CUET UG Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in CUET UG, not a summary of it.

1. 1

   Relations, Functions and Algebra

   4 topics

   • Relations and Functions
     • Types of relations and functions
     • Composition and inverse of functions
     • Binary operations
   • Inverse Trigonometric Functions
     • Domain, range and principal values
     • Elementary properties
   • Matrices
     • Types and operations on matrices
     • Transpose, symmetric and skew-symmetric matrices
     • Inverse using elementary operations
   • Determinants
     • Properties and minors and cofactors
     • Adjoint and inverse of a matrix
     • Solution of linear equations by matrix method
2. 2

   Calculus

   4 topics

   • Continuity and Differentiability
     • Continuity and differentiability of functions
     • Derivatives of composite, implicit and inverse functions
     • Logarithmic differentiation
     • Rolle's and Mean Value theorems
   • Applications of Derivatives
     • Rate of change and increasing/decreasing functions
     • Tangents and normals
     • Maxima and minima
   • Integrals
     • Integration by substitution and parts
     • Partial fractions
     • Definite integrals and properties
   • Applications of Integrals and Differential Equations
     • Area under curves
     • Order, degree and formation of differential equations
     • Variable separable and linear differential equations
3. 3

   Vectors and Three-Dimensional Geometry

   3 topics

   • Vector Algebra
     • Types of vectors and components
     • Scalar (dot) product
     • Vector (cross) product
   • Three-Dimensional Geometry
     • Direction cosines and direction ratios
     • Equation of a line in space
     • Equation of a plane and distance measures
   • Lines and Planes Applications
     • Angle between lines and planes
     • Coplanarity and shortest distance
4. 4

   Probability and Linear Programming

   3 topics

   • Probability
     • Conditional probability and multiplication theorem
     • Bayes' theorem
     • Random variables and probability distribution
   • Linear Programming
     • Formulation of LPP
     • Graphical solution and feasible region
   • Optimisation Problems
     • Manufacturing and diet problems
     • Transportation and allocation problems
5. 5

   Applied Mathematics Topics

   4 topics

   • Numbers, Quantification and Numerical Applications
     • Modulo arithmetic and congruence
     • Allegation and mixture
     • Boats, streams, pipes and cisterns
   • Index Numbers and Time-Based Data
     • Index numbers and their construction
     • Time series and moving averages
   • Financial Mathematics
     • Perpetuity, sinking funds and EMI
     • Depreciation
   • Inferential Statistics
     • t-test and population mean

Mathematics flashcards for CUET UG

21 of 50 cards from the Mathematics deck — real questions with worked answers.

1. In relations and functions, what is the definition of a one-one (injective) function?

   A function f: A→B is one-one if distinct elements of A have distinct images, i.e. f(x1)=f(x2) implies x1=x2 for all x1,x2 in A.

2. What conditions must a function f: A→B satisfy to be both an injection and a surjection, and what is such a function called?

   It must be one-one (distinct inputs give distinct outputs) and onto (every element of B is an image). Such a function is called a bijection, and only bijections are invertible.

3. State the three properties a relation must satisfy to be an equivalence relation.

   Reflexive (aRa for all a), symmetric (aRb implies bRa), and transitive (aRb and bRc imply aRc).

4. What is the principal value range of the inverse trigonometric function sin⁻¹x?

   [-π/2, π/2], with domain [-1, 1].

5. What is the principal value range of cos⁻¹x?

   [0, π], with domain [-1, 1].

6. State the identity relating sin⁻¹x and cos⁻¹x.

   sin⁻¹x + cos⁻¹x = π/2, valid for x in [-1, 1].

7. What is the formula for tan⁻¹x + tan⁻¹y when xy < 1?

   tan⁻¹x + tan⁻¹y = tan⁻¹[(x + y)/(1 - xy)], provided xy < 1.

8. What is a symmetric matrix and what is a skew-symmetric matrix?

   A symmetric matrix satisfies A' = A (a_ij = a_ji); a skew-symmetric matrix satisfies A' = -A (a_ij = -a_ji), forcing all diagonal entries to be zero.

9. Under what condition is the product of two matrices A and B defined, and what is the order of the product?

   AB is defined only when the number of columns of A equals the number of rows of B. If A is m×n and B is n×p, then AB is m×p.

10. How can any square matrix A be expressed as the sum of a symmetric and a skew-symmetric matrix?

    A = ½(A + A') + ½(A - A'), where ½(A + A') is symmetric and ½(A - A') is skew-symmetric.

11. What is the relationship between a square matrix A, its inverse, and its determinant?

    A⁻¹ exists iff |A| ≠ 0 (A is non-singular), and A⁻¹ = (1/|A|)·adj(A), where adj(A) is the adjoint (transpose of the cofactor matrix).

12. How is the area of a triangle with vertices (x1,y1), (x2,y2), (x3,y3) computed using determinants?

    Area = ½ |Δ| where Δ is the determinant with rows (x1,y1,1), (x2,y2,1), (x3,y3,1). The points are collinear if Δ = 0.

13. State the property of determinants when two rows (or columns) are interchanged.

    Interchanging any two rows or two columns of a determinant changes the sign of the determinant (multiplies its value by -1).

14. What is the relationship |adj A| = ? for an n×n matrix, and what is |kA|?

    |adj A| = |A|^(n-1) and |kA| = kⁿ|A| for an n×n square matrix A.

15. State the condition for continuity of a function f at a point x = c.

    f is continuous at c if lim(x→c) f(x) exists, f(c) is defined, and lim(x→c) f(x) = f(c).

16. State the chain rule for differentiating a composite function y = f(g(x)).

    dy/dx = f'(g(x))·g'(x); equivalently if y = f(t) and t = g(x), then dy/dx = (dy/dt)·(dt/dx).

17. What does Rolle's Theorem state?

    If f is continuous on [a,b], differentiable on (a,b), and f(a) = f(b), then there exists at least one c in (a,b) such that f'(c) = 0.

18. State the Mean Value Theorem (Lagrange's MVT).

    If f is continuous on [a,b] and differentiable on (a,b), then there exists c in (a,b) such that f'(c) = [f(b) - f(a)]/(b - a).

19. How do you find the slope of the tangent and the normal to a curve y = f(x) at a point?

    The slope of the tangent is dy/dx at that point; the slope of the normal is -1/(dy/dx), the negative reciprocal.

20. What is the second derivative test for local maxima and minima?

    At a critical point c where f'(c) = 0: if f''(c) < 0 then f has a local maximum; if f''(c) > 0 then a local minimum; if f''(c) = 0 the test fails (use first derivative test).

21. What does it mean for a function to be increasing or decreasing on an interval in terms of its derivative?

    f is increasing on an interval if f'(x) > 0 there, and decreasing if f'(x) < 0 there (strictly).

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