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Entrance Exam : KLUEEE-2015 KLU Engineering Entrance Examination

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Issue of Hall Tickets (To be downloaded from kluniversity.in) 30-04-2015
Exam Date of KLUEEE-2015 02-05-2015

Update : K L University KLEEE 2019 Engineering Entrance Examination : www.entrance.net.in/14242.html

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INSTRUCTIONS TO THE CANDIDATES:
The Candidate must take the exam only at centre specified.
No Candidate is allowed inside the examination hall after 30 min of the commencement of exam.
Use only Black Ball Point Pen to bubble the answers on OMR Answer sheet.
Cell phones, Digital dairy, Calculator and any other such material is not allowed into the exam hall.
Candidate should not tear or damage OMR Answer sheet. It should be returned to the Invigilator before leaving the exam hall.

Note: Candidates whose photograph is not printed on their hall ticket may affix the latest photograph at the space provided on the hall ticket. Such candidates should also bring a photocopy of their SSC/10th mark list (or) 10+2/Intermediate Hall Ticket having photograph for proof.

Mathematics Syllabus :
Unit1. Algebra
Functions – Types of functions – Algebra of real valued functions, Surds and Logarithms, Mathematical Induction and its applications, Permutations and combinations – Linear and Circular Permutations – Combinations, Binomial Theorem – for a positive integral index – for any rational index – applications – Binomial coefficients – Partial Fractions Exponential and Logarithmic Series – Quadratic Expressions – Quadratic inequations, Theory of Equations – Relations between the roots and coefficients in any equation – Transformation of equations – reciprocal equations – cubic equations – Cardan’s solution – Biquadratic equations – Ferrari and Decarte’s solutions. Matrices and Determinants – Definition – Types of Matrices – Algebra of Matrices – Properties of determinants of 2X2 and 3X3 order matrices – Simultaneous Linear equations in two and three variables – Rank of matrix. Complex numbers – their properties – Demoivre’s Theorem – Applications – Expansions of Trigonometric functions.

Unit 2. Trigonometry
Trigonometric functions – Graphs – Periodicity, trigonometric ratios of compound angles, multiple and sub-multiple angles, Transformations, Trigonometric Equations, Inverse Trigonometric functions, Hyperbolic and inverse hyperbolic functions, Properties of Triangles, Heights and Distances (in two dimensional plane)

Unit 3. 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.

Unit 4. Probability
Addition and multiplication theorems of probability – their applications – conditional probability and Baye’s Theorem, . Mean and Variance of a random variable – Binomial and Poisson, normal distributions.

Unit 5. Coordinate Geometry
Locus – Translation and Rotation of Axes, The Straight Line, The Pair of Straight Lines, Coordinate planes in three dimensions – distance between two points – section formula and their applications, Direction cosines and direction ratios of a line – angle between two lines – projection of a line, The plane and its general equation – Equation of the plane in different forms, Circles and system of Circles, Conics – Parabola – Ellipse – Hyperbola – their applications – Equations of Tangent, Normal, Polar and Pole to these conics, Polar Coordinates.

Unit 6. Calculus
Functions – Limits – Continuity, Differentiation – Different Methods, Successive Differentiation including Leibnitz’s Theorem, Applications of Differentiation, Partial Differentiation including Euler’s Theorem on homogeneous functions, Different methods of Integration, Definite integrals and their applications to areas – reduction formulae. Numerical Integration – Trapezoidal and Simpson’s Rules, Differential equations – Formation and solution of first order, first degree differential equations, Second order linear homogenous equations with constant coefficients.