The syllabus for CUET UG 2023 Mathematics was released by the National Testing Agency on its official website. Students must scrutinize the syllabus in detail in order to be able to do well in their examinations.

This article offers you a detailed overview of the CUET maths syllabus and this will help you have a clear-cut preparation strategy and excel in your examination. The syllabus was released by the National Testing Agency on its official website. Students must scrutinize the syllabus in detail in order to be able to do well in their examinations.

#### Question Paper Pattern for CUET UG Mathematics

- One question paper will be offered with two sections, i.e. section A and section B.
- Section A will have 15 questions. Topics from Mathematics/ Applied Mathematics will be compulsory.
- Section B1 will have 35 questions purely from Mathematics. Out of these 35 questions, 25 questions must be attempted.
- Section B2 will have 35 questions purely from applied mathematics. Out of these 35 questions, 25 questions need to be attempted.

#### CUET UG 2023 – Mathematics Syllabus

#### Section A – Compulsory Section

**UNIT I – Algebra **

Matrices and types of matrices; Equality of matrices, transpose of a matrix, symmetric and skew-symmetric matrix; Algebra of matrices; Determinants; Inverse of a matrix; Solving of simultaneous equations using matrix method

**UNIT II – Calculus**

Higher-order derivatives; Tangents and normals; Increasing and decreasing functions; Maxima and minima

**UNIT III – Integration and its applications**

Indefinite integrals of simple functions; Evaluation of indefinite integrals; Definite integrals; Application of integration as the area under the curve

**UNIT IV – Differential Equations**

Order and degree of differential equations; Formulating and solving differential equations with variable separable

**UNIT V – Probability Distributions**

Random variables and their probability distribution; Expected value of a random variable; Variance and standard deviation of a random variable; Binomial distribution

**UNIT IV – Linear programming **

Mathematical formulation of linear programming problem; Graphical method of solution for problems in two variables; Feasible and infeasible regions; Optimal feasible solution

#### Section B1 – Mathematics

**UNIT I – RELATIONS AND FUNCTIONS**

**Relations and Functions –** Types of relations: Reflexive, symmetric, transitive and equivalence relations. One-to-one and onto functions, composite functions, the inverse of a function. Binary operations.

**Inverse trigonometric functions –** Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

**UNIT II – ALGEBRA**

**Matrices – **Concept, notation, order, equality, types of matrices, zero matrices, transpose of a matrix, symmetric and skew-symmetric matrices. Addition, multiplication, and scalar multiplication of matrices, simple properties of addition, multiplication, and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices (restricted to square matrices of order 2). Concept of elementary row and column operations.Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

**Determinants – **Determinants of a square matrix (up to 3×3 matrices), properties of determinants, minors, co-factors, and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix.Consistency, inconsistency, and a number of solutions of a system of linear equations by examples solving systems of linear equations in two or three variables(having a unique solution) using the inverse of a matrix.

**UNIT III – CALCULUS**

**Continuity and differentiability – **Continuity and differentiability, derivatives of composite functions, chain rules, derivatives of inverse trigonometric functions, and derivatives of implicit functions. Concepts of exponential, logarithmic functions. Derivatives of log x and ex. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second-order derivatives.Rolle’s and Lagrange’s Mean Value theorems (without proof) and their geometric interpretations.

**Applications of derivatives –** Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and normals, approximation, maxima, and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations). Tangent and normal.

**Integrals –** Integration as an inverse process of differentiation. Integration of a variety of functions by substitution, partial fractions, and parts, only simple integrals of the type – is to be evaluated. Definite integrals as a limit of a sum. Fundamental theorem of calculus(without proof). Basic properties of definite integrals and evaluation of definite integrals.

**Applications of the integrals – **Applications in finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses (in standard form only), and the area between the two above said curves (the region should be clearly identifiable).

**Differential equations –** Definition, order, and degree, general and particular solutions of a differential equation. Formation of differential equations whose general solution is given.Solution of differential equations by the method of separation of variables, homogeneous differential equations of the first order, and first degree.

**UNIT IV – VECTORS & THREE – DIMENSIONAL GEOMETRY**

**Vectors –** Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, the addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar(dot) product of vectors, projection of a vector on a line. Vector(cross) product of vectors, scalar triple product.

**Three-dimensional Geometry –** Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane.The angle between (i)two lines,(ii)two planes, and (iii) a line and a plane. Distance of a point from a plane.

**UNIT V – LINEAR PROGRAMMING**

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming(L.P.) problems, mathematical formulation of L.P .problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

**UNIT VI – PROBABILITY **

Multiplications theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem. Random variable and its probability distribution, mean, and variance of haphazard variable. Repeated independent(Bernoulli) trials and binomial distribution.

#### Section B2 – Applied Mathematics

**UNIT I – NUMBERS, QUANTIFICATION, AND NUMERICAL APPLICATIONS**

Modulo arithmetic, Congruence modulo, Allegation and mixture, Numerical problems, Boats and streams, Pipes and cisterns, Races and games, Partnership, Numerical inequalities

**UNIT II – ALGEBRA**

Matrices and types of matrices, Equality of matrices, Transpose of the matrix, Symmetric and Skew symmetric matrix

**UNIT III – CALCULUS**

Higher order derivatives, Marginal cost and marginal revenue using derivatives, Maxima and minima

**UNIT IV – PROBABILITY DISTRIBUTIONS**

Probability distribution, Mathematical expectation, Variance

**UNIT V – INDEX NUMBERS AND TIME-BASED DATA**

Index numbers, Construction of index numbers, Test of the adequacy of index numbers

**UNIT VI – INDEX NUMBERS AND TIME-BASED DATA**

Population and Sample, Parameter and statistics and statistical interferences

**UNIT VII – INDEX NUMBERS AND TIME-BASED DATA**

Time series, Components of time series, Time Series analysis for univariate data

**UNIT VIII – FINANCIAL MATHEMATICS**

Perpetuity, sinking funds, Valuation of bonds, Calculation of EMI, Linear method of depreciation

**UNIT IX – LINEAR PROGRAMING**

Introduction and related terminology, Mathematical formulation of a linear programming problem, Different types of linear programming problems, Graphical method of solution for problems in two variables, Feasible and Infeasible regions, Feasible and infeasible solutions, optimal feasible solution

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