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20th August 2018, 01:48 PM
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| Re: Karunya Entrance Exam Syllabus
Karunya University conducts Karunya University Engineering Entrance Examination (KEE) for admissions to undergraduate engineering programmes. KEE is a university level online examination which is conducted for admissions in Coimbatore campus The Syllabus of the Karunya University Entrance Examination Mathematics is given below MATHEMATICS - KEE 2018 Applications of Matrices and Determinants: Adjoint, inverse properties, computation of inverses, solution of system of linear equations bymatrix inversion method. Rank of a matrix elementary transformation on a matrix, Cramersrule, non-homogeneous equations, homogeneous linear system and rank method. Complex Numbers: Complex number system - conjugate, properties, ordered pair representation. Modulus Properties, geometrical representation, polar form, principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De Moivres theoremand its applications. Roots of a complex number n th roots, cube roots, fourth roots. Analytical Geometry of two dimensions: 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. Equations of conic sections (parabola, ellipse and hyperbola) in standard forms and general forms- Directrix, Focus and Latus rectum - parametric form of conics and chords. Tangents and normals Cartesian form and parametric form- equation of chord of contact of tangents from a point (x1 ,y1 ) to all the above said curves. Asymptotes, Rectangular hyperbola Standard equation of a rectangular hyperbola. Vector Algebra: Scalar Product angle between two vectors, properties of scalar product and applications of dot products. Vector product right handed and left handed systems, properties of vector product and applications of cross product - Product of three vectors Scalar triple product, properties ofscalar triple product, vector triple Product. Differential Calculus: Derivative as a rate measurer - rate of change, velocity, acceleration, related rates, derivative as a measure of slope, tangent, normal and angle between curves, maxima and minima. Mean value theorem - Rolles Theorem, Lagrange Mean Value Theorem, Taylors and Maclaurins series, L Hospitals Rule, stationary points, increasing, decreasing, maxima, minima, concavity, convexity and points of inflexion. Integral Calculus and its Applications: Simple definite integrals fundamental theorems of calculus, properties of definite integrals. Reduction formulae reduction formulae for ∫ sinnx dx and ∫ cosnx dx , Bernoullis formula.Area of bounded regions, length of the curve. Differential Equations: Differential equations - formation of differential equations, order and degree, solving differential equations (1st order), variables separable, homogeneous and linear equations. Second order linear 4differential equations - second order linear differential equations with constant co-efficients, finding the particular integral if f (x) = emx, sinmx, cosmx, x, x2 . Probability Distributions: Probability Axioms Addition law - Conditional probability Multiplicative law - BayesTheorem - Random variable - probability density function, distribution function, mathematicalexpectation, variance Theoretical distributions - discrete distributions, Binomial, Poissondistributions- Continuous distributions, Normal distribution. Discrete Mathematics: Mathematical logic logical statements, connectives, truth tables, logical equivalence, tautology. Groups: Binary operations, semigroups, monoids, groups, order of a group, order of an element,properties of groups Syllabus of the Karunya University Entrance Examination Mathematics     Contact Information Karunya University Address: Karunya Nagar, Coimbatore, Tamil Nadu 641114 |