CHAPTER I: RELATIONS AND FUNCTIONS
CHAPTER II: Inverse Trigonometrical Functions
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Definition, range, domain, principal value branches
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Graphs of inverse trigonometric functions
CHAPTER VI: APPLICATIONS OF DERIVATIVE
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Geometrical application-tangent and normal at a point
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Rolle’s theorem and Mean value theorem and their geometrical interpretation (without proof)
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Derivative as a rate measure-introduction
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Approximation (without proof)
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Introduction of extrema and extreme values
CHAPTER VIII: APPLICATIONS OF DEFINITE INTEGRAL
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Area bounded by curve and axis (simple problems)
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Area bounded by two curves
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Volume of solid of revolution-volume of solid obtained by revolving the area under the curve about the axis (simple problems)
CHAPTER IX: DIFFERENTIAL EQUATION
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Definition-differential equation
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Particular solution of differential equation
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Formation of differential equation-formation of differential equation by eliminating arbitary constants (at most two constants)
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Solution of first order and first degree differential equation-variable separable method
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Homogeneous differential equation (equation reducible to homogeneous form are not expected)
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Linear differential equation
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Applications : population growth, bacterial colony growth, surface area, Newton’s laws of cooling, radioactive decay
CHAPTER X: VECTORS ALGEBRA
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Magnitude and direction of a vector
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Direction cosines/ratios of vectors
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Types of vectors (equal, unit, zero, parallel and collinear vectors)
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Position vector of a point
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Multiplication of a vector by a scalar
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Position vector of a point dividing a line segment in a given ratio
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Scalar (dot) product of vectors
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Projection of a vector on a line
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Vector (cross) product of vectors
CHAPTER XI: THREE-DIMENSIONAL GEOMETRY
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Direction cosines/ratios of a line joining two points
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Cartesian 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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Angle between (i) two lines (ii) two planes (iii) a line and a plane
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Distance of a point from a plane
CHAPTER XII: LINEAR PROGRAMMING
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Definition of related terminology such as constraints, objective function, optimization
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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
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Feasible and infeasible solutions
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Optimal feasible solutions (up to three non-trivial constraints)
CHAPTER XIII: PROBABILITY
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Multiplication theorem on probability Conditional probability
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Random variable and its probability distribution mean and variance of random variable
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Repeated independent (Bernoulli) trials and Binomial distribution
BETA
