Operation on Matrices, Types of Matrices, Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and through Matrix Method, The Determinant of Matrix, And then Basic properties of determinants, Also adjoin and inverse of a square matrix.
Analytical Geometry of Two & Three Dimensions
Distance formula, Equation of a plane and a line in various forms, Rectangular Cartesian Coordinate system, the angle between the two lines, Standard forms of parabola, hyperbola, and ellipse, Then Equation of a line in various forms, Eccentricity, and axis of a conic, Equation of a sphere, The angle between two lines and the angle between two planes, The distance of a point from a line, Direction Cosines and direction ratios, the distance between two points, Equation of a circle in standard and a general form, Equation two points, A point in a three-dimensional space, Direction Cosines and direction ratios.
Complex numbers—basic properties, modulus, argument, cube roots of unity, Then Concept of the set, Operation on Sets, Logarithms and their applications, Venn diagrams, Binomial theorem and its applications, De Morgan laws, Permutation, and Combination, Conversion of a number in decimal system to binary system and vice-versa, After that solution of linear inequations of two variables by graphs, Cartesian product, Equivalence relation, simple relation, Binary System of Numbers, Representation of real numbers on a line, Geometric and Harmonic progressions, Arithmetic and Quadratic equations with real coefficients.
Integral Calculus and Differential Equations
Application in problems of growth and decay, Integration as inverse of differentiation, standard integrals involving algebraic expressions, then integration by substitution and by parts, exponential and hyperbolic functions and trigonometric, determination of areas of plane regions bounded by curves and their application, Evaluation of definite integrals, solution of the first order and first-degree differential equations, General and particular solution of a differential equation, Definition of order and degree of a differential equation and formation of a differential equation.
Statistics & Probability
Frequency distribution, Conditional probability, Binomial distribution, Elementary theorems on probability, Random variable as function on a sample space, Measures of Central tendency, Classification of data, Graphical representation like Pie charts, Histogram, Polygon, etc. Correlation and regression, Union and Intersection of events and other topics.
Vectors in two and three dimensions, Unit and null vectors, Vector product or cross product of two vectors, geometrical problems, magnitude, and direction of a vector, etc.
Differential Calculus and their concepts
Trigonometry and all types of theorem and functions.