Functions is part of the JEE Advanced Mathematics syllabus and carries 3% weightage in the JEE Advanced Mathematics Question Paper, generally 1-2 questions are asked from this topic.
Functions are the special case of relation and as said Every function is a relation but every relation is not necessarily a function. It is considered to be easy to moderate with major focus on subtopics such as Types of Functions, Domain & Range, Invertible Functions.
Must Read Articles:
- Download JEE Advanced Question Last 10 year PYQ for Free
- Download JEE 2024 Paper with Detailed Solutions
Listed below the most repeated questions JEE Advanced Previous Year Questions (PYQs) for Functions along with detailed solutions:
Question 1:
Let the function f:R→R be defined by
Then the number of solutions of f (x) = 0 in R is __.
Question 2:
Let f:R→R be a function such that f(x + y) = f(x) + f(y) for all x, y ∈ R, and g:
Question 3:
Let f:R→R be a function defined by
Then which of the following statements is TRUE ?
Question 4:
Question 5:
Let the functions
f:(−1,1)→R and g:(−1,1)→(−1,1) be defined by f(x)=∣2x−1∣+∣2x+1∣ and g(x)=x−[x],
where [x] denotes the greatest integer less than or equal to x.
Let fog : (−1,1)→R be the composite function defined by (fog)(x)=f(g(x)). Suppose c is the number of points in the interval (−1,1) at which fog is NOT continuous, and suppose d is the number of points in the interval (−1,1) at which fog is NOT differentiable. Then the value of c+d is ____
Question 6:
Let f:R→R and g:R→R be functions satisfying f(x+y)=f(x)+f(y)+f(x)f(y) and f(x)=xg(x) for all x,y∈R. If limx→0 g(x)=1, then which of the following statements is/are TRUE?
- f is differentiable at every x∈R
- If g(0)=1, then g is differentiable at every x∈R
- The derivative f′(1) is equal to 1
- The derivative f′(0) is equal to 1
Question 7:
Let S={1,2,3,……,9}. For k=1,2,……,5, let Nk be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N1+N2+N3+N4+N5=
- 210
- 252
- 125
- 126
Question 8:
Let f(x)=sin(π/6sin(π/2sinx)) for all x∈R and g(x)=π/2 sinx for all x∈R. Let (fog)(x) denote f(g(x)) and (gof)(x) denote g(f(x)). Then which of the following is (are) true ?
JEE Advanced Exam Pattern 2025
- Mode of the exam: The examination conducted ONLY in the Computer Based Test (CBT) mode.
- Number of papers: Two question papers: Paper 1 and Paper 2 of three hours duration each. Both papers are compulsory.
- Language: English and Hindi
- Total duration: 6 hours
- Number of sections: Each question paper consisted of three separate sections, viz., Physics, Chemistry and Mathematics.
- Marking scheme: Details of the marking scheme provided in the “Instructions to Candidates” section at the time of examination. The same is also explained further below.
JEE Advanced 2025 Mathematics Syllabus
JEE Advanced Mathematics Syllabus consists of nine units- Sets, Relations and Functions ; Algebra ; Matrices; Probability and Statistics; Trignometry; Analytical Geometry; Differential Calculus ; Integral Calculus and Vectors. Check JEE Advanced 2025 Syllabus
JEE Advanced Mathematics Syllabus according to the seven units is defined below.
| Units | Sub Units |
|---|---|
| Sets, Relations, and Functions | - Sets and their representations, different kinds of sets (empty, finite, and infinite), algebra of sets, intersection, complement, difference, and symmetric difference of sets and their algebraic properties, De-Morgan’s laws on union, intersection, and difference (for finite number of sets), and practical problems based on them.- Cartesian product of finite sets, ordered pair, relations, domain, and codomain of relations, equivalence relation.- Function as a special case of relation, functions as mappings, domain, codomain, range of functions, invertible functions, even and odd functions, into, onto and one-to-one functions, special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer, etc.), sum, difference, product, and composition of functions. |
| Algebra | - Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.- Statement of fundamental theorem of algebra, quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.- Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, sum of the first n natural numbers, sums of squares and cubes of the first n natural numbers.- Logarithms and their properties, permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients. |
| Matrices | - Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, elementary row and column transformations, determinant of a square matrix of order up to three, adjoint of a matrix, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric, and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables. |
| Probability and Statistics | - Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes Theorem, computation of probability of events using permutations and combinations.- Measure of central tendency and dispersion, mean, median, mode, mean deviation, standard deviation, and variance of grouped and ungrouped data, analysis of the frequency distribution with the same mean but different variance, random variable, mean, and variance of the random variable. |
| Trigonometry | - Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.- Inverse trigonometric functions (principal value only) and their elementary properties. |
| Analytical Geometry | - Topics related to coordinate geometry, straight lines, circles, conic sections, and other geometric properties. |
| Differential Calculus | - Concepts of limits, continuity, differentiation, derivatives of functions, application of derivatives, increasing and decreasing functions, maxima and minima. |
| Integral Calculus | - Indefinite and definite integrals, properties of integrals, fundamental theorem of calculus, methods of integration, applications of integration. |
| Vectors | - Vectors and their properties, operations on vectors, scalar and vector products, applications in geometry and physics. |
JEE Advanced Mathematics Chapter-wise Weightage
However, based on the previous year's analysis, the chapters along with the number of questions and marks tabulated below:
| Chapter Name | Number of Questions | Marks |
|---|---|---|
| Application of Derivatives | 3 | 9 |
| Ellipse | 1 | 3 |
| Circles | 2 | 6 |
| Parabola | 2 | 7 |
| Definite Integral | 2 | 7 |
| Permutations and Combinations | 1 | 3 |
| Sequence and Series | 1 | 3 |
| Matrices | 2 | 7 |
| Limit and Continuity | 1 | 4 |
| Probability | 1 | 4 |
| Complex Numbers | 1 | 4 |
| Hyperbola | 1 | 4 |
JEE Advanced - Marks wise Weightage of Topics
| Topics | Marks |
|---|---|
| Calculus | 40-50 marks |
| Vector and 3D Geometry | 15-20 marks |
| Probability & Permutation & Combination | 15-20 marks |
| Parabola, Hyperbola, Ellipse, Rectangular Hyperbola | 15 marks |
| Complex Numbers | 15 marks |
Important Books for Mathematics:
JEE Advanced 2024 Question Paper PDF with Solutions
| Paper Name | Question Paper Link | Solutions Link |
|---|---|---|
| JEE Advanced 2024 Paper 1 Question Paper (English) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 2 Question Paper (English) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 1 Question Paper (Hindi) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 1 Question Paper (Hindi) | Download PDF | Check Solutions |
JEE Advanced Last 5 Year Mathematics Papers Pdf
Download free JEE Advanced Previous Year Question Paper PDFs from the table provided below:-
| JEE Advanced Paper Name | Question Paper Link |
|---|---|
| JEE Advanced 2024 Question Paper PDF | Click Here |
| JEE Advanced 2023 Question Paper PDF | Click Here |
| JEE Advanced 2022 Question Paper PDF | Click Here |
| JEE Advanced 2021 Question Paper PDF | Click Here |
| JEE Advanced 2020 Question Paper PDF | Click Here |
| JEE Advanced 2019 Question Paper PDF | Click Here |
| JEE Advanced 2018 Question Paper PDF | Click Here |
| JEE Advanced 2017 Question Paper PDF | Click Here |
| JEE Advanced 2016 Question Paper PDF | Click Here |
JEE Advanced 2023 Question Paper PDF Download With Solutions
| Paper | Question Paper PDF | Answer Key PDF |
|---|---|---|
| Question Paper 1 PDF | Download PDF | Check Solutions |
| Question Paper 2 PDF | Download PDF | Check Solutions |
| Question Paper AAT PDF | Download PDF | Check Solutions |
JEE Advanced 2022 Question Paper
| 2022 Question Paper | PDF Download |
|---|---|
| Question Paper 1 PDF | Click here |
| Question Paper 2 PDF | Click here |
JEE Advanced 2021 Question Paper
| Question Paper | PDF Download | ||
|---|---|---|---|
| Question Paper 1 PDF | Physics | Chemistry | Maths |
| Question Paper 2 PDF | Physics | Chemistry | Maths |
JEE Advanced 2020 Question Paper
| Question Paper | PDF Download |
| Question Paper 1 PDF | Click here |
| Question Paper 2 PDF | Click here |
Frequently Asked Questions
What is Relation and Function?
A relation is a set of ordered pairs that describes a relation between two sets whereas a function is a specific type of relation where each input (x value) corresponds to only one output (y value).
What is Function and its types?
A function is a special class of relation. There are several types of functions :
- One – one function (Injective function)
- Many – one function
- Onto – function (Surjective Function)
- Into – function
- Polynomial function
- Linear Function
- Identical Function
- Quadratic Function
- Rational Function
- Algebraic Functions
- Cubic Function
- Modulus Function
- Greatest Integer Function
- Fractional Part Function
- Even and Odd Function
- Periodic Function
- Composite Function
- Constant Function
- Identity Function
What is a function in mathematics?
In mathematics, a function from a set X to a set Y means that each element of X is assigned to exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
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