NDA Maths Syllabus 2025: Check Chapter-wise Weightage and Important Topics

NDA syllabus is prescribed by the examination authority so that candidates can know what they need to prepare for the exam. The standard of NDA syllabus is of Class 10, 11 and 12 levels. NDA syllabus is divided into two parts-Maths and GAT. NDA Maths syllabus carries questions from Algebra Calculus, Matrices and Determinants Integral Calculus and Differential Equations Trigonometry Vector Algebra Analytical Geometry Of Two and Three Dimension and Statistics and Probability.. NDA GAT syllabus carries questions from topics such as Usage, Vocabulary, Comprehension, and Cohesion. Questions in General Knowledge are asked from Physics Chemistry Social Studies, General Science, Geography, and Current Events.

NDA syllabus is prescribed by UPSC. The syllabus is mentioned on the notification. NDA syllabus is divided into Maths and GAT. The standard of NDA syllabus is of Class 10, 11 and 12 levels. The total marks allotted to the written exam are 900. NDA Maths syllabus comprises topics such as Algebra, Calculus, Matrices and Determinants, Integral Calculus and Differential Equations, Trigonometry, Vector Algebra, Analytical Geometry Of Two and Three Dimension and Statistics and  Probability. NDA GAT syllabus comprises topics such as Grammar and Usage, Vocabulary, Comprehension, and Cohesion, Physics, Chemistry, Social Studies, General Science, Geography, and Current Events.

NDA Maths syllabus covers the topics from higher secondary Mathematics on Trigonometry Algebra Differential Calculus, 2D and 3D Geometry, Matrix and Determinants etc. A total of 120 questions are asked in the Maths section and carry 300 marks. Candidates must clear their basics from Class 10, 11 and 12 Maths books. NDA syllabus for Maths is given below:

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 vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations, Linear inequations, Permutation and Combination, Binomial theorem and Logarithms.

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, Continuity of functions, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivative-application. Derivatives of sum, product and quotient of functions, 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

Matrices and Determinants: Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. 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.

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 first order and first-degree differential equations of various types—examples. Application in problems of growth and decay.

Trigonometry: Angles and their measures in degrees and in radians. Trigonometric ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications-Height 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 in a general form. Standard forms of parabola, ellipse, and hyperbola. Eccentricity and axis of a conic. Point in a three-dimensional 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. Angle between two lines and 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.

NDA exam is conducted for admission to the Army, Navy and Air Force wings of National Defence Academy and Indian Naval Academy Course. CDS exam is conducted to select eligible candidates for Indian Military Academy (IMA), Indian Naval Academy (INA), Air Force Academy (AFA) and Officers Training Academy (OTA).

NDA and CDS syllabus are different. Candidates can check below in detail:

The level of NDA syllabus is of Class 10, 11 and 12 levels. Whereas, the standard of CDS syllabus is of graduation level. NDA syllabus is divided into Maths and GAT. CDS syllabus is divided into Elementary Maths, English and General Awareness. The total marks allotted to the NDA written exam are 900. The total marks allotted to the written exam of CDS are 300 for IMA, INA and AFA and 200 for OTA. 

Yes, the NDA syllabus is the same as class 12. To crack the NDA exam, candidates must have conceptual clarity for better application while handling tricky and simple questions. Candidates must practice previous years' question papers. For Maths candidates must practice from NCERT Class 11 books. Jot down important Mathematical formulas and concepts. For English, candidates must brush up on the concepts of English. Candidates must clear their basic grammar, improve reading comprehension, and build vocabulary to tackle Antonyms and Synonyms.

NDA syllabus PDF is provided on this page. The syllabus PDF comprises the important topics related to the exam. Candidates can download the syllabus PDF and start preparing for the exam. With good practice, candidates can ace the exam. 

NDA syllabus is prescribed by the examination authority. The syllabus comprises the topics that candidates need to prepare for the exam. The first and foremost step towards preparation is going through the syllabus. Knowing the syllabus helps candidates to plan a strategy to ace the exam, thereby, giving them the right direction for preparation. NDA syllabus has two sections for the written exam, General Ability Test (GAT) and Mathematics. GAT aims to test the candidate's basic knowledge of History, GK, Current Affairs of National and International Events, English, Science, and Geography. On the other hand, the Mathematics paper of NDA comprises questions based on Class 12. The GAT paper holds the maximum weightage in the syllabus.