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

## 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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