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For the Year 2025 
 
  
Mathematics/ 
Applied 
Mathematics – 319 
Syllabus for 
CUET(UG) 
 
Page 2


 
 
For the Year 2025 
 
  
Mathematics/ 
Applied 
Mathematics – 319 
Syllabus for 
CUET(UG) 
 
 
 
Section A1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1. Algebra (iv). Application of Integration as area 
under the curve (simple curve) 
(i) Matrices and types of Matrices 
 
(ii) Equality of Matrices, transpose 
of a Matrix, Symmetric and Skew 
Symmetric Matrix 
4. Differential Equations 
(iii) Algebra of Matrices (i) Order and degree of differential 
equations 
(iv) Determinants (ii) Solving of differential equations 
with variable separable 
(v) Inverse of a Matrix 
 
(vi) Solving of simultaneous 
equations using Matrix Method 
5. Probability Distributions 
 (i) Random variable 
2. Calculus 
 
(i) Higher order derivatives(second 
order) 
6. Linear Programming 
(ii) Increasing and Decreasing 
Functions 
(i) Graphical method of solution for 
problems in two variables 
(iii). Maxima and Minima (ii) Feasible and infeasible regions 
 (iii). Optimal feasible solution 
3. Integration and its Applications 
 
(i) Indefinite integrals of simple 
functions 
 
(ii) Evaluation of indefinite integrals 
 
(iii) Definite Integrals 
 
Page 3


 
 
For the Year 2025 
 
  
Mathematics/ 
Applied 
Mathematics – 319 
Syllabus for 
CUET(UG) 
 
 
 
Section A1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1. Algebra (iv). Application of Integration as area 
under the curve (simple curve) 
(i) Matrices and types of Matrices 
 
(ii) Equality of Matrices, transpose 
of a Matrix, Symmetric and Skew 
Symmetric Matrix 
4. Differential Equations 
(iii) Algebra of Matrices (i) Order and degree of differential 
equations 
(iv) Determinants (ii) Solving of differential equations 
with variable separable 
(v) Inverse of a Matrix 
 
(vi) Solving of simultaneous 
equations using Matrix Method 
5. Probability Distributions 
 (i) Random variable 
2. Calculus 
 
(i) Higher order derivatives(second 
order) 
6. Linear Programming 
(ii) Increasing and Decreasing 
Functions 
(i) Graphical method of solution for 
problems in two variables 
(iii). Maxima and Minima (ii) Feasible and infeasible regions 
 (iii). Optimal feasible solution 
3. Integration and its Applications 
 
(i) Indefinite integrals of simple 
functions 
 
(ii) Evaluation of indefinite integrals 
 
(iii) Definite Integrals 
 
 
 
 
Section B1: Mathematics 
UNIT I: RELATIONSAND FUNCTIONS 
1. Relations and Functions 
Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. 
2. Inverse Trigonometric Functions 
Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions.  
UNIT II: ALGEBRA 
 
1. 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 is the 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). 
2. Determinants 
Determinant of a square matrix (up to 3 × 3 matrices), minors, cofactors 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 
 
1. Continuity and Differentiability 
Continuity and differentiability, chain rule, derivatives of inverse trigonometric functions, like sin
-1
?? , cos
-1
?? and 
tan
-1
?? , 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. 
2. 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 as real-life situations).  
Page 4


 
 
For the Year 2025 
 
  
Mathematics/ 
Applied 
Mathematics – 319 
Syllabus for 
CUET(UG) 
 
 
 
Section A1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1. Algebra (iv). Application of Integration as area 
under the curve (simple curve) 
(i) Matrices and types of Matrices 
 
(ii) Equality of Matrices, transpose 
of a Matrix, Symmetric and Skew 
Symmetric Matrix 
4. Differential Equations 
(iii) Algebra of Matrices (i) Order and degree of differential 
equations 
(iv) Determinants (ii) Solving of differential equations 
with variable separable 
(v) Inverse of a Matrix 
 
(vi) Solving of simultaneous 
equations using Matrix Method 
5. Probability Distributions 
 (i) Random variable 
2. Calculus 
 
(i) Higher order derivatives(second 
order) 
6. Linear Programming 
(ii) Increasing and Decreasing 
Functions 
(i) Graphical method of solution for 
problems in two variables 
(iii). Maxima and Minima (ii) Feasible and infeasible regions 
 (iii). Optimal feasible solution 
3. Integration and its Applications 
 
(i) Indefinite integrals of simple 
functions 
 
(ii) Evaluation of indefinite integrals 
 
(iii) Definite Integrals 
 
 
 
 
Section B1: Mathematics 
UNIT I: RELATIONSAND FUNCTIONS 
1. Relations and Functions 
Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. 
2. Inverse Trigonometric Functions 
Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions.  
UNIT II: ALGEBRA 
 
1. 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 is the 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). 
2. Determinants 
Determinant of a square matrix (up to 3 × 3 matrices), minors, cofactors 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 
 
1. Continuity and Differentiability 
Continuity and differentiability, chain rule, derivatives of inverse trigonometric functions, like sin
-1
?? , cos
-1
?? and 
tan
-1
?? , 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. 
2. 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 as real-life situations).  
 
 
 
3. 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. 
 
?
????
?? 2
+ ?? 2
, ?
????
v ?? 2
± ?? 2
, ?
????
?? 2
- ?? 2
, ?
????
v?? 2
- ?? 2
, ?
????
????
2
+ ???? + ?? , ?
????
v ????
2
+ ???? + ?? , 
 
 
?
(???? + ?? )????
????
2
+ ???? + ?? , ?
(???? + ?? )????
v ????
2
+ ???? + ?? ,   ? v?? 2
± ?? 2
???? ,   ? v?? 2
- ?? 2
???? 
 
 
 
Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite 
integrals. 
4. Applications of the Integrals 
Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only) 
5. 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: 
dy 
+ Py = Q , 
where P and Q are functions of x or constants 
dx 
 
dx 
+ Px  
dy 
 
= Q , 
where P and Q are functions of y or constants 
Page 5


 
 
For the Year 2025 
 
  
Mathematics/ 
Applied 
Mathematics – 319 
Syllabus for 
CUET(UG) 
 
 
 
Section A1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1. Algebra (iv). Application of Integration as area 
under the curve (simple curve) 
(i) Matrices and types of Matrices 
 
(ii) Equality of Matrices, transpose 
of a Matrix, Symmetric and Skew 
Symmetric Matrix 
4. Differential Equations 
(iii) Algebra of Matrices (i) Order and degree of differential 
equations 
(iv) Determinants (ii) Solving of differential equations 
with variable separable 
(v) Inverse of a Matrix 
 
(vi) Solving of simultaneous 
equations using Matrix Method 
5. Probability Distributions 
 (i) Random variable 
2. Calculus 
 
(i) Higher order derivatives(second 
order) 
6. Linear Programming 
(ii) Increasing and Decreasing 
Functions 
(i) Graphical method of solution for 
problems in two variables 
(iii). Maxima and Minima (ii) Feasible and infeasible regions 
 (iii). Optimal feasible solution 
3. Integration and its Applications 
 
(i) Indefinite integrals of simple 
functions 
 
(ii) Evaluation of indefinite integrals 
 
(iii) Definite Integrals 
 
 
 
 
Section B1: Mathematics 
UNIT I: RELATIONSAND FUNCTIONS 
1. Relations and Functions 
Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. 
2. Inverse Trigonometric Functions 
Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions.  
UNIT II: ALGEBRA 
 
1. 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 is the 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). 
2. Determinants 
Determinant of a square matrix (up to 3 × 3 matrices), minors, cofactors 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 
 
1. Continuity and Differentiability 
Continuity and differentiability, chain rule, derivatives of inverse trigonometric functions, like sin
-1
?? , cos
-1
?? and 
tan
-1
?? , 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. 
2. 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 as real-life situations).  
 
 
 
3. 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. 
 
?
????
?? 2
+ ?? 2
, ?
????
v ?? 2
± ?? 2
, ?
????
?? 2
- ?? 2
, ?
????
v?? 2
- ?? 2
, ?
????
????
2
+ ???? + ?? , ?
????
v ????
2
+ ???? + ?? , 
 
 
?
(???? + ?? )????
????
2
+ ???? + ?? , ?
(???? + ?? )????
v ????
2
+ ???? + ?? ,   ? v?? 2
± ?? 2
???? ,   ? v?? 2
- ?? 2
???? 
 
 
 
Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite 
integrals. 
4. Applications of the Integrals 
Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only) 
5. 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: 
dy 
+ Py = Q , 
where P and Q are functions of x or constants 
dx 
 
dx 
+ Px  
dy 
 
= Q , 
where P and Q are functions of y or constants 
 
 
 
 
UNIT IV: VECTORSAND THREE-DIMENSIONALGEOMETRY 
 
1. 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 of vectors. 
2. 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.  
 
 
                                    Section B2: Applied Mathematics 
Unit I: Numbers, Quantification and Numerical Applications 
A. Modulo Arithmetic 
? Define modulus of an integer 
? Apply arithmetic operations using modular arithmetic rules 
B. Congruence Modulo 
? Define congruence modulo 
? Apply the definition in various problems 
 
C. Allegation and Mixture 
? Understand the rule of allegation to produce a mixture at a given price 
? Determine the mean price of a mixture 
? Apply rule of allegation 
 
D. Numerical Problems 
? Solve real life problems mathematically
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