RD Sharma Solutions Class 12 Mathematics Chapter 13 VSA

Edited By Satyajeet Kumar | Updated on Jan 27, 2022 10:01 AM IST

Students in class 12 will have to face tough competition in their board exams. Due to the minimal time, it becomes almost impossible for them to complete the syllabus and understand all the concepts clearly. Hence, students are recommended to use the RD Sharma class 12th exercise VSA solutions for their home practice. RD Sharma Solutions It will help them to improve their performance and enhance their math skills. Everyone knows that RD Sharma class 12 chapter 13 exercise VSA is the top choice of students who have scored high in their board exams.
The 13th chapter of the NCERT recommended Mathematics Textbook has Differentials, Errors, and Approximations which is a complex topic. The concepts that are covered in this section are Absolute error, Relative error, Percentage error. It will also talk about the Geometrical meaning of differentials and many more. The exercise VSA in the book and the RD Sharma class 12 chapter 13 exercise VSA contain six questions based on the entire chapter.

JEE Main 2025: Sample Papers | Mock Tests | PYQs | Study Plan 100 Days

JEE Main 2025: Maths Formulas | Study Materials

JEE Main 2025: Syllabus | Preparation Guide | High Scoring Topics

This Story also Contains

RD Sharma Class 12 Solutions Chapter 13 VSA Differentials, Errors and Approximations - Other Exercise
Differentials, Errors and Approximations Excercise: VSA
RD Sharma Chapter wise Solutions

RD Sharma Class 12 Solutions Chapter 13 VSA Differentials, Errors and Approximations - Other Exercise

Differentials, Errors and Approximations Excercise: VSA

Differentials Errors and Approximations exercise very short answer question 1

Answer: 2
Hint: Here we use this below formula,

Δ y = F (x + Δ x) - F (x)

Given:

\begin{aligned} y = x^{2} \\ x = 10 and Δ x = 0.1 \end{aligned}

Solution:

\begin{aligned} y = x^{2} \\ and Δ x = 0.1 \end{aligned}

Let’s take Differentiate of y

\begin{aligned} y = x^{2} \\ \frac{d y}{d x} = 2 x \end{aligned}

\begin{aligned} \Rightarrow (\frac{d y}{d x}) = 2 \times 10 (x = 10) (given) \\ \Rightarrow Δ y = d y = \frac{d y}{d x} \times Δ x = 20 \times 0.1 = 2 (d x = Δ x = 0.1) (Given) \end{aligned}

Differentials Errors and Approximations exercise very short answer question 2

Answer: 0.01
Hint: Here we use basic formula,

Δ y = d y = \frac{d y}{d x} \times d x

Given:

\begin{aligned} x = 3, Δ x = 0.03 \\ y = \log_{e} x \end{aligned}

Solution:
For

\begin{aligned} x = 3 \\ y = \log_{e} 3 \end{aligned}

Also,

\frac{d y}{d x} = \frac{1}{x}

So,

{(\frac{d y}{d x})}_{x = 3} = \frac{1}{3} Δ y = d y = \frac{d y}{d x} \times Δ x Δ y = \frac{1}{3} \times 0.03 Δ y = 0.01

So, our answer is 0.01

Differentials Errors and Approximations exercise very short answer question 3

Answer:

2 α (2 alpha)

Hint:
Here, we use the concept of approximation.
Given:
Relative error in measuring the radius of circular plan is

α

.
Solution:
Let

x

be the radius and

y

be the area of the circular plan.
We have,

\begin{aligned} \frac{Δ x}{x} = α and y = x^{2} \\ \frac{d y}{d x} = 2 x \frac{Δ y}{y} = \frac{2 x}{y} Δ x = \frac{2 x}{x^{2}} Δ x \end{aligned}

\frac{Δ y}{y} = 2 α

[∵ \frac{d (x^{n})}{d x} = n x^{n - 1}]

Hence the relative error in the area of the circular plan is

2 α

Differentials Errors and Approximations exercise very short answer question 4

Answer:

3 α

Hint:

Here we use the basic concept of approximation.

Given:
The percentage error in radius of sphere is

α

Solution:
Let

V

be the volume of the sphere

V = \frac{4}{3} π r^{3}

let radius

r = x

We have,

\frac{Δ x}{x} \times 100 = α

After differentiating,

\begin{aligned} \frac{d V}{d x} = 4 π x^{2} \\ \frac{d V}{V} = \frac{4 π x^{2}}{V} d x \end{aligned}

\begin{aligned} \frac{Δ V}{V} = \frac{4 π x^{2}}{\frac{4}{3} π x^{3}} \times \frac{x α}{100} \\ \frac{Δ V}{V} \times 100 = 3 α \end{aligned}

Hence, the percentage error in volume of sphere is

3 α

Differentials Errors and Approximations exercise very short answer question 5
Answer: $3 a$

Hint:
Here we use basic formula of cube,

V = x^{3}

Given:
The percentage error in the edge of cube is

a

Solution:
Let

x

be the side and

V

be the volume of the cube

V = x^{3}

We have,

\frac{Δ x}{x} \times 100 = a

\frac{d V}{d x} = 3 x^{2}

\frac{Δ V}{V} = \frac{3 x^{2}}{V} \times Δ x

\frac{Δ V}{V} = \frac{3 x^{2}}{x^{3}} \times \frac{Δ x}{100}

\frac{Δ V}{V} \times 100 = 3 a

[∵ \frac{d (x^{n})}{d x} = n x^{n - 1}]

Hence, the percentage error in volume of cube is

3 a

Differentials Errors and Approximations exercise very short answer question 6

Answer: $F (2.1) = 9.2$
Hint: Here we use this below formula,
$F (x + Δ x) = F (x) + F^{'} (x) Δ x$
Given:
$F (x) = x^{4} - 10$
Solution:
We have,
$F (x) = x^{4} - 10$
So, $F^{'} (x) = 4 x^{3}$
and $x = 2, Δ x = 0.1$
The let’s put the value in formula
$F (2 + 0.1) = F (2) + F^{'} (2) Δ x$
$\begin{aligned} = 2^{4} - 10 + 4 (2)^{3} (0.1) \\ = 16 - 10 + (32) (0.1) \\ = 16 - 10 + 3.2 \\ = 9.2 \end{aligned}$
${So}_{,} F (2.1) is 9.2$

The students who are preparing for their public exams lookout for reliable resources to study. Many such students of class12 depend on the RD Sharma class 12th exercise VSA book during their preparation. Here are a few reasons on why there is a huge demand for the RD Sharma books:

The answers for the book back questions are framed by certain experts who have an in-depth knowledge in the field of mathematics. They have provided various tricks and techniques in the RD Sharma Class 12th Exercise VSA book that can be used to solve the sums easily.
Homework and assignments can also be completed by referring to the RD Sharma Class 12 Solutions Differentials, Errors, and Approximations ex VSA resource material.
The Class 12 RD Sharma Chapter 13 Exercise VSA solution material is available in the updated according to the current academic year’s textbook.
The Career 360 website gives the access for everyone to download the PDF format of the RD Sharma Class 12 Solutions Chapter 13 Ex VSA book.

RD Sharma Chapter wise Solutions

Frequently Asked Questions (FAQs)

1. How can the class 12 students prepare for their classes in advance?

As the class 12 students are capable of understanding certain concepts even without the guidance of teacher, they can refer to the RD Sharma solutions to learn in advance.

2. What are the exams where the RD Sharma Class 12th exercise VSA books can be used for preparation?

The students can use the RD Sharma Class 12th exercise VSA reference book to prepare for the class tests, public exams, JEE Mains and other entrance and competitive exams.

3. What is the profitable way to attain the Class 12 RD Sharma Chapter 12 Exercise VSA Solution material?

It is better for the students to download the class 12 RD Sharma Chapter 13 Exercise VSA solution from the Career 360 website as it is available for free.

4. Why is it essential for the class 12 students to prepare using the RD Sharma Class 12th Exercise VSA book?

As the teachers use the RD Sharma Class 12th Exercise VSA reference material to set the question paper for tests and exams, it is vital for a student to refer to this set of solutions.

5. Are there any restrictions towards who can access the RD Sharma Class 12 Solutions Chapter 13 Ex VSA book?

There is no restrictions towards who can access the RD Sharma Class 12 Solutions Chapter 13 Ex VSA book at the Career 360 website. Anyone can utilize this resource material.

Articles

NCERT Class 11 Physics Chapter 2 Notes Units and Measurement - Download PDF

Apr 03, 2025

NCERT Class 11 Chemistry Chapter 13 Notes Hydrocarbons - Download PDF

Apr 03, 2025

NCERT Class 11 Physics Chapter 12 Notes Thermodynamics - Download PDF

Apr 03, 2025

Application of Derivatives Class 12th Notes - Free NCERT Class 12 Maths Chapter 6 Notes - Download PDF

Apr 03, 2025

NCERT Class 11 Physics Chapter 7 notes System of Particles and Rotational Motion - Download PDF

Apr 03, 2025

Matrices Class 12th Notes - Free NCERT Class 12 Maths Chapter 3 Notes - Download PDF

Apr 03, 2025

NCERT Class 11 Physics Chapter 6 Work, Energy and Power Notes - Download PDF

Apr 03, 2025

NCERT Class 11 Physics Chapter 3 Notes Motion in a straight Line - Download PDF

Admit Card

Result

View All School Exams

Exams

Top Schools

Products & Resources

NCERT Study Material

Exams

Colleges

Predictors

Resources

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Exams

Predictors & Articles

Colleges

Resources

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Colleges

Resources

Quick Links

Exams

Colleges

Resources

Exams

Colleges

Resources

Diploma Colleges

Exams

Resources

Upcoming Events

Other Exams

Exams

Colleges

Top Countries

Student Visas

Exams

Colleges

Upcoming Events

Resources

Engineering Preparation

Medical Preparation

Online Courses

Products

Top Streams

Specializations

Resources

Top Providers

RD Sharma Solutions Class 12 Mathematics Chapter 13 VSA

RD Sharma Class 12 Solutions Chapter 13 VSA Differentials, Errors and Approximations - Other Exercise

Differentials, Errors and Approximations Excercise: VSA

Differentials Errors and Approximations exercise very short answer question 1

RD Sharma Chapter wise Solutions

Frequently Asked Questions (FAQs)

Articles

Upcoming School Exams

Andhra Pradesh Residential Junior Colleges Common Entrance Test

Karnataka Secondary School Leaving Certificate Examination

Telangana Residential Junior Colleges Common Entrance Test

Chattisgarh State Open School 12th Examination

Chattisgarh State Open School 10th Examination

Also Read

Study Resources, Applications and Opportunities

NEET/JEE Coaching Scholarship

NEET Most scoring concepts

NEET Previous 10 Year Questions