Vignan University VSAT 2013 Entrance Test Maths Syllabus
Vignan University VSAT 2013 Online Test Maths Syllabus is made available for Students. All Students who aspires to apply and appear for VSAT 2013 Entrance Test are hereby informed to check the VSAT 2013 Maths Syllabus.
Students can check the Subject wise and Topic wise Syllabus that should be Covered in Order to Crack the VSAT 2013 Entrance Exam. Students can check the Details of VSAT 2013 Entrance Test Maths syllabus.
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Vignan University VSAT 2013 Maths Syllabus :
Unit 1: Algebra Sets, relations and functions Sets and their representation, union, intersection of two sets and complement of a set and their algebraic properties, power set, Relation-types of relations, equivalence relation, Functions-types of functions, one-one and onto functions, composition of functions, inverse functions, algebra of real valued functions
Quadratic equations and expressions Quadratic equations in real and complex number system and their solutions , relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots, maximum and minimum values of quadratic expressions, quadratic inequations in one variable
Matrices, determinants and linear equations Types of matrices, algebra of matrices; transpose of a matrix, determinants of matrices of order 2 and 3; properties of determinants, evaluation of determinants, adjoint and inverse of a square matrix, solution of simultaneous linear equations in two and three unknowns using determinants and matrices, consistency and inconsistency of simultaneous linear equations, Rank of a matrix
Permutations and combinations Fundamental principle of counting, permutation as an arrangement and combination as a selection, linear and circular permutations, permutations when repetition of object is allowed, combinations
Binomial theorem and partial fractions Binomial theorem for a positive integral index, general term, middle term (s), greatest term, properties of binomial coefficients, binomial theorem for rational index, partial fractions
Sequences and series Arithmetic, geometric and harmonic progressions, insertion of arithmetic, geometric and harmonic means between two numbers, arithmetico-geometric progression
Unit 2: Trigonometry Trigonometric Functions (1) Trigonometric ratios of compound angles, multiple and sub-multiple angles, transformations and identities, extreme values, periodicity (2) Trigonometric equations, (3) Inverse trigonometric functions (4) Hyperbolic and inverse hyperbolic functions (5) Properties of triangle, (6) Heights and distances (in two dimensional plane) (7) Complex numbers : complex number as an ordered pair of real numbers, 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, De-moivres theorem and its applications, expansions of trigonometric functions
Unit 3: Vector Algebra Vectors and scalars, addition of vectors, linear combination of vectors, linear dependence and independence, components of a vector in two and three dimensions, vector equations of a line and a plane, scalar and vector products of two vectors and their applications, scalar and vector triple products, scalar and vector products of four vectors
Unit 4: Probability Random experiment, sample space, event, probability of an event, addition theorem of probability; conditional event,
conditional probability, multiplication theorem of probability, Bayes theorem Probability distribution of a random variable, mean and variance of a random variable, Binomial and Poisson distributions
Unit 5: Coordinate Geometry Coordinate system in two dimensions, locus and its equation, translation and rotation of axes
Straight Line Various forms of equation of straight line, intersection of lines, angle between two lines, condition for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, centroid, circumcentre, in-centre and orthocenter of triangle, equation of family of lines passing through the point of intersection of two lines
Pair of straight lines
Combined equation of a pair of lines passing through the origin, angular bisectors, condition for general equation of second degree in x and y to represent a pair of lines, angle between a pair of lines
Circle Standard form of equation of a circle, general form of the equation of a circle and its parametric representation, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle, equation of tangent, normal, chord of contact, pole and polar, pair of tangents from an external point
System of circles Angle between two circles, common tangents to two circles, orthogonality, radical axis, radical centre, coaxial system of circles, orthogonal system to a coaxial system of circles
Conic sections Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y=mx+c to be a tangent, normal, equation of chord of contact, polar with respect to a conic Unit 6: Calculus
Limits and continuity Left limit, right limit and existence of limit of a function, continuity of a function
Differentiation and differentiability Differentiability of a function, differentiation of the sum, product and quotient of two functions, Rolles and Lagranges mean value theorems
Applications of derivatives Monotonic increasing and decreasing functions, maxima and minima of functions of one variable, tangents and normals
Integration Integral as anti-derivative, integrals involving standard functions, methods of integration, integration by parts, reduction formulae
Definite integrals Evaluation of definite integrals, properties of definite integrals
Areas Areas of the regions formed by simple curves in standard form
Differential equations Ordinary differential equations, their order and degree, formation of differential equations, solutions of differential equations by the method of variables separable, solution of homogeneous, non-homogeneous and linear differential equations of first degree
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