RD SHARMA Solutions for Class 12-science Maths Chapter 14 - Differentials, Errors and Approximations

Your CBSE Class 12 syllabus for Maths consists of topics such as linear programming, vector quantities, determinants, etc. which lay the foundation for further education in science, engineering, management, etc. Studying differential equations will be useful for exploring subjects such as Physics, Biology, Chemistry, etc. where your knowledge can be applied for scientific investigations.

On TopperLearning, you can find study resources such as sample papers, mock tests, Class 12 Maths NCERT solutions and more. These learning materials can help you understand concepts such as differentiation of functions, direction cosines, integrals, and more. Also, you can practise the Maths problems by going through the solutions given by our experts.

Maths is considered as one of the most difficult subjects in CBSE Class 12 Science. Our Maths experts simplify complex Maths problems by assisting you with the right methods to solve problems and score full marks. You may still have doubts while referring to the Maths revision notes or Maths NCERT solutions. Solve those doubts by asking an expert through the “Undoubt” feature on the student dashboard.

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Chapter 14 - Differentials, Errors and Approximations Exercise Ex. 14.1

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7

Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19

Solution 19

Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25

Solution 25

Question 26
Solution 26
Question 27
Solution 27
Question 28
Solution 28
Question 29
Solution 29
Question 30
Solution 30
Question 31
Solution 31
Question 32
Solution 32
Question 33
Solution 33
Question 34

Using differentials, find the approximate values of the following:

 

Solution 34

Question 35

Using differentials, find the approximate values of (3.968)3/2

Solution 35

Question 36

Using differentials, find the approximate values of the following:

 

(1.999)5

Solution 36

Question 37

Using differentials, find the approximate values of the following:

 

Solution 37

Question 38
Solution 38
Question 39
Solution 39
Question 40
Solution 40
Question 41
Solution 41
Question 42
Solution 42
Question 43
Solution 43
Question 44

Solution 44

Chapter 14 - Differentials, Errors and Approximations Exercise Ex. 14VSAQ

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

A piece of ice is in the form of a cube melts so that the percentage error in the

edge of a cube is 'a', then find the percentage error in its volume.

Solution 5

Chapter 14 - Differentials, Errors and Approximations Exercise MCQ

Question 1

If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is

a. 1 %

b. 2 %

c. 3 %

d. 4 %

 

Solution 1

Correct option: (a)

  

Question 2

If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is

  1. 2a%
  2. 3a %
  3. none of these
Solution 2

Correct option: (a)

  

Question 3

If an error k % is made in measuring the radius of a sphere, then percentage error in its volume is

  1. k%
  2. 3k%
  3. 2k%
  4. k/3%

 

Solution 3

Correct option: (b)

  

Question 4

The height of a cylinder is equal to the radius. If an error of a% is made in the height, then percentage error in its volume is

  1. a %
  2. 2a%
  3. 3a%
  4. none of these

 

Solution 4

Correct option: (c)

  

Question 5

While measuring the side of an equilateral triangle an error of k% is made, the percentage error in its area is

  1. k%
  2. 2k%
  3. 3k%
Solution 5

Correct option: (b)

  

Question 6

If loge 4 = 1.3868, then loge 4.01 =

  1. 1.3968
  2. 1.3898
  3. 1.3893
  4. None of these

 

Solution 6

Correct option: (c)

  

Question 7

A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in the volume is

  1. 12000π  mm3
  2. 800π  mm3
  3. 80000π  mm3
  4. 120π  mm
Solution 7

Correct option: (c)

  

Question 8

If the ratio of base radius and height of a cone is 1:2 and percentage error in radius is λ %, then the error in its volume is

  1. λ %
  2. 2λ %
  3. 3λ %
  4. None of these

 

Solution 8

Correct option: (c)

  

Question 9

The pressure P and volume V of a gas are connected by the relation PV1/4 = constant. The percentage increase in the pressure corresponding to a diminution of 1/2 % in the volume is

  

 

Solution 9

Correct option: (c)

  

Question 10

If y = xn , then the ratio of relative errors is y and x is

  1. 1:1
  2. 2:1
  3. 1:n
  4. n:1

 

Solution 10

Correct option: (d)

  

Question 11

The approximate value of (33)1/5 is

  1. 2.0125
  2. 2.1
  3. 2.01
  4. None of these

 

Solution 11

Correct option: (a)

Question 12

The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is

  

 

Solution 12

Correct option: (a)

  

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Why CBSE Class 12 Science Maths solutions are important?

Maths is a subject which requires practising a variety of problems to understand concepts clearly. By solving as many problems as you can, you’ll be able to train your brain in thinking the logical way to solve maths problems. For practising problems, study materials such as sample papers, previous year papers, and NCERT solutions are needed.

Some of the best Maths experts work with us to give you the best solutions for Maths textbook questions and sample paper questions. Chapter-wise NCERT solutions for Class 12 Science Maths can be easily accessible on TopperLearning. Use these solutions to practise problems based on concepts such as direction ratios, probability, area between lines, inverse trigonometric functions, and more.

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