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

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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(i)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(i)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(ii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(iii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(iv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(iv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(v)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(v)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(vi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(vi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(vii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(vii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(viii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(viii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(ix)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(ix)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(x)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(x)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xiii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xiii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xiv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xiv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xvi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xvi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xvii)

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

Solution 9(xvii)

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

Question 9(xviii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xviii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xix)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xix)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xx)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xx)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xxi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xxi)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xxii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xxii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xxiii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xxiii)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xxiv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xxiv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xxv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Solution 9(xxv)
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Differentials Errors And Approximations
Question 9(xxvi)

Using differentials, find the approximate values of the following:

 

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

Solution 9(xxvi)

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

Question 9(xxvii)

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

Solution 9(xxvii)

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

Question 9(xxviii)

Using differentials, find the approximate values of the following:

 

(1.999)5

Solution 9(xxviii)

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

Question 9(xxix)

Using differentials, find the approximate values of the following:

 

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

Solution 9(xxix)

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

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 

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