Based on the latest syllabus for Mathematics Domain (319) for CUET-UG 2025 as per NTA
Section A1
1. Algebra |
(iv). Application of Integration as area under the curve (simple curve) |
(i) Matrices and types of Matrices |
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(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 |
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(vi) Solving of simultaneous equations using Matrix Method |
5. Probability Distributions |
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(i) Random variable |
2. Calculus |
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(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 |
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(iii). Optimal feasible solution |
3. Integration and its Applications |
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(i) Indefinite integrals of simple functions |
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(ii) Evaluation of indefinite integrals |
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(iii) Definite Integrals |
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Section B1: Mathematics
UNIT I: RELATIONS AND 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, l ike 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 and problems based on them:
∫ dx/x² + a²' ∫ dx/√x² + a²' ∫ dx/√a² - x²' ∫ dx/ax² + bx + c' ∫ dx/√ax² + bx + c' ∫ (px + q)dx/ax² + bx + c' ∫ (px + q)dx/√ax² + bx + c' ∫ √a² + x² dx, ∫ √x² - a² dx
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:
dy/dx + Py = Q, where P and Q are functions of x or constants
dx/dy + Px = Q, where P and Q are functions of y or constants
UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY
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.