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NDA Algebra syllabus topics
Arithmetic
Concept of a set
operations on sets
modulus argument
equivalence relation
Cartesian product relation
modulus argument
Cube roots of unity
Binary system of numbers
Permutation and Combination
Venn diagrams. De Morgan laws
Complex numbers – basic properties
Binomial theorem and its application
Logarithms and their applications.
Geometric and Harmonic Progressions
Quadratic equations with real coefficients
Representation of real numbers on a line
Solution of linear in equations of two variables by graphs
Conversion of a number in decimal system to binary system and vice-versa.
NDA Trigonometry Syllabus topics
Properties of triangles.
Trigonometrical ratios
Trigonometric identities Sum and difference formula
Multiple and Sub-multiple angles
Inverse trigonometric functions
Applications – Height and distance
Angles and their measures in degrees and in radians
Types of matrices
Determinant of a matrix
Adjoint and inverse of a square matrix
Operations on matrices
Basic properties of determinants
Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.
Composite functions
Derivatives of sum
Concept of a real-valued function – domain
range and graph of a function
Second order derivatives
Derivative of function at a point
Product and quotient of functions
Derivative of a composite function
Increasing and decreasing functions
Derivative of a function with respect to another function
Application of derivatives in problems of maxima and minima.
Distance formula
Ellipse and hyperbola
Angle between two lines
Distance of a point from a line
Standard forms of parabola
Equation of a line in various forms
Eccentricity and axis of a conic
Rectangular Cartesian Coordinate system
Equation of a circle in standard and in general form
Integral Calculus and Differential Equations topics
Trigonometric
Integration as inverse of differentiation
Integration by substitution and by parts
Exponential and hyperbolic functions
Standard integrals involving algebraic expressions
General and particular solution of a differential equation
Vectors in two and three dimensions
Scalar multiplication of vector
Magnitude and direction of a vector
Unit and null vectors addition of vectors
NDA Statistics and Probability Syllabus topics
Pie Chart
Frequency distribution
Statistics: Classification of data
Frequency Polygon – examples
Graphical representation – Histogram
Correlation and regression
Measures of Central Tendency – Mean Median and Mode
Cumulative frequency distribution – examples
Variance and standard deviation – determination and comparison
Events
Complimentary
Random experiment
Binomial distribution
Conditional probability
Outcomes and associated sample space
Impossible and certain events
Union and Intersection of events
elementary and composite events
Bayes’ theorem – simple problems
Random variable as function on a sample space
Mutually exclusive and exhaustive events
Examples of random experiments giving rise to Binominal distribution.
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