{
  "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"
        }
      ]
    }
  ]
}