Chapter test · Mathematics · Class 12

Limits, Continuity and Differentiability

This test asks up to 25 questions on the real pattern and marking, and hands you a concept-by-concept report the moment you finish. It covers 3 key concepts: Continuity, Differentiability and advanced derivatives and Applications of derivatives.

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Questions

Up to 25 — 20 MCQ + 5 numerical

Time

60 minutes, fixed

Marking

JEE Main: +4 / −1 on A, +4 / 0 on B

Class

Class 12 · Mathematics

Report

Concept breakdown + cognitive demand, instantly

What this test covers

3 key concepts, tested the way the exam tests them.

Mapped from EduPeak’s learning framework for this chapter — the same map your report scores you against.

1
Continuity
- Tests continuity of functions at a point and over intervals, including piecewise cases.Apply & Analyse
2
Differentiability and advanced derivatives
- Tests differentiability and differentiates composite, implicit, parametric and logarithmic forms.Apply & Analyse
3
Applications of derivatives
- Applies derivatives to rate of change, monotonicity and maxima-minima.Apply & Analyse

Level of thinking demanded3 learning objectives

Recall & understandingApply & AnalyseHigher-order

This chapter is tested mostly at the Apply & Analyse level.

In your board

Where this chapter sits in your syllabus.

The same EduPeak test, found under your own textbook’s chapter name.

CBSE
Limits and Derivatives · Continuity and Differentiability · Application of Derivatives
✓ in your syllabus
Gujarat (GSEB)
Limits and Derivatives · Continuity and Differentiability · Application of Derivatives
✓ in your syllabus
Madhya Pradesh (MPBSE)
Limits and Derivatives · Continuity and Differentiability · Application of Derivatives
✓ in your syllabus
Rajasthan (RBSE)
Limits and Derivatives · Continuity and Differentiability · Application of Derivatives
✓ in your syllabus
Bihar (BSEB)
Unit-V Elements of Calculus · Unit-III Calculus — Differentiability · Unit-III Calculus — Applications of Derivatives
✓ in your syllabus
Uttar Pradesh (UPMSP)
कलन - सीमा तथा अवकलज / Limits and Derivatives · कलन - सांतत्य तथा अवकलनीयता / Continuity and Differentiability · कलन - अवकलनों के अनुप्रयोग / Applications of Derivatives
✓ in your syllabus
ISC (CISCE)
Calculus - Limits and Derivatives · Calculus - Continuity, Differentiability and Differentiation · Calculus - Applications of Derivatives
✓ in your syllabus
Cambridge International A Level
Differentiation (P1 · P3)
✓ in your syllabus
IB Diploma Programme (HL)
SL 5.1 Introduction to the concept of a limit (Topic 5: Calculus) · SL 5.2 Increasing and decreasing functions (Topic 5: Calculus) · SL 5.3 Derivative of ax^n; differentiation from first principles (Topic 5: Calculus) · SL 5.4 Tangents and normals at a given point (Topic 5: Calculus) · SL 5.6 Derivatives of x^n, sin, cos, e^x, ln x; chain, product, quotient rules (Topic 5: Calculus) · SL 5.7 The second derivative (Topic 5: Calculus) · SL 5.8 Local maximum and minimum points; optimisation (Topic 5: Calculus) · SL 5.9 Kinematic problems: displacement, velocity, acceleration (Topic 5: Calculus) · AHL 5.12 Continuity and differentiability; higher derivatives (Topic 5: Calculus) · AHL 5.13 Limits and L'Hopital's rule (Topic 5: Calculus) · AHL 5.14 Implicit differentiation; related rates (Topic 5: Calculus) · AHL 5.15 Derivatives of tan, sec, cosec, cot, a^x, log_a x, arcsin, arccos, arctan (Topic 5: Calculus)
✓ in your syllabus

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Try one

A sample question from this chapter.

Drawn fresh from the chapter’s bank on every visit. Reveal the worked solution when you are ready — the way your report explains every question.

SampleMathematics· MCQ+4 / -1

Let

g (x)

be a linear function and

f (x) = ⎩ ⎨ ⎧ g (x), (\frac{1 + x}{2 + x})^{1/ x}, x \leq 0 x > 0

be continuous at

x = 0

. If

f^{'} (1) = f (- 1)

, then the value

g (3)

is:

A. $lo g_{e} (\frac{4}{9}) - 1$
B. $lo g_{e} (\frac{4}{9 e ^{1/3}})$
C. $\frac{1}{3} lo g_{e} (\frac{4}{9}) + 1$
D. $\frac{1}{3} lo g_{e} (\frac{4}{9 e ^{1/3}})$

Worked, step by step — the way your report explains every question. Loads on request.

In the real test, every question is fresh from the chapter’s bank — and your report shows the worked solution for each one.

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Related Class 12 Mathematics chapters

Sets, Relations and Functions Matrices and Determinants Integral Calculus Differential Equations Three Dimensional Geometry Vector Algebra

Good to know

About this chapter test

How is the test scored?

Exactly like JEE Main: +4 for a correct answer, −1 for a wrong MCQ, and no negative marking on numericals. Your total, pacing and concept-by-concept accuracy appear in your report the moment you submit.

Which class is Limits, Continuity and Differentiability in?

Limits, Continuity and Differentiability sits in Class 12 Mathematics here. Pick your class when you start — the whole chapter list is organised the same way.

Can I take it more than once?

Yes — each attempt draws from the chapter’s bank, and your report tracks your best and your progress across attempts.

Is it free?

Free chapter tests are included with every account, and each one comes with the complete report. No card needed to start.

25 questions. 60 minutes. One honest answer.

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