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VITEEE

# Mathematics SyllabusVellore Institute of Technology Engineering Entrance (VITEEE):

**Keep in mind, this syllabus is not for Biology stream students, go through biology syllabus for VITEEE for bio-medical courses entrance exam .

MATRICES AND DETERMINANTS

Types of matrices, addition and multiplication of matrices-Properties, 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, Non-homogeneous 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 Progressions-Relation 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 non-collinear 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 function-Trigonometrical ratios of related angles - Addition formula and their applications - Trigonometric equations - Inverse trigonometric functions-Properties 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 - velocity-acceleration - 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 co-efficient 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 distributions-Binomial , Poisson, continuous distribution - Normal.

For VITEEE engineering entrance preparing aspirants (including bio-medical courses),prepare  physics according to Physics Exam Syllabus VITEEE .

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