NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability
Welcome to Myclass24's NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability. These solutions are prepared to help Class 12 students understand each problem clearly and build the confidence needed for CBSE board examinations. Whether you're revising at the last minute or studying systematically, you'll find these solutions accurate, easy to follow, and aligned with the NCERT textbook.
Summary of Chapter 5 Continuity and Differentiability
Limit, Continuity and Differentiability-Limits, Indeterminate forms, Evaluation of limit’ Hospital rule. Continuity, Definition, Differentiability: Definition, LHD, RHD, Chain rule, Differentiation of composite, Implicit, Inverse Trigonometric function, Differentiation of logarithmic, Parametric forms, Implicit, Inverse Trigonometric function, Differentiation of logarithmic, Parametric forms,2nd Order derivative, Rolle's theorem, LMVT, Examples, Functional equations and assignment discussion.
Find the PDF of NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability
The PDF of NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability is available on Myclass24. Students can refer to it chapter-wise for quick revision or download it for offline use. The solutions in the PDF are written in a clear format that makes it easy to revise during exam preparation.
Chapter 5 – Continuity and Differentiability: Quick Overview
| Detail | Information |
| Chapter Number | Chapter 5 |
| Chapter Name | Continuity and Differentiability |
| Subject | Mathematics |
| Class | Class 12 |
| Board | CBSE (NCERT) |
| Total Exercises | 8 Exercises + Miscellaneous |
| Key Topics | Continuity, Differentiability, Chain Rule, Implicit Differentiation, Logarithmic, Parametric, Second Order Derivatives, Rolle's and MVT |
| Difficulty Level | High |
| Marks Weightage | Approx. 12-14 marks in board exams |
About NCERT Solutions for Class 12 Maths Chapter 5 – Continuity and Differentiability
Chapter 5 is widely considered one of the most important and most challenging chapters in the entire Class 12 Maths syllabus. It carries a very high marks weightage in board exams and also forms the backbone of calculus for competitive exams. Students who invest time in this chapter consistently see a significant improvement in their overall maths scores.
The chapter begins with continuity. A function is continuous at a point if the limit of the function at that point equals the function's value there. The chapter explores continuity of composite functions, the sum, product, and quotient of continuous functions, and deals with checking continuity at points where functions are defined piecewise.
Key Concepts in Chapter 5
Differentiability comes next. A function that is differentiable at a point is also continuous there, but the converse is not always true. Students learn to test differentiability at specific points and to understand why certain functions like |x| are continuous but not differentiable at x = 0.
The chain rule for differentiation is one of the most used tools in this chapter. It allows students to differentiate composite functions, and once this is understood, topics like implicit differentiation and parametric differentiation follow naturally. Implicit differentiation involves finding dy/dx when y is not expressed explicitly in terms of x, and this is a very common board exam question type.
Differentiation of exponential and logarithmic functions is covered thoroughly. The technique of logarithmic differentiation is introduced for functions like x^x or complicated products and quotients, where direct differentiation would be very messy. This is an area where students often lose marks due to algebraic errors, and Myclass24 solutions provide clean, step-by-step working.
Inverse trigonometric functions from Chapter 2 reappear here in the context of differentiation. Derivatives like d/dx[sin⁻¹(x)] = 1/√(1-x²) need to be memorised and applied. The chapter also covers second-order derivatives and concludes with two important theorems: Rolle's Theorem and the Mean Value Theorem (MVT).
Exercise-wise Overview
This chapter has eight exercises plus a miscellaneous exercise.
Exercise 5.1 (34 questions) deals with continuity.
Exercises 5.2 to 5.6 progressively cover differentiability, the chain rule, implicit, exponential, logarithmic, and parametric differentiation.
Exercise 5.7 covers second-order derivatives.
Exercise 5.8 has questions on Rolle's and MVT.
The Miscellaneous Exercise contains 23 problems combining all the methods from the chapter.
Given the breadth and difficulty of this chapter, having reliable NCERT solutions is essential. Myclass24 solutions for Chapter 5 are crafted to match the exact level of detail expected in CBSE board exams, helping students understand not just the 'how' but also the 'why' behind each differentiation technique.
NCERT Solutions for Class 12 Maths Chapter 4 – Determinants FAQs
A determinant is a numerical value associated with a square matrix that helps in solving various mathematical problems. It is represented using vertical bars around a matrix and plays a significant role in algebra and coordinate geometry. In Chapter 4, students learn how determinants are evaluated and applied to solve equations. NCERT exercises focus on properties, expansion methods, and applications of determinants. Understanding determinants is important because they help determine whether a matrix is invertible and are widely used in solving systems of linear equations. A strong understanding of this concept makes many advanced mathematical topics easier to understand.
Evaluating determinants is one of the most common topics in this chapter. For a determinant of order 2, students apply a simple formula involving cross multiplication and subtraction. For a determinant of order 3, methods such as expansion along a row or column are used. Many students make mistakes in sign conventions while expanding determinants. NCERT exercises provide numerous examples that help develop accuracy in calculations. Practising step-by-step evaluation is essential because determinants appear repeatedly throughout the chapter. Once students understand the expansion process correctly, solving larger determinant-based problems becomes much more manageable and less time-consuming.
Determinants have several useful properties that simplify calculations and help solve complex problems efficiently. For example, interchanging two rows or columns changes the sign of the determinant, while multiplying a row or column by a constant multiplies the determinant by the same factor. If two rows or columns are identical, the determinant becomes zero. NCERT questions frequently test these properties directly and indirectly. Understanding them helps students avoid lengthy calculations and recognise shortcuts during examinations. Regular practice with determinant properties improves problem-solving skills and enables students to tackle challenging questions with greater confidence and accuracy.
One of the practical applications covered in this chapter is finding the area of a triangle using determinants. When the coordinates of the three vertices are given, a determinant can be formed and evaluated to calculate the area. This method provides a systematic approach and is commonly asked in board examinations. Students must carefully substitute coordinate values into the determinant and apply the formula correctly. NCERT exercises include several examples that demonstrate this application. Understanding this concept not only strengthens determinant skills but also helps students connect algebraic methods with coordinate geometry, making mathematical concepts more meaningful and interconnected.
Determinants are widely used to solve systems of linear equations through methods such as Cramer's Rule. This technique involves forming determinants from the coefficients of the equations and comparing their values to obtain the solution. Students often encounter questions where they must determine whether a system has a unique solution, no solution, or infinitely many solutions. NCERT exercises help students understand how determinant values influence these outcomes. Learning this application is important because it demonstrates the practical usefulness of determinants beyond simple calculations. Consistent practice helps students solve equation-based problems accurately and strengthens their overall mathematical reasoning skills.