NDA Syllabus 2025

The NDA syllabus 2025 has been released by the UPSC (Union Public Service Commission) on the official website. The candidates must check the syllabus in order to understand the topics they are required to study for the NDA exam. The syllabus is divided into mainly two subjects such as Mathematics and General Ability Test. The paper pattern consists of objective type questions. Candidates must check not only the syllabus but also the exam pattern for the upcoming NDA exam. Check the below guide to know more about the exam pattern, NDA syllabus, marking scheme, etc.

Overview of NDA Syllabus

The syllabus is divided into mainly two parts such as Mathematics and the General Ability Test. The syllabus will guide them about the topics and the sub topics that can be asked in the exam. They should begin the preparation after they have evaluated the syllabus. 

NDA Syllabus – Mathematics

The mathematics syllabus in the NDA exam consists of various sections such as Matrices, Trigonometry, Analytical Geometry, Algebra, Vector Algebra, Integral Calculus, Statistics, Probability. Check below the detailed NDA syllabus for mathematics:

Algebra

• Concept of set, operations on sets, Venn diagrams.  
• Logarithms and their applications.
• Solution of linear inequalities of two variables by graphs.
• Representation of real numbers on a line. Complex numbers—basic properties, modulus, argument, cube roots of unity. Binary system of numbers.
• De Morgan laws, Cartesian product, relation, equivalence relation. 
• Permutation and Combination. Binomial theorem and its applications.
• Conversion of a number in a decimal system to a binary system and vice-versa. 
• Arithmetic, Geometric, and Harmonic progressions. Quadratic equations with real coefficients. 

Trigonometry

• Inverse trigonometric functions. 
• Applications-Height and distance, properties of triangles.
• Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. 
• Angles and their measures in degrees and radians. Trigonometric ratios. 

Matrices and Determinants

• Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method, Adjoint and inverse of a square matrix,.
• Determinant of a matrix, basic properties of determinants. 
• Types of matrices, operations on matrices. 

Trigonometry

• Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. 
• Inverse trigonometric functions. 
• Angles and their measures in degrees and radians. Trigonometric ratios. 
• Applications-Height and distance, properties of triangles.

Differential Calculus

• The notion of limit, Standard limits—examples. Continuity of functions—examples, algebraic operations on continuous functions. 
• Composite functions, one-to-one, onto, and inverse functions. 
• Concept of a real-valued function–domain, range, and graph of a function. 
• Second-order derivatives. Increasing and decreasing functions. 
• Derivative of function at a point, geometrical and physical interpretation of a derivative—applications. Derivatives of sum, product, and quotient of functions, derivative of a function concerning another function, derivative of a composite function. 
• Application of derivatives in maxima and minima problems

Geometry

• Equation of a circle in standard and general form. Standard forms of parabola, ellipse, and hyperbola. Eccentricity and axis of a conic. 
• 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. 
• Direction Cosines and direction ratios. 
• The angle between two lines and the angle between two planes. 
• Equation of a sphere.
• Point in a three-dimensional space, the distance between two points. Direction Cosines and direction ratios. 
• Equation two points. 
• Equation of a plane and a line in various forms. 

Vector Algebra

• Vector product or cross product of two vectors. Application work done by a force and moment of a force and in geometrical problems
• Unit and null vectors, addition of vectors, scalar multiplication of a vector, scalar product or dot product of two vectors. 
• Vectors in two and three dimensions, magnitude, direction of a vector.

Statistics and Probability

• Graphical representation—Histogram, Pie Chart, frequency polygon— examples. 
• Statistics Classification of data, cumulative frequency distribution, Frequency distribution, —examples. 
• Measures of Central tendency—Mean, median, and mode. Variance and standard deviation—determination and comparison. Correlation and regression. 

Probability

• Complementary, elementary, and composite events. Definition of probability—classical and statistical—examples. Elementary theorems on probability—simple problems.
• Random experiment, outcomes, associated sample space, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. 
• Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binomial distribution
• Conditional probability, Bayes’ theorem—simple problems.