CUET UG Mathematics Syllabus 2025: Syllabus, Pattern and Preparation Tips
Examining the CUET UG Mathematics Syllabus is complex for anyone interested in pursuing higher education in Mathematics. Check the CUET Mathematics Syllabus 2025 here
Published on March, 12th 2025 Time To Read: 4 mins
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CUET UG Mathematics Exam 2025
TheCUET UG Mathematics Exam is part of the Common University Entrance Test (CUET) for Undergraduate (UG) programs in India. It is conducted by the National Testing Agency (NTA) to facilitate admission into various undergraduate courses in central universities and other participating institutions across the country.
The CUET UG Mathematics Exam specifically tests the mathematical knowledge and problem-solving abilities of students seeking admission to undergraduate courses in fields related to Mathematics, Science, Engineering, Economics, Statistics, and other related disciplines.
CUET UG Mathematics Syllabus 2025
The Common University Entrance Test (CUET) Undergraduate (UG) Mathematics syllabus for 2025 is structured to assess a candidate's proficiency in various mathematical domains. The syllabus is primarily based on the NCERT Class 12 curriculum and is divided into two main sections: Section A and Section B.
Section A
Units |
|
Unit I: Algebra
|
Unit IV: Differential Equations
|
Unit II:Calculus
|
Unit V:Probability Distributions
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Unit III:Integration and its Applications
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Unit VI:Linear Programming
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Section B: Mathematics
Unit I: Relations And Functions
- Relations and Functions:Types of relations:
Reflexive,symmetric, transitive and equivalence relations. One to one and
onto functions.
- Inverse Trigonometric Functions:Definition, range,
domain, principal value branches. Graphs of inverse trigonometric
functions.
Unit II: Algebra
Matrices:
- Concept, notation, order, equality, types of matrices, zero matrix,
transpose of a matrix, symmetric and skew symmetric matrices.
- Operations on matrices:Addition, multiplication and
multiplication with a scalar. Simple properties of addition, multiplication
and scalar multiplication.
- Non-commutativity of multiplication of matrices and existence of non-zero
matrices whose product isthe zero matrix (restrict to square matrices of
order 2).
- Invertible matrices and proof of the uniqueness of inverse,if it exists;
(Here all matrices will have real entries).
Determinants:
- Determinant of a square matrix (upto 3×3 matrices), minors, co-factors and
applications of determinants in finding the area of a triangle.
- Adjoint and inverse of a square matrix.
- Consistency, inconsistency and number of solutions of system of linear
equations by examples
- Solving system of linear equations in two or three variables (having
unique solution) using inverse of a matrix.
Unit III: Calculus
Continuity and Differentiability:
- Continuity and differentiability, chain rule, derivatives of inverse
trigonometric functions, like sin-1x, cos-1x, and
tan-1x, derivative of implicit functions.
- Concepts of exponential, logarithmic functions.
- Derivatives of logarithmic and exponential functions.
- Logarithmic differentiation, derivative of functions expressed in
parametric forms.
- Second-order derivatives.
Applications of Derivatives:
- Rate of change of quantities, increasing/decreasing functions, maxima and
minima (first derivative test motivated geometrically and second derivative
test given as provable tool).
- Simple problems (that illustrate basic principles and understanding of the
subject as well asreal-life situations).
Integrals:
- Integration as inverse process of differentiation.
- Integration of a variety of functions by substitution, by partial
fractions and by parts,
- Evaluation of simple integrals of the following types and problems based on them:
- 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,
circles/parabolas/ellipses(in standard form only).
Differential Equations:
- Definition, order and degree, general and particular solutions of a
differential equation.
- Solution of differential equations by method of separation of variables,
solutions of homogeneous differential equations of first order and first
degree.
- Solutions of linear differential equation of the type:
Unit IV: Vectors And Three Dimensional Geometry
Vectors:
- Vectors and scalars, magnitude and direction of a vector.
- Direction cosines and direction ratios of a vector.
- Types of vectors (equal, unit, zero, parallel and collinear vectors),
position vector of a point, 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.
- Definition, Geometrical interpretation, properties and application of
scalar (dot) product of vectors, vector(cross) product ofvectors
Three-dimensional Geometry:
- Direction cosines and direction ratios of a line joining two points.
- Cartesian equation and vector equation of a line, skew lines, shortest
distance between two lines.
- Angle between two lines.
Unit V: Linear Programming
Introduction, related terminology such as constraints, objective function,
optimization, graphical method of solution for problems in two variables,
feasible and infeasible regions (bounded or unbounded), feasible and
infeasible solutions, optimal feasible solutions (up to three non-trivial
constraints).
Unit VI: Probability
- Conditional probability, Multiplications theorem on probability,
independent events, total probability, Baye’s theorem.
- Random variable
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