations on matrices Determinant of a matrix, basic  properties of determinant. 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.
• 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.
• 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.
• 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 a function at a point, geometrical and physical interpreatation of a derivative – applications.  Derivatives of sum, product and quotient of functions, derivative of a function with respect of 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 &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 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, addition of vectors, scalar multiplication of vector, scalar product or dot product of two-vectors. Vector product and 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

PAPER-II GENERAL ABILITY (02)

There is a negative (-) marking of (1.32) for each WRONG Answer.

The General Ability test comprises of two parts
PART-A (ENGLISH)

The syllabus covers various topics like: Grammar and its usage, vocabulary, use of words, comprehension. The question paper of English is so designed to test the candidate's overall proficiency in English.

PART-B (GENERAL KNOWLEDGE)
The paper of General Knowledge consists of the following five sections.
•    Section-A- Physics
•    Section-B- Chemistry.
•    Section-C- General sciences.
•    Section-D- History & Geography.
•    Section- E- Current Events.

You can get the previous years Question Papers here:

2015- NDA/NA-1   MATHS , GENERAL ABILITY TEST.

2015- NDA/NA-2   MATHS , GENERAL ABILITY TEST.

2014- NDA/NA-1   MATHS , GENERAL ABILITY TEST.

2014- NDA/NA-2   MATHS , GENERAL ABILITY TEST.