VITEEE
VITEEE Maths Syllabus
Engineering Entrance , VITEEE
Mathematics Syllabus Vellore Institute of Technology Engineering Entrance (VITEEE):
**Keep in mind, this syllabus is not for Biology stream students, go through biology syllabus for VITEEE for biomedical courses entrance exam .
MATRICES AND DETERMINANTS
Types of matrices, addition and multiplication of matricesProperties, computation of inverses, solution of system of linear equations by matrix inversion method. Rank of a Matrix  Elementary transformation on a matrix, consistency of a system of linear equations, Cramer's rule, Nonhomogeneous equations, homogeneous linear system, rank method.
THEORY OF EQUATIONS, SEQUENCE AND SERIES
Quadratic equations  Relation between roots and coefficients  Nature of roots  Symmetric functions of roots  Diminishing and Increasing of roots  Reciprocal equations. Arithmetic, Geometric and Harmonic ProgressionsRelation between A.M., G. M ., and H.M. Special series: Binomial, Exponential and Logarithmic series  Summation of Series.
VECTOR ALGEBRA
Scalar Product  Angle between two vectors, properties of scalar product, applications of dot products. Vector Product  Right handed and left handed systems, properties of vector product, applications of cross product. Product of three vectors  Scalar triple product, properties of scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors. Lines  Equation of a straight line passing through a given point and parallel to a given vector, passing through two given points, angle between two lines. Skew lines  Shortest distance between two lines, condition for
two lines to intersect, point of intersection, collinearity of three points. Planes  Equation of a plane, passing through a given point and perpendicular to a vector, given the distance from the origin and unit normal, passing through a given point and parallel to two given vectors, passing through two given points and parallel to a given vector, passing through three given noncollinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines, angle between two given planes, angle between a line and a plane. Sphere  Equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.
COMPLEX NUMBERS & TRIGONOMETRY
Complex number system, conjugate  properties, ordered pair representation. Modulus  properties, geometrical representation meaning, polar form principal value, conjugate, sum, difference, product quotient, vector interpretation, solutions of polynomial equations, De Moivre's theorem and its applications. Roots of a complex number  nth roots, cube roots, fourth roots. Angle measures
Circular functionTrigonometrical ratios of related angles  Addition formula and their applications  Trigonometric equations  Inverse trigonometric functionsProperties and solutions of triangle.
ANALYTICAL GEOMETRY
Definition of a Conic  General equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity. Parabola  Standard equation of a parabola tracing of the parabola, other standard parabolas, the process of shifting the origin, general form of the standard equation, some practical problems. Ellipse  Standard equation of the ellipse, tracing of the ellipse (x^2/a^2 )+(y^2/a^2 ) = 1 (a> b). Other standard form of the ellipse, general forms, some practical problems Hyperbola  standard equation, tracing of the hyperbola (x^2/a^2 )(y^2/a^2 ) = 1
, other form of the hyperbola, parametric forms of a conics, chords, tangents and normals  Cartesian
form and parametric form, equation of chord of contact of tangents from a point (x1 ,y1 ) Asymptotes, Rectangular Hyperbola standard equation of a rectangular hyperbola.
DIFFERENTIAL CALCULUS
Derivative as a rate measure  rate of change  velocityacceleration  related rates  Derivative as a measure of slopetangent, normal and angle between curves. Maxima and Minima. Mean value theorem Rolle's Theorem  Lagrange Mean Value Theorem  Taylor's and Maclaurin's series, L' Hospital's Rule, Stationary Points  Increasing, decreasing, maxima, minima, concavity convexity points of inflexion. Errors and approximations  absolute, relative, percentage errors, curve tracing, partial derivatives  Euler's theorem.
INTEGRAL CALCULUS AND ITS APPLICATIONS METHODS OF INTEGRATION STANDARD TYPES
Properties of definite integrals, reduction formulae for sin^n (x) and cos^n (x) , Area, length, volume and surface area.
DIFFERENTIAL EQUATIONS
Formation of differential equations, order and degree, solving differential equations (1st order)  variable separable homogeneous, linear equations. Second order linear equations with constant coefficient f (x)=e^m(x), sin mx, cos mx,x, x^2.
DISCRETE MATHEMATICS
Mathematical Logic  Logical statements, connectives, truth tables, tautologies, sets, algebraic properties, relations, functions, permutation, combination, Induction. Binary Operations  Semi groups  monoids, groups (Problems and simple properties only), order of a group, order of an element.
PROBABILITY DISTRIBUTIONS
Probability, axioms, theorems on probability, conditional probability, Random Variable, Probability density function, distribution function, mathematical expectation, variance, discrete distributionsBinomial , Poisson, continuous distribution  Normal.
For VITEEE engineering entrance preparing aspirants (including biomedical courses),prepare physics according to Physics Exam Syllabus VITEEE .
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