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- Types of relations: reflexive, symmetric, transitive and equivalence relations.
- One to one and onto functions, composite functions, inverse of a function
- Binary operations
- Composition of function and invertible function

- Definition
- Range
- Domain
- Graphs of inverse trigonometric functions
- Properties of inverse trignometric functions

- Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices
- Operation on matrices: Addition and multiplication and multiplication with a scalar
- Simple properties of addition, multiplication and scalar multiplication
- Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2)
- Concept of elementary row and column operations
- Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

- Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle
- Adjoint and inverse of a square matrix
- Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix

- Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions
- Concept of exponential and logarithmic functions.
- Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms
- Second order derivatives.
- Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.

- Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool)
- Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations)
- Maximum and minimum value of function in closed interval

- Integration as inverse process of differentiation
- Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.
- Geometric interpretation of indefinite integral
- Some properties of indefinite integrals
- Comparison between differentiation and integration

- Area under simple curves
- Concept of exponential and logarithmic functions.
- Area of a region bounded by curve and a line
- Area between two curves

- Basic conceptn
- Degree of a differential equation
- General and particular solutions of differential equation
- Formation of differential equation whose general solution is given
- Methods of solving first order, first degree differential equation
- Homogeneous differential equation
- Solutions of linear differential equation of the type: dy/dx + py = q, where p and q are functions of x or constants. dx/dy + px = q, where p and q are functions of y or constants.

- Some basic concepts
- Types of vectors
- Addition of vectors
- Multiplication of vector by a scalar: components of vector
- Vector joing two points
- Section formula
- Product of two vectors: scalar product and application
- Scalar triple product
- Cross product of two vectors

- Direction cosines and direction ratios of a line
- Equation of a line in space
- Angle between two lines
- Shortest distance between two lines
- Plane: equation of plane in normal form
- "Equation of a plane perpendicular to a given vector and passing through a given point"
- "Equation of plane passing through three non collinear points"
- "Intercept form of equation of line and a plane passing throug through the intersection of two given plane"
- Coplanarity of two lines
- Angle between two planes
- Distance of a point from a plane
- Angle between a line and a plane

- Linear programming problem and its mathematical formulation
- Graphical method of solving linear programming problem
- Different types of linear programming problem

- Conditional probability
- independent events
- total probability
- Baye's theorem
- Random variable and its probability distribution
- mean and variance of random variable
- Repeated independent (Bernoulli) trials and Binomial distribution