NDA Maths Syllabus, Check topic-wise detailed syllabus here!

NDA Maths Syllabus

NDA Maths Syllabus for 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 inequations of two variables by graphs.
• Permutation and Combination.
• Binomial theorem and its applications.
• Logarithms and their applications.

NDA Maths Syllabus for 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.

NDA Maths Syllabus: Trignometry

• 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.

NDA Maths Syllabus: Geometry of Two or Three Dimensions

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

NDA Maths Syllabus for Differential Calculas

• 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.

NDA Maths Syllabus: Integral Calculas 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.

NDA Maths Syllabus for Vector Algebra

• Vectors in two and three dimensions, magnitude, and direction of a vector.
• Unit and null vectors, the 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.

NDA Maths Syllabus: Statistics and Probability

• 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.

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

NDA Maths Syllabus: Topic-wise Distribution of Marks

Topic	Marks (Approximately)
Algebra and Vector Algebra	100
Trigonometry	50
Determinants and Matrices	25
Statistics and Probability	25
Analytical Geometry	50
Differential and Integral Calculus	50

Best Books for NDA Maths

NCERT Mathematics Textbook of Class 11 and Class 12	NCERT
Mathematics	R.S. Aggarwal
Mathematics for NDA and NA	S Chand publication
R.S. Agarwal
NDA Entrance Exam	E. S. Ramasamy