Most Important Differential Equations Questions for 2025–26 Students
Differential Equations is a foundational chapter in JEE Maths, testing your grasp on first and second order ODEs, integrating factors, and modeling real-world problems mathematically. Conquering this topic is crucial for scoring in the calculus section and to build logical problem-solving skills for the JEE Main exam. Take this mock test to solidify your concepts and get exam-ready!
Mock Test Instructions for the Differential Equations Mock Test 1:
- 20 questions from Differential Equations
- Time limit: 20 minutes
- Single correct answer per question
- Correct answers appear in bold green after submission
How Can JEE Mock Tests Help You Master Differential Equations?
- Identify your strengths and weaknesses in solving first and second order ODEs through regular practice.
- Use mock tests to practice the application of integrating factors and variable separable methods efficiently.
- Increase familiarity with JEE-style MCQs on forming and solving differential equations from word problems.
- Improve your speed in recognizing linear, separable, and exact equations commonly asked in JEE.
- Get instant feedback to revise error-prone concepts, boosting confidence before the exam.
Sharpen Problem-Solving in Differential Equations with Expert-Designed JEE Mock Tests
- Practice questions modeled on previous year papers to match the latest JEE trend.
- Refine your understanding of initial value and boundary value problems with time-bound tests.
- Solve mixed-difficulty problems to learn the right approach for tricky differential equations questions.
- Mock tests help perfect the application of general and particular solutions in real-world contexts.
- Enhance retention of essential formulas with regular exposure to concept-based MCQs.
Subject-Wise Excellence: JEE Main Mock Test Links
| S.No. | Subject-Specific JEE Main Online Mock Tests |
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| 1 | Online FREE Mock Test for JEE Main Chemistry |
| 2 | Online FREE Mock Test for JEE Main Maths |
| 3 | Online FREE Mock Test for JEE Main Physics |
Important Study Materials Links for JEE Exams
FAQs on Differential Equations Mock Test 2025–26: Practice for Exam Success
1. What is a differential equation?
A differential equation is a mathematical equation that involves derivatives of a function. It shows how a function changes and is commonly used to express physical laws and phenomena. Differential equations can be classified as ordinary differential equations (ODEs) or partial differential equations (PDEs) depending on whether they involve derivatives with respect to one or multiple variables.
2. What are linear equations?
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. Linear equations can be written in the form ax + b = 0, and their graphs are always straight lines. They are fundamental in topics like coordinate geometry and algebra.
3. What is the general solution of a first-order linear differential equation?
A first-order linear differential equation has the form dy/dx + P(x)y = Q(x). Its general solution is given by y(x) = [∫Q(x)μ(x)dx + C]/μ(x), where μ(x) = e^{∫P(x)dx} is called the integrating factor.
4. How can we check if a differential equation is linear?
A differential equation is linear if the dependent variable and its derivatives appear to the power of one and are not multiplied together. There should be no products or nonlinear functions of the dependent variable or its derivatives.
5. How many solutions can a linear equation in one variable have?
A linear equation in one variable typically has one unique solution. However, if both sides are identical, it can have infinitely many solutions, and if there is no possibility of equality, it has no solution.
6. What is a system of linear equations?
A system of linear equations is a set of two or more linear equations that have the same variables. The solution to the system is the set of values that satisfy all equations simultaneously. Systems can be solved by substitution, elimination, or graphical methods.
7. What are the types of solutions for a pair of linear equations in two variables?
A pair of linear equations in two variables can have:
- One unique solution (lines intersect at a point)
- No solution (lines are parallel)
- Infinitely many solutions (lines coincide)
8. Write the standard form of a linear equation in two variables.
The standard form of a linear equation in two variables is ax + by + c = 0, where a, b, and c are constants and x, y are variables.
9. What methods are used to solve linear equations in two variables?
The main methods to solve linear equations in two variables are:
- Graphical method (plotting lines and finding intersection)
- Substitution method
- Elimination method
10. What is the integrating factor in a first-order linear differential equation?
An integrating factor (I.F.) is a function, usually denoted by μ(x) = e^{∫P(x)dx}, that is multiplied with both sides of a linear differential equation to make it easier to integrate and find the general solution.
11. What is the difference between homogeneous and non-homogeneous linear equations?
A homogeneous linear equation has all terms containing variables or their derivatives and equals zero (e.g., ax + by = 0). A non-homogeneous equation has a nonzero constant term on one side (e.g., ax + by = c, where c ≠ 0).
12. How are differential equations used in real-life applications?
Differential equations are widely used to model real-world problems such as population growth, radioactive decay, motion of objects, electrical circuits, spread of diseases, and many more. They help describe how quantities change over time or with respect to other variables.
