Maximum marks – 300

1) ALGEBRA :

                  Concept   of   set,   operations   on   sets,  Venn   diagrams.  De Morgan laws, Cartesian product, relation, equiva lence relation.

Representation of real numbers on a  line. Complex numbers—basic  properties,  modulus,  argument,  cube  roots  of  unity.   Binary  system  of  numbers. Conversion of a number in decimal system t o binary system and vice-versa.  Arithmetic,  Geometric  and  Harmonic  prog ressions.  Quadratic  equations  with  real  coefficients.  Solution  of  linea r  inequations  of  two  variables by graphs. Permutation and Combination. B inomial theorem and its  applications. Logarithms and their applications.

2) MATRICES AND DETERMINANTS  :

Types of matrices, operations on matrices.  Determinant of a matrix, basic  properties  of  determinants.  Adjoint  and  inverse  of  a  square  matrix,  Applications-Solution  of  a  system  of  linear  equatio ns  in  two  or  three  unknowns by Cramer’s rule and by Matrix Method.

3) TRIGONOMETRY :

Angles and their measures in degrees and  in radians. Trigonometrical  ratios.  Trigonometric identities  Sum  and  difference   formulae.  Multiple  and  Sub-multiple  angles.  Inverse  trigonometric  function s.  Applications-Height  and distance, properties of triangles.

4) ANALYTICAL GEOMETRY OF TWO AND THREE DIMENSIONS :

Rectangular Cartesian Coordinate system. Distance f ormula. Equation  of a line in various forms. Angle between two lines . Distance of a point from a  line. Equation of a circle in standard and in gener al form. Standard forms of  parabola, ellipse and hyperbola. Eccentricity and a xis of a conic. Point in a  three dimensional space, distance between two point s. Direction Cosines and  direction ratios. Equation two points. Direction Co sines and direction ratios.  Equation of a plane and a line in various forms. An gle between two lines and  angle between two planes. Equation of a sphere.

5) DIFFERENTIAL CALCULUS  :

Concept  of  a  real  valued  function–dom ain,  range  and  graph  of  a  function. Composite functions, one to one, onto and  inverse functions. Notion  of  limit,  Standard  limits—examples.  Continuity  of  f unctions—examples,  algebraic  operations  on  continuous  functions.  Deriv ative  of  function  at  a  point, geometrical and physical interpretation of a  derivative—applications.  Derivatives  of  sum,  product  and  quotient  of  functio ns,  derivative  of  a  function with respect to another function, derivati ve of a composite function.  Second order derivatives. Increasing and decreasing  functions. Application of  derivatives in problems of maxima and minima.

6) INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS :

Integration as inverse of different iation, integration by substitution  and  by  parts,  standard  integrals  involving  algebrai c  expressions,  trigonometric,  exponential  and  hyperbolic  functions .  Evaluation  of  definite  integrals—determination  of  areas  of  plane  regions  b ounded  by  curves— applications.

Definition of order and degree of a  differential equation, formation  of a differential equation by examples. General and  particular solution of a  differential  equations,  solution  of  first  order  and   first  degree  differential  equations  of  various  types—examples.  Application  in   problems  of  growth  and decay.

7. VECTOR ALGEBRA :

Vectors in two and three dimensions, m agnitude and direction of a  vector. Unit and null vectors, addition of vectors,  scalar multiplication of a  vector, scalar product or dot product of two vector s. Vector product or cross  product of two vectors. Applications—work done by a  force and moment of a  force and in geometrical problems.

8. STATISTICS AND PROBABILITY :

Statistics : Classification of data,  Frequency distribution, cumulative  frequency distribution—examples. Graphical represen tation—Histogram, Pie  Chart, frequency polygon—examples. Measures of Cent ral tendency—Mean,  median  and  mode.  Variance  and  standard  deviation—de termination  and  comparison. Correlation and regression.

Probability  :  Random  experiment,  outcomes  and  ass ociated  sample  space,  events,  mutually  exclusive  and  exhaustive  events,  i mpossible  and  certain  events.  Union  and  Intersection  of  events.  Complemen tary,  elementary  and  composite  events.  Definition  of  probability—classic al  and  statistical— examples.   Elementary   theorems   on   probability—simple    problems.  Conditional probability, Bayes’ theorem—simple prob lems. Random variable  as  function  on  a  sample  space.  Binomial  distributio n,  examples  of  random  experiments giving rise to Binominal distribution.