Update Maths.json

Maths.json

@@ -1,357 +1,358 @@
-{
-  "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 Applicatio",
-      "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"
-        }
-      ]
-    }
-  ]
-}
+{
+  "chapters": [
+    {
+      "chapter": "Sets, Relations and Functions",
+      "total_hours": "4",
+      "subtopics": [
+        {"subtopic": "start", "subtopic_hours":"1"},
+        {
+          "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 Applicatio",
+      "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"
+        }
+      ]
+    }
+  ]
+}