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RD Sharma Solution CLass 12 Mathematics Chapter 14 Differentials , Errors and Approximations

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

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 24
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 24
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Question 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 27
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 27
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 28
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 28
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 29
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 29
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 30
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 30
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 31
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 31
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 32
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 32
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 33
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 33
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 34

Using differentials, find the
approximate values of the following:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Question 35

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

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Question 36

Using differentials, find the
approximate values of the following:

(1.999)5

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Question 37

Using differentials, find the
approximate values of the following:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Solution 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Question 38
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 38
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 39
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 39
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 40
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 40
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 41
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 41
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 42
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 42
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 43
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 43
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 44
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 44
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
  3. 3a %
  4. none of these
Solution 2

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
  4. 3k%
Solution 5

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations 

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

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations 

Solution 9

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

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

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

Solution 12

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations

 

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