**NDA Syllabus Details:**

The Union Public Service Commission (UPSC) conducts the National Defence Academy (NDA) & Naval Academy (NA) exam twice a year, offering admission to the Indian Navy, Army, and Air Force Wings. The minimum educational qualification required is the completion of the 12th class in the 10+2 pattern. The examination comprises two stages: a written examination and an interview. The detailed syllabus is as follows:

**PAPER-I: MATHEMATICS (Maximum Marks – 300)**

**ALGEBRA:**- Concept of 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 the decimal system to the binary system and vice versa.
- Arithmetic, geometric, and harmonic progressions.
- Quadratic equations with real coefficients, solution of linear inequalities of two variables by graphs.
- Permutation and combination, binomial theorem, logarithms, and their applications.

**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.

**TRIGONOMETRY:**- Angles and their measures in degrees and radians.
- Trigonometrical ratios, identities, sum and difference formulae.
- Multiple and sub-multiple angles, inverse trigonometric functions.
- Applications – height and distance, properties of triangles.

**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, standard forms of parabola, ellipse, and hyperbola.
- Point in three-dimensional space, direction cosines, and ratios.
- Equation of a plane and a line in various forms, angle between two lines and planes.
- Equation of a sphere.

**DIFFERENTIAL CALCULUS:**- Concept of a real-valued function, composite functions, limits.
- Continuity of functions, derivatives, second-order derivatives.
- Increasing and decreasing functions, applications in problems of maxima and minima.

**INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS:**- Integration as the inverse of differentiation.
- Integration by substitution and by parts, standard integrals.
- Definite integrals, determination of areas of plane regions.
- Definition of order and degree of a differential equation, general and particular solutions.

**VECTOR ALGEBRA:**- Vectors in two and three dimensions, magnitude, direction, and operations.
- Scalar and vector products, applications in work done and moments of a force.

**STATISTICS AND PROBABILITY:**- Classification of data, frequency distribution, graphical representation.
- Measures of central tendency, correlation, regression.
- Probability, random experiment, sample space, events, and probability distribution.

**PAPER-II: GENERAL ABILITY TEST (Maximum Marks – 600)**

**Part ‘A’ – ENGLISH (Maximum Marks 200):**

- Grammar and usage, vocabulary, comprehension, and cohesion in extended text.

**Part ‘B’ – GENERAL KNOWLEDGE (Maximum Marks 400):**

**Section ‘A’ (Physics):**Physical properties, laws of motion, gravitation, thermodynamics, electricity, magnetism.**Section ‘B’ (Chemistry):**Elements, compounds, acids, bases, salts, metals, non-metals, organic chemistry.**Section ‘C’ (General Science):**Living and non-living, cell biology, human anatomy, epidemics, food constituents, solar system, achievements in science.**Section ‘D’ (History, Freedom Movement, etc.):**Indian history, freedom movement, Indian constitution, world history, social and economic topics.**Section ‘E’ (Geography):**Earth, rocks, weathering, ocean currents, atmosphere, climate, natural resources, regional geography of India.**Section ‘F’ (Current Events):**Important events in India and the world, prominent personalities, current affairs.

**Note:** Out of the maximum marks assigned to Part ‘B,’ questions on Sections ‘A,’ ‘B,’ ‘C,’ ‘D,’ ‘E,’ and ‘F’ will carry approximately 25%, 15%, 10%, 20%, 20%, and 10% weightages, respectively.