UNIT I: Relations and Functions
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transitive and equivalence relations
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inverse of a function. Binary operations
UNIT II: Inverse Trigonometric Functions
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Graphs of inverse trigonometric functions
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Elementary properties of inverse trigonometric functions
UNIT V: Continuity and Differentiability
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derivative of composite functions
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Concept of exponential and logarithmic functions
UNIT VI: Application of Derivatives
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use of derivatives in approximation
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maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool)
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Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations)
UNIT VIII: Applications of Integrals
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Applications in finding the area under simple curves
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circles/parabolas/ellipses (in standard form only)
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Area between any of the two above said curves (the region should be clearly identifiable)
UNIT IX: Differential Equations
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general and particular solutions of a differential equation
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Formation of differential equation whose general solution is given
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Solution of differential equations by method of separation of variables
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solutions of homogeneous differential equations of first order and first degree
UNIT XI: Three-dimensional Geometry
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Direction cosines and direction ratios of a line joining two points
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Cartesian equation and vector equation of a line
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shortest distance between two lines
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Cartesian and vector equation of a plane
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distance of a point from a plane
UNIT XII: Linear Programming
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related terminology such as constraints
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different types of linear programming (L.P.) problems
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mathematical formulation of L.P. problems
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graphical method of solution for problems in two variables
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feasible and infeasible regions (bounded)
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feasible and infeasible solutions
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optimal feasible solutions (up to three non-trivial constraints)
BETA
