Chapter 5 of NCERT Class 12 Mathematics is titled Continuity and Differentiability. This chapter lays the foundation for understanding the behavior of functions in calculus. The concept of continuity deals with the smoothness of a function, while differentiability ensures that a function can be represented by its slope at any point in its domain. Together, these concepts are essential for solving problems in both the theoretical and practical aspects of calculus.
In this article, we provide a collection of MCQs and subjective questions for Class 12 Mathematics Chapter 5: Continuity and Differentiability. The resources cover sample questions for both CBSE and CUET, alongside downloadable PDFs that include a complete set of MCQs and previous years' questions.
|
NCERT Class 12 Mathematics Chapters
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Class 12 Mathematics Chapter 5 MCQs
The following MCQs for Class 12 Mathematics Chapter 5: Continuity and Differentiability have been carefully selected to help students practice key concepts. For the full set of 50 questions, download the PDF via the link provided below.
|
1.
|
The value of k for which f(x) = is a continuous function, is : |
|
2.
|
For what value of k may the function f(x) = become continuous? (a) 0 (b) 1 (c) (d) No value |
|
3.
|
The function f(x) = [x], where [x] denotes the greatest integer less than or equal to x, is continuous at
(a) x = 1 (b) x = 1.5 (c) x = -2 (d) x = 4
|
|
4.
|
If tan = 𝑘, then is equal to: |
|
5.
|
The value of k for which function f(x) = is differentiable at x = 0 is : (a) 1 (b) 2 (c) any real number (d) 0
|
CUET Free Master Classes:
Class 12 Mathematics Chapter 5 Subjective Questions Without Solutions
This section provides subjective questions for practice, including previous years' CBSE subjective questions (2 marks and above), along with expert-curated questions. Below are 5 sample subjective questions for Class 12 Mathematics Chapter 5: Continuity and Differentiability. For the full set, download the PDF via the link provided below.
|
1.
|
Find the value(s) of ‘λ’, if the function f(x) = |
|
2.
|
Find the value of k for which the function f given as f(x) = is continuous at x = 0. |
|
3.
|
If y = (x + )2, then show that (x2 - 1) = 4y 2. |
|
4.
|
If f (𝑥) = is a differentiable function in (0, 2), then find the values of 𝑎 and 𝑏. |
|
5.
|
If (x 2 + y 2) 2 = xy, then find |
NCERT Mathematics Topics
|
Chapter Name
|
Sub Topics
|
|
Chapter 5: Continuity and Differentiability
|
5.1 Introduction to Continuity and Differentiability
|
|
5.2 Continuity of a Function
|
|
5.3 Differentiability of a Function
|
|
5.4 Chain Rule of Differentiation
|
|
5.5 Differentiability and Continuity at a Point
|
|
5.6 Applications of Continuity and Differentiability
|
|
5.7 Theorems Related to Differentiability and Continuity
|
Review of NCERT Class 12 Mathematics Chapter 5
Chapter 5: Continuity and Differentiability plays a crucial role in the understanding of calculus, focusing on the continuity and differentiability of functions. The chapter introduces two core ideas in calculus that ensure a function behaves predictably and smoothly: continuity ensures there are no jumps or breaks in the function, while differentiability guarantees the function has a defined slope at any given point in its domain. The chapter covers key results like the continuity and differentiability at a point, the chain rule, and various conditions under which a function can be continuous or differentiable.
This chapter is vital for higher studies in calculus, physics, engineering, and economics, where continuous changes are analyzed. Mastery of this chapter provides a strong foundation for solving complex problems in real analysis and mathematical modeling.