National Defence Academy (NDA) is the Joint Services academy of the Indian Armed Forces. The Union Public Service Commission (UPSC) conducts the NDA Exam twice a year as a nationallevel exam. Male candidates typically seek this highly desirable defence job, and selection is based on a written test followed by a Personality Test. The NDA written examination consists of two papers: Mathematics and General Ability Test (GAT). Aspiring applicants, both male and female, should refer to the detailed NDA Syllabus 2023 outlined in this article to begin their exam preparation.
NDA Mathematics Syllabus:
The chapters covered for NDA Maths Syllabus are given in the table below.
Mathematics 

Topic 
Topicwise Syllabus 
Algebra 
Sets, Venn diagrams, De Morgan laws, Cartesian product, relation, equivalence relation. Real numbers, Complex numbers, Modulus, Cube roots, Conversion of a number in Binary system to Decimals, and viceversa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations, Linear inequations, Permutation and Combination, Binomial theorem, and Logarithms. 
Calculus 
Concept of a realvalued function, domain, range, and graph of a function. Composite functions, onetoone, onto, and inverse functions. The notion of limit, Standard limits, Continuity of functions, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivativeapplication. Derivatives of sum, product, and quotient of functions, a derivative of a function concerning another function, the derivative of a composite function. Secondorder derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima 
Matrices and Determinants 
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. 
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 differential equations, solution of the first order, and firstdegree differential equations of various types—examples. Application in problems of growth and decay. 
Trigonometry 
Angles and their measures in degrees and radians. Trigonometric ratios. Trigonometric identities Sum and difference formulae. Multiple and Submultiple angles. Inverse trigonometric functions. ApplicationsHeight and distance, properties of triangles. 
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 done by a force and moment of a force and in geometrical problems. 
Analytical Geometry Of Two and Three Dimension 
Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. The angle between two lines. Distance of a point from a line. Equation of a circle in standard and a general form. Standard forms of parabola, ellipse, and hyperbola. 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. Equation of a plane and a line in various forms. The angle between two lines and the angle between two planes. Equation of a sphere. 
Statistics and Probability 
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 Binomial distribution. 
The General ability test comprises two papers English and General Knowledge. The English paper consists of 200 Marks while the General Knowledge is of 400 Marks.
Topic 
No. of Questions 
No. of Marks 
Spotting Errors 
5 
20 
Comprehension 
6 
24 
Selecting Words 
10 
40 
Ordering of Words in a Sentence 
9 
36 
Sentence Improvement 
10 
40 
Antonyms 
5 
20 
Synonyms 
5 
20 
Total 
50 
NDA Syllabus General Knowledge
Topic 
No. of Questions 
No. of Marks 
Physics 
23 
92 
Chemistry 
16 
64 
General Science 
11 
44 
History & Freedom Movement 
16 
64 
Geography 
17 
68 
Current Events 
17 
68 
Total 
100 
400 
NDA Syllabus Physics
NDA Syllabus Chemistry
NDA Syllabus General Science
NDA Syllabus History, Freedom Movement
NDA Syllabus Geography
Intelligence and Personality Test
NDA SSB Personality Test 

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