CUET UG Maths Pattern 2025

Language of Exam 

13 languages 

Difficulty level

10+2 

Type of Questions

Multiple Choice Questions (MCQ)

Duration of Exam 

60 minutes 

Total number of Questions 

50 (all compulsory)

Scheme of Marking 

+5 for every correct answer

–1 for every incorrect one

No marks or penalty for unattempted questions

Maximum Marks 

250

Section A

Chapter Name 

Topics included 

Algebra 

• Matrices & Types of Matrices 
• Equality of matrices, transpose of a matrix, & symmetric and skew-symmetric matrix.
• Algebra of Matrices 
• Determinants
• The inverse of a matrix 
• Solving the simultaneous equations using the matrix method 

Calculus 

• Higher order derivatives
• Tangents and Normals 
• Increasing and Decreasing Functions 
• Maxima and Minima 

Integration and its Applications 

• Indefinite integrals of simple functions 
• Definite integrals
• Evaluation of indefinite integrals 
• Application of Integration as area under the curve. 

Differential Equations

• Order & Degree of differential equations 
• Formulating & Solving differential equations with variable separable 

Probability Distributions 

• Random variables; their probability distribution 
• Expected value of a random variable 
• Variance & Standard Deviation of a random variable 
• Binomial Distribution 

Linear Programming 

• Mathematical formulation of problems related to Linear Programming 
• Graphical method of solution for the problems in two variables
• Feasible and infeasible regions 
• Optimal feasible solution 

Section B1: Mathematics 

Units 

Sub Units 

UNIT I: Relations and Functions

1. Relations and Functions

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

2. Inverse Trigonometric Functions

• Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions.
• Elementary properties- inverse trigonometric functions.

UNIT II: ALGEBRA

1. Matrices

• Concept, order, notation, equality, types of matrices, zero matrices, transpose of a matrix, symmetric & skew-symmetric matrices. 
• Simple properties of addition, multiplication, & scalar multiplication. 
• Concept of elementary row & column operations. Invertible matrices and stating proof of the uniqueness of inverse, if it exists;(all matrices will have real entries).
• Non-commutativity of multiplication of matrices along with the existence of non-zero matrices whose product is the 0 (Zero) matrix (restricted to square matrices of 2nd Order).

2. Determinants

• Determinant of a square matrix (up to 3 × 3 matrices), cofactors, minors, & properties of determinants
• Applications of determinants in finding the area of a triangle. 
• Adjoint & Inverse of a square matrix. 
• Consistency, inconsistency, & number of solutions of system of linear equations by examples
• Solving a system of linear equations in two(2) or three(3) variables (having unique solutions) using the inverse of a matrix.

UNIT III: Calculus

1. Continuity & Differentiability

• Continuity and differentiability, chain rule,  derivative of composite functions, derivatives of inverse trigonometric functions, derivative of implicit function. Concepts of logarithmic & exponential functions.
• Derivatives of logx and Logarithmic differentiation. Derivative functions expressed in different parametric forms. Also, Second-order derivatives. 
• Rolle’s and Lagrange’s Mean Value Theorems (no proof required) and & geometric interpretations.

2. Applications of Derivatives

• Applications of derivatives: Rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima, and minima (the first derivative test is motivated geometrically, & second derivative test is given as a proving tool). 
• Simple problems (illustrating all basic principles & understanding of the subject as well as real-life situations). Tangent & Normal.

3. Integrals

• Integration (the inverse process of differentiation).
• Definite integrals as a limit of a sum. 
• Basic properties of definite integrals and evaluation of definite integrals.
• Fundamental Theorem of Calculus (without any proof).
• Integration of a variety of functions by substitution, by partial fractions & by parts, only simple integrals of the type to be evaluated are –

$\int \frac{dx}{x^2\pm a^2},\int \frac{dx}{\sqrt{x^2\pm a^2}},\int \frac{dx}{a{x}^2+bx+c},\int \frac{dx}{\sqrt{a{x}^2+bx+c}}$

$\int \frac{(px+q)}{a{x}^2+bx+c}dx,\int \frac{(px+q)}{\sqrt{a{x}^2+bx+c}}dx,\int \sqrt{a^2\pm x^2}dx\text{and}\int \sqrt{x^2-a^2}dx$

$\int \sqrt{a{x}^2+bx+c}dx\text{and}\int (px+q)\sqrt{a{x}^2+bx+c}dx$

4. Applications of Integrals: 

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

5. Differential Equations: 

• Definition, order & degree, general and particular solutions of a differential equation. 
• Formation of differential equation whose general solution is given.
• Solution of differential equations by method of separation of variables, homogeneous differential equations of first order & first degree. 
• Solutions of linear differential equations such as – 

$\frac{dy}{dx}+Py=Q$, where P and Q are the functions of x or constant. 

$\frac{dx}{dy}+Px=Q$, where P and Q are the functions of y or constant. 

UNIT IV: Vectors and three-dimensional Geometry

1. Vectors

• Vectors & scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. 
• Types of vectors (equal, unit, zero, parallel, & collinear vectors), 
• The position vector of a point, the negative of a vector, components of a vector. 
• 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.

2. Three-dimensional Geometry

• Direction cosines/ratios of a line joining two points.
• Cartesian and vector equation of a line, coplanar & skew lines, the shortest distance between two lines. Vector & Cartesian equation of a plane.
• The angle between (i) 2 lines,(ii) 2 planes, (iii) a line & a plane. Distance of a point from a plane.

Unit V: Linear Programming

• Introduction, related terminologies, such as constraints, objective function, & optimisation. 
• Different types of L.P. (linear programming) problems,
• Mathematical formulation of L.P. problems. 
• Feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions(up to three non-trivial constraints)
• Graphical method of solution for problems in two variables.

Unit VI: Probability

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

Section B2: Applied Mathematics 

Unit I: Numbers, Quantification and Numerical Applications

A. Modulo Arithmetic

• Define the modulus of an integer
• Applying arithmetic operations while using modular arithmetic rules

B. Congruence Modulo

• Define congruence modulo
• Applying the definition to its various problems

C. Allegation and Mixture

• Understand the rule of allegation to produce any mixture at any given price
• Determine the mean price of any mixture. Applying the rule of allegation

D. Numerical Problems

• Solve real-life problems mathematically

E. Boats & Streams

• Distinguish between upstream and downstream flows
• Expressing the problem in the form of an equation

F. Pipes and Cisterns

• Determine the time taken by two or more pipes to fill or empty a tank/container

G. Races and games

• Compare the performance of two players w.r.t. Time, distance covered/ Work done from the given data

H. Partnership

• Differentiate between active partner & sleeping partner
• Determine the gain or loss to be divided among the partners in the ratio of their investments with due consideration of the time volume/surface area for a solid formed using 2 or more shapes

I. Numerical Inequalities

• Describe the basic concepts of general numerical inequalities
• Understand & Write numerical inequalities

UNIT II: Algebra

A. Matrices and types of matrices

• Define matrix
• Identify different kinds of matrices

B. Equality of matrices, Transpose of a matrix, Symmetric & Skew symmetric matrix

• Determine the equality of two matrices
• Write transpose of the given matrix
• Define symmetric & skewsymmetric matrix

UNIT III: Calculus

A. Higher Order Derivatives

• Determine second & higher-order derivatives
• Understand the differentiation of parametric functions and implicit functions 
• Identify dependent & independent variables

B. Marginal Cost & Marginal Revenue using derivatives

• Define marginal cost along with marginal revenue
• Find marginal cost and related marginal revenue

C. Maxima & Minima

• Determine critical points of the function
• Find the point(s) of local maxima and local minima and the corresponding local maximum and local minimum values
• Find the absolute maxima and absolute minima values of any given function

UNIT IV: Probability Distributions

A. Probability Distribution

• Understand the concept of Random Variables & Probability Distributions
• Find the probability distribution of any discrete random variable

B. Mathematical Expectation

• Apply the arithmetic mean of frequency distribution to find the expected value of a random variable

C. Variance

• Calculate the Variance and S.D.of a random variable

UNIT V: Index Numbers and Time Based Data

A. Index Numbers

• Define Index numbers as a special type of average

B. Construction of Index numbers

• Construct different types of index numbers

C. Test of Adequacy of Index Numbers

• Apply time reversal test

D. Time Series

• Identify time series as chronological data

E. Components of Time Series

• Distinguish between different components of the time series

F. Time Series Analysis for Univariate Data

• Solve practical problems based on statistical data and Interpret

UNIT VI: Inferential Statistics

A. Population & Sample

• Define Population & Sample
• Differentiate between population and sample
• Define a representative sample from a population

B. Parameter and Statistics and Statistical Interferences

• Define Parameter with reference to Population
• Define Statistics with reference to the Sample
• Explain the relation between Parameter and Statistic
• Explain the limitation of Statisticto generalize the estimation for population
• Interpret the concept of Statistical Significance and Statistical Inferences
• State Central Limit Theorem
• Explain the relation between Population-Sampling Distribution-Sample

UNIT VII: Financial Mathematics

A. Perpetuity, Sinking Funds

• Explain the concept of perpetuity and sinking fund
• Calculate perpetuity
• Differentiate between sinking funds & savings account

B. Valuation of bonds

• Define the concept of valuation of bonds and related terms
• Calculate the value of the  bond using the present value approach

C. Calculation of EMI

• Explain the concept of EMI
• Calculate EMI using various methods

D. Linear Method of Depreciation

• Define the concept of the linear method of Depreciation
• Interpret the cost, residual value, & useful life of an asset from the given information
• Calculate depreciation

UNIT VIII: Linear Programming

A. Introduction and related terminology

• Familiarize with terms related to Linear Programming Problem

B. Mathematical formulation of Linear Programming Problem

• Formulate Linear ProgrammingProblem

C. Different types of Linear Programming Problems

• Identify & formulate different types of LPP

D. Graphical Method of Solution for problems in 2 Variables

• Draw the Graph for a system of linear inequalities involving 2 variables and find a solution graphically

E. Feasible & Infeasible Regions

• Identify feasible, infeasible, & bounded regions

F. Feasible & infeasible solutions, optimal feasible solution

• Understand feasible & infeasible solutions
• Find the optimal feasible solution