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CUET UG Mathematics Syllabus
The Mathematics syllabus for CUET UG in full: 5 chapters, 18 topics and 47 sub-topics, every one listed below, plus 50 Mathematics flashcards with answers.
Mathematics syllabus: all 5 chapters
Expand any chapter to see its topics and sub-topics.
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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
- Relations and Functions
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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
- Continuity and Differentiability
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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
- Vector Algebra
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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
- Probability
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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
- Numbers, Quantification and Numerical Applications
CUET UG Mathematics flashcards — 50 questions with answers
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.
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.
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).
What is the principal value range of the inverse trigonometric function sin⁻¹x?
[-π/2, π/2], with domain [-1, 1].
What is the principal value range of cos⁻¹x?
[0, π], with domain [-1, 1].
State the identity relating sin⁻¹x and cos⁻¹x.
sin⁻¹x + cos⁻¹x = π/2, valid for x in [-1, 1].
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.
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.
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.
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.
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).
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.
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).
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.
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).
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).
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.
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).
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.
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).
Show the other 30 Mathematics flashcards
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).
State the integration by parts formula.
∫ u·v dx = u·∫v dx - ∫ [u'·(∫v dx)] dx; choose u using the ILATE order (Inverse, Logarithmic, Algebraic, Trigonometric, Exponential).
What is the value of ∫ dx/(x² + a²)?
(1/a) tan⁻¹(x/a) + C.
State the fundamental theorem of calculus (second part) for evaluating a definite integral.
If F is an antiderivative of f, then ∫ₐᵇ f(x) dx = F(b) - F(a).
What is the property ∫₀ᵃ f(x) dx in terms of f(a - x)?
∫₀ᵃ f(x) dx = ∫₀ᵃ f(a - x) dx (king property of definite integrals).
How is the area between two curves y = f(x) and y = g(x) from x = a to x = b found, where f(x) ≥ g(x)?
Area = ∫ₐᵇ [f(x) - g(x)] dx (upper curve minus lower curve).
What are the order and degree of a differential equation?
The order is the highest order derivative present; the degree is the power of the highest order derivative when the equation is a polynomial in derivatives (free of radicals/fractions in derivatives).
State the general method to solve a first-order linear differential equation dy/dx + Py = Q.
Find the integrating factor I.F. = e^(∫P dx); the solution is y·(I.F.) = ∫ Q·(I.F.) dx + C.
How do you solve a variable separable differential equation?
Rewrite as f(y) dy = g(x) dx so each variable is on its own side, then integrate both sides: ∫f(y) dy = ∫g(x) dx + C.
What is the formula for the dot (scalar) product of two vectors a and b, and what does it equal geometrically?
a·b = |a||b|cos θ, where θ is the angle between them; it is a scalar and equals zero when the vectors are perpendicular.
What is the cross (vector) product a × b and its magnitude?
a × b is a vector perpendicular to both a and b with magnitude |a||b|sin θ; its magnitude equals the area of the parallelogram formed by a and b.
How do you find the projection of vector a on vector b?
Projection of a on b = (a·b)/|b|.
What are the direction cosines of a line, and what relation do they satisfy?
Direction cosines l, m, n are the cosines of the angles the line makes with the x, y, z axes; they satisfy l² + m² + n² = 1.
Write the vector equation of a line passing through point a with direction vector b.
r = a + λb, where λ is a scalar parameter.
What is the equation of a plane in normal form, and what does each term mean?
r·n̂ = d, where n̂ is the unit normal vector to the plane and d is the perpendicular distance of the plane from the origin.
How is the angle between two planes found?
It equals the angle between their normal vectors: cos θ = |n1·n2|/(|n1||n2|).
What is the shortest distance between two skew lines r = a1 + λb1 and r = a2 + μb2?
Shortest distance = |(a2 - a1)·(b1 × b2)| / |b1 × b2|.
State the formula for conditional probability P(A|B).
P(A|B) = P(A ∩ B)/P(B), provided P(B) ≠ 0.
State Bayes' Theorem.
P(Eᵢ|A) = [P(Eᵢ)·P(A|Eᵢ)] / Σ[P(Eⱼ)·P(A|Eⱼ)], where the Eⱼ form a partition of the sample space.
When are two events A and B said to be independent in probability terms?
A and B are independent if P(A ∩ B) = P(A)·P(B), equivalently P(A|B) = P(A).
State the multiplication theorem of probability for two events A and B.
P(A ∩ B) = P(A)·P(B|A) = P(B)·P(A|B).
In linear programming, what is the feasible region and where does the optimal solution occur?
The feasible region is the set of all points satisfying every constraint (including non-negativity). The optimal value of the objective function occurs at a corner (vertex) point of the feasible region (Corner Point Theorem).
What is the difference between a bounded and an unbounded feasible region in LPP regarding optimal solutions?
A bounded feasible region always has both a maximum and a minimum at corner points. An unbounded region may have no maximum (or no minimum); existence must be verified using an open half-plane test.
In optimisation problems, what is the general procedure to find the absolute maximum/minimum of a continuous function on a closed interval [a,b]?
Find critical points where f'(x)=0 or is undefined within [a,b], evaluate f at these points and at the endpoints a and b, then compare values — the largest is the absolute maximum and the smallest the absolute minimum.
In numerical applications, what does the LCM and HCF relationship for two numbers a and b state?
HCF(a,b) × LCM(a,b) = a × b (the product of two numbers equals the product of their HCF and LCM).
What is the rule of allegation (alligation) used for in numerical applications?
It finds the ratio in which two ingredients at different prices/concentrations must be mixed to produce a mixture of a desired mean value: (Quantity cheaper)/(Quantity dearer) = (Dearer price - Mean)/(Mean - Cheaper price).
What is an index number, and how is the simple aggregative price index computed?
An index number measures the relative change in a variable (e.g. price) over time relative to a base period. Simple aggregative price index = (Σ current year prices / Σ base year prices) × 100.
In time-based data, what are the four components of a time series?
Secular trend (long-term direction), seasonal variation (regular short-term periodic), cyclical variation (recurring over years), and irregular/random variation.
In financial mathematics, what is the formula for the future value of an ordinary annuity with payment R, rate i per period, for n periods?
FV = R·[((1 + i)ⁿ - 1)/i], where each payment is made at the end of each period.
In inferential statistics, what is the difference between a population parameter and a sample statistic, and what is a null hypothesis?
A parameter is a numerical characteristic of the whole population (e.g. μ); a statistic is computed from a sample (e.g. x̄) and estimates the parameter. The null hypothesis (H₀) is the default assumption of no effect/no difference that a test seeks to reject or fail to reject.
CUET UG Mathematics FAQ
What is in the CUET UG Mathematics syllabus?
CUET UG Mathematics is split into 5 chapters: Relations, Functions and Algebra, Calculus, Vectors and Three-Dimensional Geometry, Probability and Linear Programming and Applied Mathematics Topics. Together they contain 18 topics and 47 sub-topics.
How many chapters are in CUET UG Mathematics?
5 chapters, containing 18 topics and 47 sub-topics. The largest chapter is Relations, Functions and Algebra, with 4 topics.
Are there flashcards for CUET UG Mathematics?
Yes — a 50-card Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.