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

Using differentials, find the

approximate values of the following:

Using differentials, find the

approximate values of (3.968)^{3/2}

Using differentials, find the

approximate values of the following:

(1.999)^{5}

Using differentials, find the

approximate values of the following:

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

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.

## Chapter 14 – Differentials, Errors and Approximations Exercise MCQ

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 %

Correct option: (a)

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

- 2a%
- 3a %
- none of these

Correct option: (a)

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

- k%
- 3k%
- 2k%
- k/3%

Correct option: (b)

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

- a %
- 2a%
- 3a%
- none of these

Correct option: (c)

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

- k%
- 2k%
- 3k%

Correct option: (b)

If log_{e} 4 = 1.3868, then log_{e} 4.01 =

- 1.3968
- 1.3898
- 1.3893
- None of these

Correct option: (c)

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

- 12000π mm
^{3} - 800π mm
^{3} - 80000π mm
^{3} - 120π mm

Correct option: (c)

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

- λ %
- 2λ %
- 3λ %
- None of these

Correct option: (c)

** **

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

Correct option: (c)

If y = x^{n} , then the ratio of relative errors is y and x is

- 1:1
- 2:1
- 1:n
- n:1

Correct option: (d)

The approximate value of (33)^{1/5} is

- 2.0125
- 2.1
- 2.01
- None of these

Correct option: (a)

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

Correct option: (a)