AIEEE 2012 MATHEMATICS SYLLABUS ALL INDIA ENGINEERING ENTRANCE EXAMINATION

 mathematics syllabus of aieee 2012 all india engineering entrance examination

MATHEMATICS SYLLABUS

UNIT 1 :   SETS, RELATIONS AND 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,  composition  of functions. 

UNIT 2 :   COMPLEX NUMBERS AND 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. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.

UNIT 3 :   MATRICES AND DETERMINANTS:
  Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, 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 AND COMBINATIONS:
  Fundamental  principle  of  counting,  permutation  as  an  arrangement  and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.

UNIT 5 :   MATHEMATICAL INDUCTION:
  Principle of Mathematical Induction and its simple applications.


UNIT 6 :   BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:
  Binomial  theorem  for  a  positive  integral  index,  general  term  and  middle  term, properties of Binomial coefficients and simple applications.

UNIT 7 :   SEQUENCES AND SERIES:
  Arithmetic  and  Geometric  progressions,  insertion  of  arithmetic,  geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series: S n, S n2, Sn3. Arithmetico – Geometric progression.

UNIT 8 :   LIMIT, CONTINUITY AND 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 upto 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.   Evaluation of simple integrals of the type
 
  Integral  as  limit  of  a  sum.  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.  Solution  of  differential  equations  by  the  method  of  separation  of variables, solution of homogeneous and linear differential equations of the type:
  dy+ p (x) y = q (x)
  dx 

UNIT 11:   CO-ORDINATE GEOMETRY:
  Cartesian  system  of  rectangular  co-ordinates  10  in a  plane,  distance  formula, section  formula,  locus  and  its  equation,  translation  of  axes,  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, orthocentre 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 end points 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:  THREE DIMENSIONAL GEOMETRY:
  Coordinates  of  a  point  in  space,  distance  between two  points,  section  formula, direction  ratios  and  direction  cosines,  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,  intersection  of  a  line  and  a  plane,  coplanar lines. 

UNIT 13:   VECTOR ALGEBRA:
  Vectors  and  scalars,  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 AND 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.