NDA Syllabus 2026: Official Mathematics and GAT Scope for NDA II

Sets and set operations, Venn diagrams, De Morgan laws, Cartesian products, relations and equivalence relations, real numbers, complex numbers, binary number system, arithmetic, geometric and harmonic progressions, quadratic equations with real coefficients, graphical solution of linear inequations in two variables, permutations and combinations, binomial theorem, logarithms and applications.

Types of matrices, matrix operations, determinants and their properties, adjoint and inverse of a square matrix, and solution of a system of linear equations by matrix methods.

Angles and their measures, trigonometric ratios and identities, sum and difference formulae, multiple and sub-multiple angles, inverse trigonometric functions, applications including height and distance and properties of triangles.

Rectangular Cartesian coordinates, distance and section formulae, straight lines, circles, standard forms of the parabola, ellipse and hyperbola, and three-dimensional work including direction cosines, the equation of a plane and a line, the angle between lines and planes, and the equation of a sphere.

Functions and their graphs, limits, continuity, derivative of a function, derivatives of sums, products, quotients and composite functions, second-order derivatives, and applications to increasing and decreasing functions, maxima and minima.

Integration as the inverse of differentiation, standard integrals, integration by substitution and by parts, definite integrals and areas, and the formation and solution of first-order and first-degree differential equations with growth and decay applications.

Vectors in two and three dimensions, magnitude and direction, unit and null vectors, addition of vectors, scalar multiplication, scalar and vector products, and applications to work, moment and geometry.

Classification and graphical representation of data, measures of central tendency and dispersion, correlation and regression, and probability including random experiments, events, conditional probability, Bayes theorem and binomial distribution.

The syllabus tests the candidate's understanding of English and workmanlike use of words. It covers grammar and usage, vocabulary, comprehension and cohesion in extended text.

Elementary mechanics, heat, sound, light, electricity, magnetism and related physical concepts named in the official syllabus.

Basic matter and changes, elements, mixtures and compounds, simple equations, air and water, common gases, acids, bases and salts, carbon, fertilisers, common industrial materials and elementary atomic ideas.

Life basics, cells and tissues, growth and reproduction, human body, diseases, food and nutrition, the solar system and eminent scientists.

Indian history and culture, the Freedom Movement, the Constitution and administration, and selected modern-world and social-development themes named in the syllabus.

Earth and coordinates, earth movements, rocks and weathering, earthquakes and volcanoes, oceans, atmosphere, weather and climate, natural regions, and Indian regional and economic geography.

Important recent Indian and world events and prominent personalities, including culture and sports.