# Mathematics syllabus for VITEEE Maths syllabus for VIT Engineering Entrance Exam

The following resource will give you the information about the VIT, VITEEE Syllabus of Mathematics syllabus for VIT exam Mathematics syllabus for VITEEE Mathematics syllabus Mathematics syllabus for entrance exams Vellore institute of technology VIT exam Mathematics syllabus.

### Mathematics syllabus for VITEEE Maths syllabus for VIT Engineering 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.