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RD Sharma Solutions are the most demanded and popular reference material that are used by students of most CBSE schools. Oftentimes a class teacher is unable to finish all chapters and this is where the book will become the holy grail of students. Home practice will be way easier with RD Sharma Solutions as it will take students in the right direction by clarifying their doubts. In the maths syllabus, chapter 12, can get complicated to master. Students can deal with such chapters by using the Class 12 RD Sharma chapter 12 exercise VSA solution.

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**Also Read - **RD Sharma Solution for Class 9 to 12 Maths

- Chapter 12 - Derivative as a Rate Measure -Ex 12.1
- Chapter 12 - Derivative as a Rate Measure -Ex 12.2
- Chapter 12 -Derivative as a rate measure -Ex-FBQ
- Chapter 12 -Derivative as a rate measure -Ex-MCQ
- Chapter 12 -Derivative as a rate measure- Ex-CSBQ

Derivative as a rate measure exercise Very short answer type question 1

Let’s differentiate along time(t)

Initial velocity= velocity at (t=0)

So, the initial velocity of the particle is 9 units/unit time.

Derivative as a rate measure exercise Very short answer type question 2

Now,let S be the surface area of sphere

So,

(because r=2)

Derivative as a rate measure exercise Very short answer type question 3

Of 2cm/sec, x=10cm. Here, x stands for edge.

Area of equilateral triangle .................(1)

Differentiating equation (1) along with time, we get

Let's put the value of x where (x=10 cm)

Derivative as a rate measure exercise Very short answer type question 4

**Answer: ****Hint: **Here we use the basic concept of rate of change of bodies and quantities**Given: **The side of square is increasing at the rate of 0.1cm/sec**Solution: **Let a be side of square

So,

We know about the formula of square perimeter (p)

So

(taking differentiate of a with respect to time)

So, the rate of increase of square’s perimeter is 0.4cm/sec

Derivative as a rate measure exercise Very short answer type question 5

**Answer: ****Hint: **Here, we use basic concept of rate change of bodies and quantities**Given: **The radius of a circle is increasing at the rate of 0.5cm/sec**Solution: ** Let r be the radius of a circle

So,

We know the formula about circumference of circle

(differentiate with respect to t)

So, the rate of increase about circle’s circumference is 3.14 cm/sec.

Derivative as a rate measure exercise Very short answer type question 6

**Answer: ****Hint: **Here, we use basic concept of rate of change of bodies and quantities.**Given: **The side of an equilateral triangle is increasing **Solution: ** Let a be the side of an equilateral triangle is

So,

We know the formula about perimeter of equilateral triangle

(differentiate with respect to time (t))

So, the rate change of the equilateral triangle’s perimeter is 1cm/sec

Derivative as a rate measure exercise Very short answer type question 7

.......................(1)

Surface of sphere is

So, surface of sphere is 1 square/unit

Derivative as a rate measure exercise Very short answer type question 10

In above diagram,the right angled is at B and left angle floor and ladder be

Let at any time ‘t’ AB=x cm and BC=y cm and we know that AC = 500 cm.

So,

Also, it is given that

Also see,

RD Sharma Solutions Class 12 Mathematics Chapter 12 exercise 12.1

RD Sharma Solutions Class 12 Mathematics Chapter 12 exercise 12.2

RD Sharma Solutions Class 12 Mathematics Chapter 12 exercise MCQ

RD Sharma Solutions Class 12 Mathematics Chapter 12 exercise FBQ

The RD Sharma class 12th exercise VSA contain concise answers of utmost importance. In RD Sharma class 12 solution chapter 12 exercise VSA, the questions will cover many important concepts that must be learned by everyone. Using RD Sharma Class 12th exercise VSA solutions, students will be prepared for their exams and even impress their peers by solving homework questions faster and with ease.

RD Sharma Class 12 solution of Derivative as a rate measure exercise VSA will follow the question pattern of NCERT Books and provide accurate answers every time. Since the RD Sharma class 12th exercise VSA has been prepared by experts, students will find some alternative methods of solving problems and add to their existing knowledge. RD Sharma Class 12 Chapter 12 exercise VSA has 10 questions and It includes the following concepts:

Meaning of derivative as a rate measurer

Theorems and remarks on derivative as a rate measurer.

Rate of change of TSA of cylinder, volume of cylinder and many more.

Application based question on derivative as a rate measurer

Benefits of picking RD Sharma Mathematics Solutions from Career360

For the convenience of students, we have provided you with a list of benefits associated with using RD Sharma solutions:-

Affordable option for everyone as it comes free of cost.

Reliable book with accurate answers from experts.

Good for solving homework questions from school.

Great for last minute preparations and revisions at home.

Easy to understand all math steps in solving questions.

RD Sharma class 12th exercise VSA is widely used for Mathematics and has helped many students reach the pinnacle of success. Solving these questions will also improve your chances of finding these questions in your final examinations.

Careers360 is a highly recommended site which has all the latest free copies of RD Sharman solutions. The site has all the maths solutions that you are looking for. You can download everything on a device of your choice and use them to improve your skills. After all, what can be more lucrative than free copies of the best guidebook in the Internet.

RD Sharma Chapter-wise Solutions

Chapter 1: Relations

Chapter 2: Functions

Chapter 3: Inverse Trigonometric Functions

Chapter 4: Algebra of Matrices

Chapter 5: Determinants

Chapter 6: Adjoint and Inverse of a Matrix

Chapter 7: Solution of Simultaneous Linear Equations

Chapter 8: Continuity

Chapter 9: Differentiability

Chapter 10: Differentiation

Chapter 11: Higher Order Derivatives

Chapter 12: Derivative as a Rate Measurer

Chapter 13: Differentials, Errors, and Approximations

Chapter 14: Mean Value Theorems

Chapter 15: Tangents and Normals

Chapter 16: Increasing and Decreasing Functions

Chapter 17: Maxima and Minima

Chapter 18: Indefinite Integrals

Chapter 19: Definite Integrals

Chapter 20: Areas of Bounded Regions

Chapter 21: Differential Equations

Chapter 22 Algebra of Vectors

Chapter 23: Scalar Or Dot Product

Chapter 24: Vector or Cross Product

Chapter 25: Scalar Triple Product

Chapter 26: Direction Cosines and Direction Ratios

Chapter 27 Straight line in space

Chapter 28: The plane

Chapter 29: Linear programming

Chapter 30: Probability

Chapter 31: Mean and variance of a random variable

1. How to clear the doubts in the class 12 mathematics chapter 12 portions?

Students are recommended to utilize the RD Sharma Class 12th books to solve all their doubts on the formulae given in the mathematics chapter 12 portion.

2. Which is the best free study material for Class 12 maths?

RD Sharma solution books for maths is the best free coursebook that students will ever find. The free pdfs of the book can be found online.

3. What makes the RD Sharma book so easy for the class 12 students to follow?

The RD Sharma Class 12th Chapter 12, VSAs contains all the sums in various methods with which they can be solved. therefore, the students find ti easy to use the RD Sharma reference books than the other materials.

4. Can I find RD Sharma solutions books for free?

Free copies of the pdf of RD Sharma books can be downloaded and viewed on the Career360 website. For a physical copy you can ask a friend or print the pdf for a nominal price.

5. Are answers to the RD Sharma Class 12th chapter 12, VSA books accurate?

RD Sharma has employed experts from around the country to write all the answers of the books. Therefore, all the solutions in RD Sharma Class 12th Chapter 12, VSA solutions are accurate and reliable for students to use whenever required.

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Application Date:09 September,2024 - 14 November,2024

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