Class 11 Mathematics — Chapter 13: Limits and Derivatives
67 practice questions · 22 Easy · 22 Medium · 23 Hard
Practise Class 11 Mathematics Chapter 13, "Limits and Derivatives", with 67 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 22 Medium and 23 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.
"Limits and Derivatives" 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 Limits and Derivatives, 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 11 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 67.
Key concepts: Limits and Derivatives (Class 11 Mathematics)
This chapter introduces the limit of a function, standard limits, and the derivative as the limit of a difference quotient with basic differentiation rules.
- Limit
- lim(x→a) f(x) is the value f(x) approaches as x → a; left- and right-hand limits must agree for the limit to exist.
- Standard limits
- e.g. lim(x→0) (sin x)/x = 1 and lim(x→0)(e^x − 1)/x = 1 are used repeatedly.
- Derivative (first principles)
- f'(x) = lim(h→0) [f(x+h) − f(x)]/h — the instantaneous rate of change.
- Rules of differentiation
- Sum, difference, product and quotient rules, and the power rule d/dx(xⁿ) = nx^(n−1).
- Derivatives of standard functions
- Polynomials, trigonometric and basic functions have standard derivatives.
Key formulas — Limits and Derivatives
💡 Exam tips for Limits and Derivatives
- For a limit to exist, the left-hand and right-hand limits must be equal.
- Memorise the standard limits (sinx/x, (eˣ−1)/x) — they unlock most limit problems.
Sample questions
d/dx (xⁿ) =
Power rule.
lim(x→0) (sin x)/x =
Standard limit.
d/dx (uv) =
Product rule.
Limits and Derivatives — FAQs
What are the key concepts in Class 11 Mathematics Limits and Derivatives?+
This chapter introduces the limit of a function, standard limits, and the derivative as the limit of a difference quotient with basic differentiation rules. Key ideas include Limit, Standard limits, Derivative (first principles), Rules of differentiation, Derivatives of standard functions.
What does Class 11 Mathematics Chapter 13 (Limits and Derivatives) cover on XamBaaz?+
It covers 67 NCERT-aligned MCQs on "Limits and Derivatives" — 22 Easy, 22 Medium and 23 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams, JEE Main and JEE Advanced.
Are these "Limits and Derivatives" questions free to practise?+
Yes — sign in with Google to practise "Limits and Derivatives" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Limits and Derivatives" 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 67 questions free
Timed quizzes, instant scoring, streaks and XP. Sign in with Google — no card needed.
Start this chapter free →