## NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.1 - FREE PDF Download

## FAQs on NCERT Solutions for Class 12 Maths Chapter 6 - Application of Derivatives Exercise 6.1

1. What is the Weightage Mark of Chapter 6 in Class 12 Maths?

Out of the total 100 marks for maths, 20 marks are for internal assessments which include midterm marks as well as project work, and 80 marks for the final written paper. There are 35 marks dedicated to the topic calculus in the final written examination. Calculus is spread out over several chapters in both the NCERT maths textbooks of class 12 and chapter 6 is one of these calculus chapters. A part of those 35 marks for calculus includes a few important questions from chapter 6, called “Applications of Derivatives.” From these 35 marks, some marks are awarded for chapter 6.

2. What are the Topics Included in Class 12 Maths Chapter 6?

The topics included in class 12 maths chapter 6 Applications of Derivatives are the various ways in which differentiation and derivatives can be used in real-life ways - this is what 12th maths chapter 6 exercise 6.1 pertains to. The following is the exhaustive list of the topics which come under class 12 maths chapter 6:

A brief introduction and recap of chapter 5.

Rate of change of quantities (applying what we’ve learnt about derivatives to practical examples).

Increasing and decreasing functions.

Tangents and normals.

Approximations.

Maxima and minima concepts.

Several miscellaneous examples of the topics mentioned above for a clearer understanding of the same.

3. What is the Chapter 6 Application of Derivatives of Class 12 Maths?

The application of derivatives is an important chapter of Class 12. In this students learn about the rate of change of quantities, increasing and decreasing functions using graphical methods, Tangents and Normals, Approximations, Maxima and Minima concepts. These topics to be understood in detail to get the proper grip of the subject. This can be best understood with Vedantu’s NCERT solutions where the practice and preparation can be done thoroughly.

4. How many questions are there in Exercise 6.1 of Chapter 6 Application of Derivatives of Class 12 Maths?

There are a total number of 18 questions in Exercise 6.1 of Chapter 6 Application Of Derivatives. Each numericals in the exercise is of a different kind and has to be practised with focus and understanding. These solutions are given systematically in NCERT solutions from Vedantu which has been curated by expert professionals having the depth knowledge of the subject. The solutions are easy to understand and even the complex numericals are solved and shown in a simple manner. Solving all these one can be sure of being thorough with the chapter.

5. An edge of a variable cube is increasing at the rate of 3cm/s. When the edge is 10cm how fast will the volume of the cube increase?

Let x be the edge of the cube and v the volume respectively. We know that the edge of the cube is increasing at 3 cm/sec.

We have to calculate that how fast it would increase when the edge is 10 cm

Let us find dv/dt when x =10 cm

Now, Volume =(Edge)^{3}

V=X^{3}

Now dv/dt=d(x)^{3}/dt

dv/dt=d(x)^{3}/dt x dx/dx

dv/dt=d(x)^{3}/dt x dx/dt

dv/dt=3x^{2}x . dx/dt

dv/dt=3x^{2}x3……………………….(1)

dv/dt=9x^{2}

Now when x=10

Then dv/dtx=10=9(10)^{2}

dv/dt_{x}=10=900

Since volume has to be in cm^{3}/sec

dv/dt=900 cm^{3}/sec

6. What is the weightage of the marks of different questions?

Relation and functions will have a weightage of 8 marks.

Algebra has a weightage of 10 marks.

Calculus has a weightage 35

Vectors and Three-Dimensional Geometry has the weightage14

Linear programming has a weightage of 5 marks.

Probability has a weightage of 8 marks.

The total will be 80.

If the preparation is correct then it's not difficult to score full marks. Practising the numerical regularly is the best method to get the proper hold of the subject.

7. What do you understand about Maxima And Minima concepts?

The maxima and minima is the concept of differential calculus. The maxima and the minima are dealt with by the branch of Mathematics called the calculus of variations. The words maxima and minima mean the maximum and the minimum value respectively. The chapter has many numericals for which conceptual understanding is required. Students can refer to Vedantu’s NCERT solutions for the details of the chapters and the solutions from the exercises. This also contains the extra questions at the end of each chapter for better practice.

8. Why are applications of derivatives important ex 6.1 class 12?

They help in understanding real-world problems involving rates of change and the behavior of functions.

9. How do you find the rate of change using derivatives in application of derivatives class 12 exercise 6.1 ?

The derivative of a function gives the rate of change of the dependent variable with respect to the independent variable.

10. What should I focus on in class 12 ex 6.1?

Focus on understanding how to apply derivatives to find rates of change, and analyze functions' behavior, and practice problems on tangents and normals.

11. How can Vedantu’s solutions help me to solve class 12 maths ch 6 ex 6.1?

Vedantu provides detailed, step-by-step solutions that make complex concepts easier to understand and apply.

12. What are common mistakes to avoid in application of derivatives class 12 exercise 6.1?

In ex 6.1 class 12 it ensure accurate calculation of derivatives and careful application of concepts like increasing/decreasing functions and tangents/normals.