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NDA 2023 Complete Video Course

• 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 a decimal system to a 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.

• 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.

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

• 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 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

• Concept of a real-valued function–domain, range, and graph of a function.
• Composite functions, one-to-one, onto, and inverse functions. The 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 concerning another function, derivative of a composite function.
• Second-order derivatives.
• Increasing and decreasing functions.
• Application of derivatives in problems of maxima and minima.

• 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 solutions of differential equations, solutions of the first order, and first-degree differential equations of various types—examples. Application in problems of growth and decay.

• 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.

• 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 Binomial distribution.