National Defence Academy(NDA & NA) Syllabus
NDA Syllabus 2019 – Union Public Service Commission (UPSC) prescribes the syllabus of NDA 2019 along with the notification. NDA exam is bifurcated into two papers – Mathematics and General Ability Test (GAT). The list of topics from which questions will be asked in the examination is provided in NDA syllabus 2019. The difficulty level of questions asked in Mathematics will be similar to that of class 12 level. NDA syllabus 2019 of General Ability Test comprises topics to assess candidates’ proficiency of English language and knowledge of subjects including Physics, Chemistry, General Science, Social Studies, Geography and Current Events. NDA is likely to be held by UPSC in September 2019.
NDA Syllabus 2019 for Mathematics
Paper 1 of NDA 2019 consists of topics pertaining to Mathematics. The syllabus of NDA 2019 Paper 1 has been provided below.
Topics  SubTopics 
Algebra  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 viceversa. Arithmetic, Geometric and Harmonic progressions. Quadratic 17 equations with real coefficients. A solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications. Concept of set Operations on sets Venn diagrams. De Morgan laws, Cartesian product, relation, equivalence relation. 
Matrices and Determinant  Types of matrices, operations on matrices.
Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix, ApplicationsSolution 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 Submultiple angles. Inverse trigonometric functions. ApplicationsHeight and distance, properties of triangles. 
Analytical Geometry of two and three dimensions  Rectangular Cartesian Coordinate system. Distance formula.
Distance formula. The equation of a line in various forms. The angle between two lines. The distance of a point from a line. The equation of a circle in standard and in general form. Standard forms of Standard forms of a parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a Eccentricity and axis of a conic. Point in a threedimensional space, the distance between two points. Direction Cosines and direction ratios. Equation two points. Direction Cosines and direction ratios. Direction Cosines and direction ratios. Equation two points. Direction Cosines and direction ratios. The equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere. Direction Cosines and direction ratios. The equation of a plane and a line in various forms. The angle between two lines and angle between two planes. The equation of a sphere. The equation of a plane and a line in various forms. The angle between two lines and angle between two planes. The equation of a sphere. The angle between two lines and angle between two planes. The equation of a sphere. 
Differential Calculus  The concept of a realvalued function–domain, range and graph of a function.
Composite functions, one to one, onto and inverse functions. The notion of limit, Standard limits—examples. Continuity of functions—examples, algebraic operations on continuous functions. Derivative of the function at a point, geometrical and physical interpretation of a derivative—applications. Derivatives of the sum, product, and quotient of functions, the derivative 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. 18 Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of differential equations, the solution of first order and firstdegree 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, the 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 was 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, Graphical representation Histogram, Pie Chart, frequency polygon, 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. 
NDA Syllabus 2019 for General Ability Test
The General Ability Test (GAT) is the second paper required for the written exam of NDA 2019. GAT paper is bifurcated into two parts – Part A: English and Part B: General Knowledge. English section (Part A) test candidates’ proficiency in English. NDA 2019 syllabus covers grammar and its usage, vocabulary, comprehension and cohesion, etc. The paper on General Knowledge (Part B) covers subjects including Physics, Chemistry, General Science, Social Studies, Geography and Current Events. Each of these subjects has been divided into sections. Questions asked in Part B will evaluate candidates’ knowledge, understanding and expertise in each of the subjects. Check below for the complete NDA syllabus 2019 of Paper 2: General Ability Test.
Sections  Topics  SubTopics 
Section A  Physics 

Section B  Chemistry 

Section C  General Science 

Section D  History, Freedom Movement etc. 

Section E  Geography 

Section F  Current Events 

NDA 2019 Exam Pattern
Candidates must be wellinformed regarding the exam pattern of NDA. As per NDA exam pattern 2019, the written exam will be held for 900 marks. Of the total marks, the Mathematics paper will comprise 300 marks while GAT paper will be conducted for 900 marks. Both the papers will be conducted for 2 hours 30 minutes each. After the completion of the written test, candidates qualifying the exam stage will be called for SSB Interview. The Interview stage will comprise a total 900 marks. The complete exam pattern of the written exam has been provided in the table below.
NDA Exam Pattern 2019 – Written examination
Subjects 
Duration 
Maximum Marks 
Mathematics 
2.5 hours 
300 
General Ability Test 
2.5 hours 
600 
Total Marks 
900 
Best Books to prepare for NDA
Some of the best books for preparation of NDA exam had been given below for the convenience of candidates. The list of books below are provided as per subject it covers for the exam. However, candidates who are searching for books that cover both papers of the exam can refer to Arihant’s “Pathfinder for NDA & NA – National Defense Academy and Naval Academy”. The paperwise best books for the preparation of NDA 2019 are as follows.