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| { | |
| "chapters": [ | |
| { | |
| "chapter": "Sets, Relations and Functions", | |
| "total_hours": "4", | |
| "subtopics": [ | |
| { | |
| "subtopic": "Sets and their representation", | |
| "subtopic_hours": "0.5" | |
| }, | |
| { "subtopic": "Union", "subtopic_hours": "0.5" }, | |
| { | |
| "subtopic": "Intersection and complement of sets and their algebraic properties", | |
| "subtopic_hours": "0.5" | |
| }, | |
| { "subtopic": "Power set", "subtopic_hours": "0.5" }, | |
| { "subtopic": "Relation", "subtopic_hours": "0.5" }, | |
| { "subtopic": "Type of relations", "subtopic_hours": "0.5" }, | |
| { "subtopic": "equivalence relations", "subtopic_hours": "0.5" }, | |
| { "subtopic": "Functions", "subtopic_hours": "0.5" }, | |
| { | |
| "subtopic": "one-one, into and onto functions", | |
| "subtopic_hours": "0.5" | |
| }, | |
| { "subtopic": "the composition of functions.", "subtopic_hours": "0.5" } | |
| ] | |
| }, | |
| { | |
| "chapter": "Complex Numbers and Quadratic Equations", | |
| "total_hours": "20", | |
| "subtopics": [ | |
| { | |
| "subtopic": "Complex numbers as ordered pairs of reals", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "Representation of complex numbers in the form a + ib and their representation in a plane", | |
| "subtopic_hours": "2" | |
| }, | |
| { "subtopic": "Argand diagram", "subtopic_hours": "2" }, | |
| { "subtopic": "algebra of complex number", "subtopic_hours": "2" }, | |
| { | |
| "subtopic": "modulus and argument (or amplitude) of a complex number", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "square root of a complex number", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "Quadratic equations in real and complex number system and their solutions", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "Relations between roots and coefficient, nature of roots", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "the formation of quadratic equations with given roots.", | |
| "subtopic_hours": "2" | |
| } | |
| ] | |
| }, | |
| { | |
| "chapter": "Matrices and Determinants", | |
| "total_hours": "11", | |
| "subtopics": [ | |
| { "subtopic": "Matrices", "subtopic_hours": "1.5" }, | |
| { "subtopic": "algebra of matrices", "subtopic_hours": "1.5" }, | |
| { "subtopic": "type of matrices", "subtopic_hours": "1.5" }, | |
| { | |
| "subtopic": "determinants and matrices of order two and three", | |
| "subtopic_hours": "1.5" | |
| }, | |
| { "subtopic": "evaluation of determinants", "subtopic_hours": "1.5" }, | |
| { | |
| "subtopic": "area of triangles using determinants", | |
| "subtopic_hours": "1.5" | |
| }, | |
| { | |
| "subtopic": "Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations", | |
| "subtopic_hours": "1.5" | |
| }, | |
| { | |
| "subtopic": "Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.", | |
| "subtopic_hours": "1.5" | |
| } | |
| ] | |
| }, | |
| { | |
| "chapter": "Permutations and Combinations", | |
| "total_hours": "10", | |
| "subtopics": [ | |
| { | |
| "subtopic": "The fundamental principle of counting", | |
| "subtopic_hours": "3" | |
| }, | |
| { | |
| "subtopic": "permutation as an arrangement and combination as section", | |
| "subtopic_hours": "3" | |
| }, | |
| { | |
| "subtopic": "Meaning of P(n,r) and C(n,r), simple applications.", | |
| "subtopic_hours": "3" | |
| } | |
| ] | |
| }, | |
| { | |
| "chapter": "Binomial Theorem and it's Simple Application", | |
| "total_hours": "10", | |
| "subtopics": [ | |
| { | |
| "subtopic": "Binomial theorem for a positive integral index", | |
| "subtopic_hours": "3" | |
| }, | |
| { "subtopic": "general term and middle term", "subtopic_hours": "3" }, | |
| { "subtopic": "simple applications.", "subtopic_hours": "3" } | |
| ] | |
| }, | |
| { | |
| "chapter": "Sequence and Series", | |
| "total_hours": "10", | |
| "subtopics": [ | |
| { | |
| "subtopic": "Arithmetic and Geometric progressions", | |
| "subtopic_hours": "3" | |
| }, | |
| { | |
| "subtopic": "insertion of arithmetic, geometric means between two given numbers", | |
| "subtopic_hours": "3" | |
| }, | |
| { "subtopic": "Relation between A.M and G.M", "subtopic_hours": "3" } | |
| ] | |
| }, | |
| { | |
| "chapter": "Limits,Continuity and Differentiability", | |
| "total_hours": "20", | |
| "subtopics": [ | |
| { "subtopic": "Real - valued functions", "subtopic_hours": "2" }, | |
| { "subtopic": "algebra of functions", "subtopic_hours": "2" }, | |
| { | |
| "subtopic": "Polynomials , rational, trigonometric, logarithmic and exponential functions, inverse function", | |
| "subtopic_hours": "2" | |
| }, | |
| { "subtopic": "Graphs of simple functions.", "subtopic_hours": "2" }, | |
| { | |
| "subtopic": "Limits, continuity and differentiability.", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "Differentiation of the sum difference, product and quotient of two functions.", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "derivatives of order up to two.", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "Applications of derivatives: Rate of change of quantities", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "monotonic increasing and Decreasing functions, Maxima and minima of functions of one variable.", | |
| "subtopic_hours": "2" | |
| } | |
| ] | |
| }, | |
| { | |
| "chapter": "Integral Calculus", | |
| "total_hours": "26", | |
| "subtopics": [ | |
| { "subtopic": "Integral as an anti-derivative", "subtopic_hours": "3" }, | |
| { | |
| "subtopic": "Fundamental Integrals involving algebraic, trigonometric, exponential and logarithms functions.", | |
| "subtopic_hours": "3" | |
| }, | |
| { | |
| "subtopic": "Integration by substitution, by parts and by partial functions.", | |
| "subtopic_hours": "3" | |
| }, | |
| { | |
| "subtopic": "Integration using trigonometric identities.", | |
| "subtopic_hours": "3" | |
| }, | |
| { | |
| "subtopic": "Evaluation of simple integrals of the type", | |
| "subtopic_hours": "3" | |
| }, | |
| { | |
| "subtopic": "The fundamental theorem of calculus, properties of definite integrals.", | |
| "subtopic_hours": "3" | |
| }, | |
| { | |
| "subtopic": "Evaluation of definite integrals", | |
| "subtopic_hours": "3" | |
| }, | |
| { | |
| "subtopic": "determining areas of the regions bounded by simple curves in standard form.", | |
| "subtopic_hours": "3" | |
| } | |
| ] | |
| }, | |
| { | |
| "chapter": "Differential Equations", | |
| "total_hours": "8", | |
| "subtopics": [ | |
| { | |
| "subtopic": "Ordinary differential equations, their order and degree", | |
| "subtopic_hours": "2.5" | |
| }, | |
| { | |
| "subtopic": "solution of differential equation by the method of separation of variables", | |
| "subtopic_hours": "2.5" | |
| }, | |
| { | |
| "subtopic": "solution of a homogeneous and linear differential equation of the type: dy/dx + p(x)y = q(x)", | |
| "subtopic_hours": "2.5" | |
| } | |
| ] | |
| }, | |
| { | |
| "chapter": "Co-ordinate Geometry", | |
| "total_hours": "47", | |
| "subtopics": [ | |
| { | |
| "subtopic": "Cartesian system of rectangular coordinates in a plane", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "distance formula, sections formula, locus and its equation", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "the slope of a line, parallel and perpendicular lines", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "intercepts of a line on the co-ordinate axis.", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "Straight line : Various forms of equations of a line, intersection of lines, angles between two lines", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "conditions for concurrence of three lines", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "the distance of a point from a line, coordinate of the centroid, orthocentre and circumcentre of a triangle.", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "Circle: A standard form of equations of a circle", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "the general form of the equation of a circle, its radius and central, equation of a circle when the endpoints of a diameter are given", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "points of intersection of a line and a circle with the centre at the origin", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "equations of conic sections : parabola", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "equations of conic sections : ellipse", | |
| "subtopic_hours": "3.5" | |
| }, | |
| { | |
| "subtopic": "equations of conic sections : Hyperbola", | |
| "subtopic_hours": "3.5" | |
| } | |
| ] | |
| }, | |
| { | |
| "chapter": "Three Dimensional Geometry", | |
| "total_hours": "7", | |
| "subtopics": [ | |
| { "subtopic": "Coordinate of a point in space", "subtopic_hours": "2" }, | |
| { | |
| "subtopic": "the distance between two points, section formula, directions ratios and direction cosines", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "the angle between two intersecting lines", | |
| "subtopic_hours": "2" | |
| }, | |
| { | |
| "subtopic": "Skew lines, the shortest distance between them and its equation", | |
| "subtopic_hours": "2" | |
| } | |
| ] | |
| }, | |
| { | |
| "chapter": "Vector Algebra", | |
| "total_hours": "11", | |
| "subtopics": [ | |
| { "subtopic": "Vectors and scalars", "subtopic_hours": "3" }, | |
| { "subtopic": "the addition of vectors", "subtopic_hours": "3" }, | |
| { | |
| "subtopic": "components of a vector in two dimensions and three-dimensional space", | |
| "subtopic_hours": "3" | |
| }, | |
| { "subtopic": "scalar and vector products", "subtopic_hours": "3" } | |
| ] | |
| }, | |
| { | |
| "chapter": "Statistics and Probability", | |
| "total_hours": "4", | |
| "subtopics": [ | |
| { "subtopic": "Measures of discretion", "subtopic_hours": "0.5" }, | |
| { | |
| "subtopic": "calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation", | |
| "subtopic_hours": "0.5" | |
| }, | |
| { | |
| "subtopic": "variance and mean deviation for grouped and ungrouped data.", | |
| "subtopic_hours": "0.5" | |
| }, | |
| { | |
| "subtopic": "Probability: Probability of an event", | |
| "subtopic_hours": "0.5" | |
| }, | |
| { | |
| "subtopic": "addition and multiplication theorems of probability", | |
| "subtopic_hours": "0.5" | |
| }, | |
| { | |
| "subtopic": "Baye's theorem, probability distribution of a random variate.", | |
| "subtopic_hours": "0.5" | |
| } | |
| ] | |
| }, | |
| { | |
| "chapter": "Trigonometry", | |
| "total_hours": "23", | |
| "subtopics": [ | |
| { | |
| "subtopic": "Trigonometrical identities and trigonometrical functions", | |
| "subtopic_hours": "12" | |
| }, | |
| { | |
| "subtopic": "inverse trigonometrical functions and their properties.", | |
| "subtopic_hours": "12" | |
| } | |
| ] | |
| } | |
| ] | |
| } | |