COMEDK UGET 2025 Mathematics Syllabus PDF - Download COMEDK UGET Mathematics Syllabus Topic wise

Unit-I: Sets and Functions

Sets

Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets, Subsets of a set of real numbers (intervals), Universal set, Venn diagrams, Union and Intersection of sets, Difference of sets, Complement, Properties of Complement.

Relations & Functions

Ordered pairs, Cartesian product of sets, Number of elements in Cartesian product, Cartesian product of reals, Definition of relation, pictorial diagrams, domain, co-domain, range, Function as a special type of relation, Real-valued functions and their types (constant, identity, polynomial, etc.), Sum, difference, product, and quotients of functions.

Unit-I: Functions

Trigonometric Functions

Positive and negative angles, Measuring angles in radians/degrees, Conversion, Trigonometric functions via unit circle, Identity sin²x + cos²x = 1, Signs of trigonometric functions, Domain/range of trigonometric functions, Graphs, Expressing sin(x±y), cos(x±y), Deduction of trigonometric identities.

Unit-II: Algebra

Complex Numbers & Quadratic Equations

Need for complex numbers (√−1), Solving quadratic equations, Algebraic properties of complex numbers, Argand plane.

Linear Inequalities

Linear inequalities, Algebraic solutions in one variable, Representation on the number line.

Permutations & Combinations

Fundamental principle of counting, Factorial n (n!), Permutations and combinations, Derivation of nPr and nCr, Simple applications.

Binomial Theorem

Historical perspective, Binomial theorem for positive integral indices, Pascal’s triangle, Simple applications.

Sequence and Series

Arithmetic Mean (A.M.), Geometric Progression (G.P.), General term, Sum of n terms of a G.P., Infinite G.P. and sum, Geometric mean (G.M.), Relationship between A.M. and G.M.

Unit-III: Coordinate Geometry

Straight Lines

Review of 2D geometry, Slope of a line, Angle between two lines, Equations of a line (various forms), Distance of a point from a line.

Conic Sections

Circles, Ellipse, Parabola, Hyperbola, Standard equations and properties, Degenerated cases (point, line, pair of intersecting lines).

Introduction to 3D Geometry

Coordinate axes, Coordinate planes, Coordinates of a point, Distance between two points in three dimensions.

Unit-IV: Calculus

Limits and Derivatives

Concept of Derivatives (rate of change), Limits (polynomials, rational, trigonometric, exponential, and logarithmic functions), Derivatives (sum, difference, product, quotient, and trigonometric functions).

Unit-V: Statistics and Probability

Statistics

Measures of Dispersion: Range, Mean deviation, Variance, Standard deviation for ungrouped/grouped data.

Probability

Events, Occurrence of events, 'Not', 'And', 'Or' events, Exhaustive events, Mutually exclusive events, Set-theoretic probability, Probability of events ('not', 'and', 'or').

Unit-I: Relations and Functions

Relations and Functions

Types of relations: reflexive, symmetric, transitive, equivalence relations. One to one and onto functions.

Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.

Unit-II: Algebra

Matrices

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose, symmetric and skew symmetric matrices, Operations: addition, multiplication, scalar multiplication. Invertible matrices, uniqueness of inverse, non commutativity of multiplication.

Determinants

Determinant of square matrices (up to 3 x 3), minors, co-factors, application in finding area of a triangle, Adjoint and inverse, Consistency and solving system of linear equations (2-3 variables).

Unit-III: Calculus

Continuity and Differentiability

Continuity, differentiability, chain rule, derivatives of inverse trigonometric functions, exponential and logarithmic functions, implicit functions, parametric functions, logarithmic differentiation, second-order derivatives.

Applications of Derivatives

Rate of change of quantities, increasing/decreasing functions, maxima and minima, first and second derivative tests, simple problems involving real-life situations.

Integrals

Integration as the inverse process of differentiation, techniques: substitution, partial fractions, by parts, simple integrals.

Applications of Integrals

Finding areas under curves (lines, circles, parabolas, ellipses).

Differential Equations

Definition, order, degree, general and particular solutions, method of separation of variables, homogeneous differential equations, linear differential equations.

Unit-IV: Vectors and Three-Dimensional Geometry

Vectors

Vectors and scalars, magnitude and direction, direction cosines and ratios, types of vectors, position vector, components, vector addition, scalar multiplication, scalar (dot) and vector (cross) products, applications.

Three-Dimensional Geometry

Direction cosines and ratios, Cartesian and vector equations of a line, skew lines, shortest distance between two lines, angle between two lines.

Unit-V: Linear Programming

Linear Programming

Introduction, constraints, objective function, optimization, graphical solution for two variables, feasible/infeasible regions, optimal solutions (up to three constraints).

Unit-VI: Probability

Probability

Conditional probability, multiplication theorem, independent events, total probability, Bayes’ theorem, random variable, probability distribution, mean of a random variable.

Unit-I: Sets and Functions

Sets

Representation of sets, Union, Intersection, Difference, and Complement of sets, Venn diagrams, Properties of complements

Relations & Functions

Domain, Co-domain, Range, Cartesian product of sets, Real-valued functions and operations (Sum, Difference, Product, Quotient)

Trigonometric Functions

Conversion between radians and degrees, Basic trigonometric identities (sin²x + cos²x = 1), Domain/Range of trigonometric functions, Sum/Difference formulas

Unit-II: Algebra

Complex Numbers & Quadratic Equations

Solving quadratic equations using complex numbers, Argand plane representation of complex numbers

Permutations & Combinations

Fundamental principle of counting, Derivation and applications of nPr and nCr formulas

Binomial Theorem

Binomial expansion for positive integral indices, Pascal’s triangle, Simple applications

Sequence and Series

Arithmetic Mean (A.M.), Geometric Progression (G.P.), Sum of n terms of a G.P., Relationship between A.M. and G.M.

Unit-III: Coordinate Geometry

Straight Lines

Slope of a line, Angle between two lines, Various forms of line equations, Distance of a point from a line

Conic Sections

Standard equations and properties of circles, parabolas, ellipses, and hyperbolas

Unit-IV: Calculus

Limits and Derivatives

Basic concepts of limits and derivatives, Limits of polynomials, rational, trigonometric, and logarithmic functions, Derivatives of basic functions

Unit-V: Statistics & Probability

Statistics

Measures of Dispersion: Variance, Standard Deviation

Probability

Basic probability concepts, Mutually exclusive events, Set-theoretic probability, Probability of 'not', 'and', 'or' events

Unit-I: Relations and Functions

Relations and Functions

Types of relations (reflexive, symmetric, transitive, equivalence), One to one and onto functions

Inverse Trigonometric Functions

Domain, range, and principal value branches of inverse trigonometric functions, Graphs of inverse trigonometric functions

Unit-II: Algebra

Matrices

Types of matrices (zero, identity, symmetric, skew-symmetric), Operations on matrices (addition, multiplication, scalar multiplication), Invertible matrices, Uniqueness of inverse matrix

Determinants

Determinants of matrices (up to 3x3), Minors, co-factors, Adjoint, Inverse, Solving systems of linear equations using determinants

Unit-III: Calculus

Continuity and Differentiability

Continuity and differentiability, Chain rule, Derivatives of inverse trigonometric, exponential, and logarithmic functions, Second-order derivatives

Applications of Derivatives

Rate of change, Increasing/decreasing functions, Maxima and minima (using first and second derivative tests), Real-life applications

Integrals

Integration techniques (substitution, partial fractions, by parts), Simple integrals

Applications of Integrals

Area under curves (lines, circles, parabolas, ellipses)

Differential Equations

General and particular solutions, Method of separation of variables, Solving homogeneous and linear differential equations

Unit-IV: Vectors & Three-Dimensional Geometry

Vectors

Magnitude and direction, Direction cosines and direction ratios, Scalar (dot) and vector (cross) products

Three-Dimensional Geometry

Cartesian and vector equations of a line, Skew lines, Shortest distance between two lines, Angle between two lines

Unit-V: Linear Programming

Linear Programming

Graphical solutions, Optimization problems with two variables, Feasible/infeasible regions, Optimal solutions

Unit-VI: Probability

Probability

Conditional probability, Bayes’ theorem, Random variable and probability distribution, Mean of random variable

Sets and Functions

5%

Trigonometric Functions

6%

Mathematical Reasoning

3%

Complex Numbers and Quadratic Equations

6%

Permutations and Combinations

5%

Binomial Theorem

5%

Sequences and Series

6%

Straight Lines and Conic Sections

5%

Matrices and Determinants

5%

Continuity and Differentiability

6%

Applications of Derivatives

6%

Integrals

7%

Differential Equations

5%

Probability

6%

Vectors and 3D Geometry

6%

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