NDA and NA Exam (II)-2015 Admit Card NDA Syllabus 27th Sept 2015

Download NDA-II September 2015 Admit Card. UPSC NDA/ NDA-2 Written Exam Date is 27-09-2015.

The Union Public Service Commission, New Delhi is ready to conduct written examination of NDA/ NA-II on 27th September 2015. The online UPSC National Defence Academy/ Naval Academy (II) application form cum registration has been over. The candidate can download e-admit card from UPSConline.nic.in website. The candidate can check NDA/ NA Form status. We also advice candidate to download latest syllabus & exam pattern. There shall be two subjects – Mathematics and General Ability Test (GAT). The shortlisted candidate are called for the SSB Interview at Bhopal/ Allahabad/ Bangalore etc.

A large number of candidate who are enrolled in 12th board/ 11th class have registered for UPSC NDA Exam 2015. We suggest you to download you e-admit card online 3 weeks before written examination. The UPSC also issue recruitment of IES/ IAS 2015-2016. Please do check UPSC official website.

Exam Scheme NDA/ NA-II 2015.

Subject Code Duration

Maximum Marks

Mathematics 01 2-½ Hours


General Ability Test 02 2-½ Hours



 900 Marks

The papers in all the subjects will consist of objective type questions only. The question papers (Test Booklets) OF MATHEMATICS AND PART “b” OF GENERAL ABILITY TESTS WILL BE SET BILINGUALLY IN HINDI AS WELL AS  English.

The candidates are not permitted to use calculator or Mathematical or logarithmic table for answering objective type papers (Test Booklets). They should not therefore, bring the same inside the Examination Hal

In the question papers, wherever necessary, questions involving the metric system of Weights and Measures only will be set.

NDA/ NA-II 2015 Post Vacancies.

  • National Defence Academy: 320 (tentative)
  • Army: 208 posts (tentative)
  • Navy: 42 posts (tentative)
  • Air Force: 70 posts (tentative)
  • Naval Academy [10+2 Cadet Entry Scheme): 55 posts
  • Total: 375 Posts.

Download Syllabus.

  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.  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.
  2. 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.
  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 a 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 of 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 equation, 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 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.
  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 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.

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