Class 12 Mathematics — Chapter 5: Continuity and Differentiability
66 practice questions · 22 Easy · 22 Medium · 22 Hard
Practise Class 12 Mathematics Chapter 5, "Continuity and Differentiability", 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.
"Continuity and Differentiability" 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 Continuity and Differentiability, 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: Continuity and Differentiability (Class 12 Mathematics)
This chapter extends differentiation to continuity, the chain rule, implicit, logarithmic and parametric differentiation, and states Rolle's and the Mean Value Theorems.
- Continuity
- f is continuous at x = a if lim(x→a) f(x) = f(a). A function is continuous on an interval if continuous at every point.
- Differentiability
- Differentiability at a point implies continuity there, but continuity does not imply differentiability (e.g. |x| at 0).
- Chain rule
- If y = f(u) and u = g(x), then dy/dx = (dy/du)(du/dx).
- Special differentiation
- Implicit (differentiate both sides), logarithmic (take log first for products/powers) and parametric (dy/dx = (dy/dt)/(dx/dt)).
- Mean Value Theorems
- Rolle's theorem and Lagrange's MVT relate the derivative to the average rate of change on a closed interval.
Key formulas — Continuity and Differentiability
💡 Exam tips for Continuity and Differentiability
- Use logarithmic differentiation for functions of the form [f(x)]^{g(x)}.
- Remember: differentiable ⇒ continuous, but the converse is false.
Sample questions
All polynomials are continuous on:
Polynomials are continuous everywhere.
d/dx [f(g(x))] =
Chain rule.
Mean Value Theorem: there exists c in (a,b) such that:
Connects average and instantaneous rates.
Continuity and Differentiability — FAQs
What are the key concepts in Class 12 Mathematics Continuity and Differentiability?+
This chapter extends differentiation to continuity, the chain rule, implicit, logarithmic and parametric differentiation, and states Rolle's and the Mean Value Theorems. Key ideas include Continuity, Differentiability, Chain rule, Special differentiation, Mean Value Theorems.
What does Class 12 Mathematics Chapter 5 (Continuity and Differentiability) cover on XamBaaz?+
It covers 66 NCERT-aligned MCQs on "Continuity and Differentiability" — 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 "Continuity and Differentiability" questions free to practise?+
Yes — sign in with Google to practise "Continuity and Differentiability" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Continuity and Differentiability" 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.
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