Differential Equations are moderate-weightage topics asked in the JEE Advanced exam 2025. The topic carries an approximate weightage of 3-4% and candidates can expect 2 to 3 questions from this topic in the exam.These concepts are the foundation of calculus and are important for solving complex problems in differentiation, and other advanced topics in mathematics.
Must Read Articles:
- Download JEE Advanced Syllabus 2025
- Download JEE Advanced 2024 Paper With Detailed Solutions
- JEE Advanced Previous Year Question Paper PDF Download
Question 1:
Let f(x) be a continuously differentiable function on the interval (0, ∞) such that f(1) = 2 and
for each x > 0. Then, for all x > 0, f(x) is equal to
Question 2:
For x∈R, let y(x) be the solution of the differential equation (x2−5) dy/dx −2xy=−2x (x2−5)2 such that y(2)=7. Then the maximum value of the function y(x) is
Question 3:
If y(x) is the solution of the differential equation xdy−(y2−4y)dx=0 for x>0,y(1)=2, and the slope of the curve y=y(x) is never zero, then the value of 10y(2) is ____.
Question 4:
For any real numbers α and β, let yα,β(x),x∈R, be the solution of the differential equation
Question 5:
Let b be a nonzero real number. Suppose f:R→R is a differentiable function such that f(0)=1. If the derivative f′ of f satisfies the equation
Question 6:
- 3
- 9
- 16
- 80
Question 7:
Let y(x) be a solution of the differential equation (1+ex)y′+yex=1. If y(0)=2, then which of the following statements is (are) true ?
- y(−4)=0
- y(−2)=0
- y(x) has a critical point in the interval (−1,0)
- y(x) has no critical point in the interval (−1,0)
Question 8:
Consider the family of all circles whose centers lie on the straight line
y=x. If this family of circles is represented by the differential equation
Py"+Qy′+1=0, where P, Q are functions of x,y and y′y (here y′=dydx,y′′=d2ydx2), then which of the following statements is (are) true?
Question 9:
If xdy=y(dx+ydy),y(1)=1 and y(x)>0. Then, y(−3) is equal to
- 3
- 2
- 1
- 0
Question 10:
If y(t) is a solution of (1+t)dydt−ty=1(1+t) Dt/dy −ty=1 and y(0)=−1, then y(1) is equal to
JEE Advanced Exam Pattern 2025
- Mode of the exam: The examination was 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 were 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
Q1. Which type of differential equation questions are most common in JEE Advanced exam 2025?
The type of differential equation questions that are most common in JEE Advanced exam 2025 are the formation of ordinary differential equations, solution of homogeneous differential equations of first order and first degree, separation of variables method, and linear first order differential equations.
Q2. How do I determine the order and degree of a given differential equation?
To determine the order and degree of a differential equation, check the highest order derivative present (i.e. order) and then, after expressing the equation find the power of that highest order derivative.
Q3. What are the most common mistakes students make while solving differential equations?
One of the most common mistakes that students make in mathematics is not understanding the basics. Students focus on memorizing formulas and equations without fully knowing the concepts behind them.
Another mistake is not taking enough time on practice problems. Many students run through practice problems without understanding how and why a particular solution works – this can lead to difficulty in understanding complex questions.
Comments