Paper I - Mathematics (300M/150min) — UPSC National Defence Academy a…

Paper I - Mathematics (300M/150min) for UPSC National Defence Academy and Naval Academy Examination (NDA and NA): all 30 topics, with study resources and previous year questions for each.

Topics in Paper I - Mathematics (300M/150min)

Sets, Relations and Venn Diagrams (NDA) — Concept of set, operations on sets, Venn diagrams. De Morgan laws, Cartesian product, relation, equivalence relation.
Real Numbers and Complex Numbers (NDA) — Representation of real numbers on a line. Complex numbers - basic properties, modulus, argument, cube roots of unity.
Binary System of Numbers (NDA) — Binary system of numbers. Conversion of a number in decimal system to binary system and vice-versa.
Arithmetic, Geometric and Harmonic Progressions (NDA) — Arithmetic, Geometric and Harmonic progressions.
Quadratic Equations (NDA) — Quadratic equations with real coefficients.
Linear Inequations in Two Variables (NDA) — Solution of linear inequations of two variables by graphs.
Permutation and Combination (NDA) — Permutation and Combination.
Binomial Theorem (NDA) — Binomial theorem and its applications.
Logarithms (NDA) — Logarithms and their applications.
Matrices and Determinants (NDA) — Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix, Applications-Solu…
Angles and Trigonometric Ratios (NDA) — Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple an…
Trigonometric Identities (NDA) — Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple an…
Inverse Trigonometric Functions (NDA) — Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple an…
Height and Distance (NDA) — Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple an…
Properties of Triangles (NDA) — Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple an…
Equation of a Line (NDA) — Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equat…
Equation of a Circle (NDA) — Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equat…
Parabola, Ellipse and Hyperbola (NDA) — Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equat…
Analytical Geometry of Three Dimensions (NDA) — Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equat…
Functions (NDA) — 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, Standa…
Limits and Continuity (NDA) — 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, Standa…
Derivatives (NDA) — 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, Standa…
Applications of Derivatives (NDA) — 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, Standa…
Integration (NDA) — Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponen…
Definite Integrals and Areas (NDA) — Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponen…
Differential Equations (NDA) — Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential…
Vector Algebra (NDA) — Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, addition of vectors, scalar multiplication of a vector, scalar…
Statistics (NDA) — Statistics: Classification of data, Frequency distribution, cumulative frequency distribution - examples. Graphical representation - Histogram, Pie Chart, freq…
Probability (NDA) — Probability: Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union an…
Random Variable and Binomial Distribution (NDA) — Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution.

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