**NATIONAL DEFENCE ACADEMY AND NAVAL ACADEMY EXAMINATION**

National Defence Academy and Naval Academy Examination is conducted by the Union Public Service Commission. The examination is for Army, Navy and Air Force Wings twice every year and this exam is conducted for unmarried male. The candidate joining this wing must undergo four years B.Tech course and would given an opportunity in joining Executive and Technical Subject for Navy Academy. The candidate opting National Defence Academy and Naval Academy must give his first preference of the option from Army, Naval and Air Wings.

__Eligibility Criteria:__

Candidate must either be

- The citizen of India
- The citizen of Bhutan
- The citizen of Nepal
- Migrated to different countries with the intention of moving to the native

Only male candidates can apply. Candidate should marry only if the training is completed. The candidate who marries on training stage is discharged and all the expenditure done to him must be refunded to the government. The candidate must be 10+2 passed for the exams based on the Higher Secondary Education System. The candidate must be physically fit.

__Selection Procedure:__

The stages of selection are

- Written Examination
- Interview

__Syllabus:__

The written Examination syllabus is

### Paper-I Mathematics

__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 and 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 and 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.

__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.

__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.

__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 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 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.

** 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.

**Paper-II **

General Ability Test

- Part ‘A’ – ENGLISH (Maximum Marks 200)
- Part ‘B’ – GENERAL KNOWLEDGE

__Exam Pattern:__

The exam consists of two papers of objective type with 300 and 600 marks respectively with two and half hours time duration. There is negative marks for wrong answer. Eligible candidates are moved to interview process.

#### How to Apply

- Log onto official website upsconline.nic.in
- Fill all the mandatory details in the application
- Upload the photo and signature
- Make the payment via Internet Banking, Credit/Debit cards
- Check for any errors in the application before submitting the application
- Submit the application
- Take the hardcopy for future reference

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