COMEDK UGET 2024 Mathematics Syllabus, Important Topics, Preparation Tips

Circles

• Equation of a Circle when the End Points of a Diameter are Given.
• Points of Intersection of a Line and a Circle with the Centre at the Standard Form of Equation of a Circle
• General Form of Equation of a Circle, its radius and center
• Equation of a Family of Circles through the Intersection of Two Circles
• Origin and Conditions for a Line to be Tangent to the Circle
• Equation of the Tangent
• Condition for Two Intersecting Circles to be Orthogonal

Vectors and three-dimensional geometry

• Components of a Vector in Two Dimensions and Three-Dimensional Space
• Scalar and Vector Products
• Vectors and Scalars
• Application of Vectors to Plane Geometry
• Addition of Vectors
• Scalar and Vector Triple Product

3D Geometry

• Section Formula
• Direction Ratios and Direction Cosines
• Angle between Two Intersecting Lines
• Diameter form of the Equation of a Sphere
• Skew Lines – The Shortest Distance between them and its Equation
• Coordinates of a Point in Space
• Distance Between Two Point
• Equations of a Line and a Plane in Different Forms: Intersection of a Line and a Plane, Coplanar Lines, Equation of a Sphere, Its Centre and Radius

Differential calculus

• Inverse Functions
• Graphs of Simple Functions
• Limits
• Polynomials, Rational, Trigonometric, Logarithmic and Exponential Functions
• Continuity: Differentiation of the Sum, Difference, Product and Quotient of Two Functions
• Applications of Derivatives: Rate of Change of Quantities, Monotonic Increasing and Decreasing Functions, Maxims and Minimum Functions of One Variable, Tangents and Normals,
• Rolle’s and Lagrange’s Mean Value Theorems
• Differentiation of Trigonometric, Inverse Trigonometric, Logarithmic, Exponential, Composite and Implicit Functions, Derivatives of Order Upto Two.

Probability

• Probability of an Event
• Probability Distribution of a Random Variate
• Addition and Multiplication Theorems of Probability and their Application
• Conditional Probability: Bayes Theorem
• Binomial and Poisson Distributions and their Properties.

Matrices and determinants

• Evaluation of Determinants
• Area of Triangles Using Determinants
• Determinants and Matrices of Order Two and Three
• Properties of Determinant
• Adjoint and Inverse of Matrix
• Test of Consistency and Solution of Similar Linear Equations using Determinants and Matrices
• Addition and Multiplication of Matrices

Integral calculus

• Coordinate geometry

Differential equations

• Solution of Differential Equations by the Method of Separation of Variables.
• Solution of Homogeneous and Linear Differential Equations and those of type d2y = f(x) dx2
• Differential Equations, Ordinary Differential Equation – Their Order and Degree
• Formation of Differential Equations

Exponential and logarithmic series

• Definite integral

Unit 1 - Relations and Functions

Composition of functions and invertible functions

Unit 2 - Inverse Trigonometric Functions

• Graphs of inverse trigonometric functions
• Elementary properties of inverse trigonometric functions

Unit 3 - Matrices

• Existence of non-zero matrices whose product is the zero matrices.
• Concept of elementary row and column operations.
• Proof of the uniqueness of the inverse, if it exists.

Unit 4 - Determinants

• Properties of determinants
• Consistency, inconsistency, and number of solutions of the system of linear equations by examples.

Unit 5 - Continuity and Differentiation

• Rolle’s and Lagrange's Mean Value Theorems( without proof) and their geometric interpretation

Unit 6 - Applications of derivatives

• Rate of change of bodies, use of derivatives in approximation

Unit 7 - Integrals

• Integrals of the functions √(ax2+bx+c), and(ax+b)√(ax2+bx+c)
• Definite integrals as a limit of a sum

Unit 8 - Application of the Integrals

The area under multiple curves

Unit 9 - Differentiation Equations

• Formation of differential equations whose general solution is given.
• Solutions of linear differential equations of the type: dx/dy+px=q, where p and q are functions of y or constants.

Unit 10 - Vectors

Scalar triple product of vectors

Unit 11 - Three-dimensional Geometry

• Calculating the Angle between (i) two lines, (ii) two planes, (iii) a line and a plane

Unit 12 - Probability

• Mean and variance of random variables. Binomial probability distribution

Exam Name

Consortium of Medical, Engineering, and Dental College of Karnataka (COMEDK)

Mode of Exam

Online (computer-based)

Duration

3 hours

Question type

Objective

Total number of sections

• Physics
• Chemistry
• Mathematics

Total number of questions

180 Questions

Total number of marks

180 Marks

Exam Medium

English

Negative marking

Nil

NCERT Textbooks Class 11thand 12th

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Objective Mathematics

R D Sharma

Mathematics Book COMEDK

M. R. Hanumantharaya, H. S. Mahadevaiah

Maths XI & XII

R D Sharma

Differential Calculus

Amit M Agarwal (Arihant Publications)

Algebra Made Easy

K.P. Basu

Mathematics for Karnataka CET & COMEDK

BASE