**A**: The code for Maths paper in NDA and NA exam is 001 and the maximum marks allotted for the same are 300. The syllabus for this subject is as follows-

**1. 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 decimal system to binary system and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients, Solution of linear in-equations of two variables by graphs. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.

**2. 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.

**3. TRIGONOMETRY**

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

**4. 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 in standard and in general form, Standard forms of parabola, ellipse, and hyperbola. Eccentricity and axis of a conic, Point in a three dimensional space, distance between 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.

**5. DIFFERENTIAL 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- examples. Continuity of functions- examples, algebraic operations on continuous 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 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.

**6. 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 a differential equations, solution of first order and first degree differential equations of various types – examples, Application in problems of growth and decay.

**7. VECTOR ALGEBRA**

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 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.

**8. STATISTICS AND PROBABILITY**

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

**Probability**: Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events.

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