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UNIT:1 Sets,Relations & Functions

  • Sets and their representation.
  • Union, intersection, and complement of sets and their algebraic properties.
  • Power set.
  • Relation, Types of relations, equivalence relations.
  • Functions; one-one, into and onto functions, the composition of functions.

UNIT:2 Complex Numbers & Quadratic Equations

  • Complex numbers as ordered pairs of reals.
  • Representation of complex numbers in the form (a+ib) and their representation in a plane, Argand diagram.
  • Algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number.
  • Triangle inequality.
  • Quadratic equations in real and complex number system and their solutions.
  • The relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots.

UNIT:3 Matrices & Determinants

  • Matrices: Algebra of matrices, types of matrices, and matrices of order two and three
  • Determinants: Properties of determinants, evaluation of determinants, the area of triangles using determinants
  • Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations.
  • Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

UNIT:4 Permutations & Combinations

  • The fundamental principle of counting.
  • Permutation as an arrangement and combination as selection
  • The meaning of P (n,r) and C (n,r). Simple applications.

UNIT:5 Mathematical Induction

  • The principle of Mathematical Induction and its simple applications.

UNIT:6 Binomial Theorem

  • Binomial theorem for a positive integral index.
  • General term and middle term.
  • Properties of Binomial coefficients and simple applications.

UNIT:7 Sequence & Series

  • Arithmetic and Geometric progressions, insertion of arithmetic.
  • geometric means between two given numbers.
  • The relation between A.M. and G.M.
  • Sum upto n terms of special series: Sn, Sn2, Sn3
  • Arithmetico – Geometric progression.

UNIT:8 Limit, Continuity & Differentiability

  • Real – valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions.
  • Graphs of simple functions.
  • Limits, continuity, and differentiability.
  • Differentiation of the sum, difference, product, and quotient of two functions.
  • Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order up to two.
  • Rolle's and Lagrange's Mean Value Theorems.
  • Applications of derivatives: Rate of change of quantities, monotonic – increasing and decreasing functions, Maxima, and minima of functions of one variable, tangents, and normals.

UNIT:9 Integral Calculus

  • Integral as an anti – derivative.
  • Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions.
  • Integration by substitution, by parts, and by partial fractions.
  • Integration using trigonometric identities
  • Integral as limit of a sum.
  • Evaluation of simple integrals:
  • Fundamental Theorem of Calculus.
  • Properties of definite integrals, evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

UNIT:10 Differential Equations

  • Ordinary differential equations, their order, and degree.
  • Formation of differential equations.
  • The solution of differential equations by the method of separation of variables.
  • The solution of homogeneous and linear differential equations of the type:

UNIT:11 Coordinate Geometry

  • Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
  • Straight lines: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines.
  • Distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentr, and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines.
  • Circles, conic sections: Standard form of equation of a circle, 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 condition for a line to be tangent to a circle, equation of the tangent.
  • Sections of cones, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.

UNIT:12 3-Dimensional Geometry

  • Coordinates of a point in space, the distance between two points.
  • Section formula, direction ratios and direction cosines, the angle between two intersecting lines
  • Skew lines, the shortest distance between them and its equation.
  • Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.

UNIT:13 Vector Algebra

  • Vectors and scalars, the addition of vectors.
  • Components of a vector in two dimensions and three-dimensional space.
  • Scalar and vector products, scalar and vector triple product.

UNIT:14 Statistics & Probability

  • Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
  • Probability: Probability of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

UNIT:15 Trigonometry

  • Trigonometrical identities and equations.
  • Trigonometrical functions.
  • Inverse trigonometrical functions and their properties.
  • Heights and Distances.

UNIT:16 Mathematical Reasoning

  • Statements, logical operations and, or, implies, implied by, if and only if.
  • Understanding of tautology, contradiction, converse, and contrapositive.