Chapters and their Topics
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Chapters and their Topics
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Integral Calculus
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Integral as an anti-derivative
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Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions
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Integration by substitution, by parts and by partial fractions
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Integration using trigonometric identities. Evaluation of simple integrals of the type
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The fundamental theorem of calculus, properties of definite integrals
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Evaluation of definite integrals, determining areas of the regions bounded by simple curves by simple curves in standard forms
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Sets, Relations and Functions
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Sets and their representation
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Union, intersection and complement of sets and their algebraic properties
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Power set
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Relations, types of relations, equivalence relations, functions
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one-one, into and onto functions, the composition of functions
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Differential Equations
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Ordinary differential equations, their order and degree
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Solution of differential equation by the method of separation of variables
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Solution of a homogeneous and linear differential equation of the type
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Complex Numbers
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Complex numbers as ordered pairs of reals
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Representation of complex numbers in the form a + ib and their representation in a plane
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Argand diagram
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Algebra of complex numbers, modulus and argument (or amplitude) of a complex number
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Quadratic equations in real and complex number systems and their solutions
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Relations between roots and coefficients, nature of roots, the formation of quadratic equations with given roots
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Coordinate Geometry
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Cartesian system of rectangular coordinates in a plane
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Distance formula, sections formula, locus, and its equation
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The slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis
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Straight line: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, the distance of a point form a line, co-ordinate of the centroid, orthocentre and circumcentre of a triangle
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Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and centre, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms.
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Matrices and Determinants
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Matrices, algebra of matrices, type of matrices
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Determinants and matrices of order two and three
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Evaluation of determinants
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Determinants, area of triangles using determinants
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Adjoint and inverse of a square matrix
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Test of consistency and solution of simultaneous linear equations in two or three variables using matrices
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Three-Dimensional Geometry
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Coordinates of a point in space
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The distance between two points
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Section formula, direction ratios and direction cosines and the angle between two intersecting lines
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Equation of a line; Skew lines, the shortest distance between them and its equation
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Permutations and Combinations
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Fundamental principle of counting
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Permutations with/without repetition
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Combinations and their properties
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Meaning of P(n, r) and C(n, r)
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Simple applications
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Vector Algebra
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Vectors and scalars
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The addition of vectors
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Components of a vector in two dimensions and three-dimensional spaces
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scalar and vector products
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Binomial Theorem and Its Simple Applications
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Binomial theorem for a positive integral index
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General term and middle term and simple applications
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Statistics and Probability
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Measures of dispersion
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Calculation of mean, median, mode of grouped and ungrouped dataC
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Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data
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Probability of an event, addition and multiplication theorems of probability, Baye's theorem, probabilitydistribution of a random variable
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Bayes’ theorem and independent events
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Sequence and Series
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Arithmetic and geometric progressions
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Insertion of Arithmetic mean and geometric mean
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Geometric mean between two given numbers
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Relation between A.M and G.M
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Trigonometry
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Trigonometrical identities and trigonometrical functions
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Inverse trigonometrical functions their properties
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Limit, Continuity and Differentiability
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Real–valued functions, algebra of functions
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Polynomial, rational, trigonometric, logarithmic and exponential functions
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Inverse functions
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Graphs of simple functions
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Limits, continuity and differentiability
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Differentiation of the sum, difference, product and quotient of two functions
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Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite, and implicit functions
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Derivatives of order upto two, Applications of derivatives
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Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
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Relations and Functions
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Ordered pairs and Cartesian product
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Types of relations: reflexive, symmetric, transitive, equivalence
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Functions: one-one, onto, into; domain, co-domain, and range
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Composite and inverse of functions
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Quadratic Equations
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Nature of roots, conditions for real, equal, or imaginary roots
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Graphical representation of quadratic functions
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Maximum and minimum values
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Relation between roots and coefficients
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Differentiability
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Concept of differentiability
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Derivative as a rate of change
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Differentiability vs continuity
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Derivatives of composite, implicit and parametric functions
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