Class 12 Mathematics — Chapter 9: Differential Equations
66 practice questions · 22 Easy · 22 Medium · 22 Hard
Practise Class 12 Mathematics Chapter 9, "Differential Equations", with 66 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 22 Medium and 22 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams, JEE Main and JEE Advanced.
"Differential Equations" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Differential Equations, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 12 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 66.
Key concepts: Differential Equations (Class 12 Mathematics)
This chapter defines differential equations and their order and degree, and solves first-order equations by variable separation and the linear (integrating-factor) method.
- Order and degree
- Order is the highest derivative present; degree is the power of the highest-order derivative (after removing radicals/fractions).
- General & particular solution
- The general solution contains arbitrary constants; a particular solution fixes them using given conditions.
- Variable separable
- If dy/dx = g(x)h(y), separate as dy/h(y) = g(x)dx and integrate both sides.
- Homogeneous equations
- If dy/dx = F(y/x), substitute y = vx to reduce it to a separable equation.
- Linear differential equation
- For dy/dx + Py = Q, the integrating factor IF = e^∫P dx gives the solution y·IF = ∫Q·IF dx + C.
Key formulas — Differential Equations
💡 Exam tips for Differential Equations
- Identify the type first: separable, homogeneous, or linear — each has its own method.
- For a linear equation, write it in the standard form dy/dx + Py = Q before finding the integrating factor.
Sample questions
Order of d²y/dx² + dy/dx + y = 0:
Highest derivative is 2nd.
Linear DE dy/dx + Py = Q has integrating factor:
Multiply by IF to integrate.
A homogeneous DE is solved by substitution:
Reduces to separable in v.
Differential Equations — FAQs
What are the key concepts in Class 12 Mathematics Differential Equations?+
This chapter defines differential equations and their order and degree, and solves first-order equations by variable separation and the linear (integrating-factor) method. Key ideas include Order and degree, General & particular solution, Variable separable, Homogeneous equations, Linear differential equation.
What does Class 12 Mathematics Chapter 9 (Differential Equations) cover on XamBaaz?+
It covers 66 NCERT-aligned MCQs on "Differential Equations" — 22 Easy, 22 Medium and 22 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams, JEE Main and JEE Advanced.
Are these "Differential Equations" questions free to practise?+
Yes — sign in with Google to practise "Differential Equations" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Differential Equations" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Practise all 66 questions free
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