#### NDA

**About National Defense Academy (NDA)
**

**The NDA (National Defense Academy) exam is held twice in a year in the months of September to October and January to April. It is conducted by the union public services commissions (UPSC), and enables the**

**aspirants to apply for Indian Army, Indian Air Force, and Naval Academy. The age limit to apply for this exam is 16½ to 19 years. If you are looking for a trustworthy coaching institute , then you have come to the right place.**

**Motion coaching is the best coaching institute for NDA Exam. Fresh batches for NDA are going to start. Motion Coaching Institute is the well known coaching institute that provides coaching for NDA entrance exams.**

**Age : between 16½ to 19 as of first day of the month in which course is due to commence.**

**Qualification : 12th class (10+2) with Physics and Mathematics for Air Force/Navy & 12th class (10+2) for Army.**

**Marital Status : Unmarried.**

**Application to be received by : As per UPSC notification.**

**Period Applying for NDA : September to October and January to April**

**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 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.**

**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.**

**Part ‘A’ – ENGLISH (Maximum Marks 200). The question paper in English will be designed to test the candidate’s understanding of English and workman like use of words. The syllabus covers various aspects like : Grammar and usage, vocabulary, comprehension and cohesion in extended text to test the candidate’s proficiency in English.**

** Part ‘B’ – GENERAL KNOWLEDGE**

**Pattern
**

**Schedule : NDA Exam will be organized two times in a year through offline mode (written test). NDA (I) will be conducted on 23rd April 2017 & NDA (II) will be held on 10th September 2017.****Exam Mode : The exam will be conducted through offline mode.****Exam Duration : The duration of the examination will be 2 hours 30 minutes.****Type of Question : The question paper will be objective type questions.****Paper : The NDA exam consists of 2 papers i.e. Mathematics and General Ability.****Total Marks : The Mathematics paper contains 300 marks while General Ability test holds 600 marks. The written test will be of total 900 marks.****Negative Marking : For every incorrect response, 0.33 marks will be deducted as negative marking in the examination.****SSB Interview : After clearing the written test, candidates have to go through the SSB Interview. The interview process will have total 900 marks.****Language : The question paper of Mathematics and PART B of General Ability test will be available in both English and Hindi languages.****The written examination of NDA 2017 is structured as follows:**

Subjects |
Marks |

Mathematics |
300 |

General Ability Test (Section-1: English) |
200 |

General Ability Test (Section-1: General Knowledge) |
400 |

Total Marks |
900 |

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