#### Chapters

Chapter 2: Functions

Chapter 3: Binary Operations

Chapter 4: Inverse Trigonometric Functions

Chapter 5: Algebra of Matrices

Chapter 6: Determinants

Chapter 7: Adjoint and Inverse of a Matrix

Chapter 8: Solution of Simultaneous Linear Equations

Chapter 9: Continuity

Chapter 10: Differentiability

Chapter 11: Differentiation

Chapter 12: Higher Order Derivatives

Chapter 13: Derivative as a Rate Measurer

Chapter 14: Differentials, Errors and Approximations

Chapter 15: Mean Value Theorems

Chapter 16: Tangents and Normals

Chapter 17: Increasing and Decreasing Functions

Chapter 18: Maxima and Minima

Chapter 19: Indefinite Integrals

Chapter 20: Definite Integrals

Chapter 21: Areas of Bounded Regions

Chapter 22: Differential Equations

Chapter 23: Algebra of Vectors

Chapter 24: Scalar Or Dot Product

Chapter 25: Vector or Cross Product

Chapter 26: Scalar Triple Product

Chapter 27: Direction Cosines and Direction Ratios

Chapter 28: Straight Line in Space

Chapter 29: The Plane

Chapter 30: Linear programming

Chapter 31: Probability

Chapter 32: Mean and Variance of a Random Variable

Chapter 33: Binomial Distribution

#### RD Sharma Mathematics Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session)

## Chapter 14: Differentials, Errors and Approximations

#### Chapter 14: Differentials, Errors and Approximations solutions [Pages 9 - 10]

If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?

The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume ?

A circular metal plate expends under heating so that its radius increases by *k*%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.

Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of edges of the cube ?

If there is an error of 0.1% in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere ?

The pressure *p* and the volume *v* of a gas are connected by the relation *pv*^{1.4} = const. Find the percentage error in *p* corresponding to a decrease of 1/2% in v ?

The height of a cone increases by *k*%, its semi-vertical angle remaining the same. What is the approximate percentage increase (i) in total surface area, and (ii) in the volume, assuming that *k* is small ?

Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius ?

1 Using differential, find the approximate value of the following:

\[\sqrt{25 . 02}\]

Using differential, find the approximate value of the following: \[\left( 0 . 009 \right)^\frac{1}{3}\]

Using differential, find the approximate value of the following: \[\left( 0 . 007 \right)^\frac{1}{3}\]

Using differential, find the approximate value of the \[\sqrt{401}\] ?

Using differential, find the approximate value of the \[\left( 15 \right)^\frac{1}{4}\] ?

Using differential, find the approximate value of the \[\left( 255 \right)^\frac{1}{4}\] ?

Using differential, find the approximate value of the \[\frac{1}{(2 . 002 )^2}\] ?

Using differential, find the approximate value of the log_{e} 4.04, it being given that log_{10}4 = 0.6021 and log_{10}*e* = 0.4343 ?

Using differential, find the approximate value of the log_{e} 10.02, it being given that log_{e}10 = 2.3026 ?

Using differential, find the approximate value of the log_{10} 10.1, it being given that log_{10}*e* = 0.4343 ?

Using differentials, find the approximate values of the cos 61°, it being given that sin60° = 0.86603 and 1° = 0.01745 radian ?

Using differential, find the approximate value of the \[\frac{1}{\sqrt{25 . 1}}\] ?

Using differential, find the approximate value of the \[\sin\left( \frac{22}{14} \right)\] ?

Using differential, find the approximate value of the \[\cos\left( \frac{11\pi}{36} \right)\] ?

Using differential, find the approximate value of the \[\left( 80 \right)^\frac{1}{4}\] ?

Using differential, find the approximate value of the \[\left( 29 \right)^\frac{1}{3}\] ?

Using differential, find the approximate value of the \[\left( 66 \right)^\frac{1}{3}\] ?

Using differential, find the approximate value of the \[\sqrt{26}\] ?

Using differential, find the approximate value of the \[\sqrt{37}\] ?

Using differential, find the approximate value of the \[\sqrt{0 . 48}\] ?

Using differential, find the approximate value of the \[\left( 82 \right)^\frac{1}{4}\] ?

Using differential, find the approximate value of the \[\left( \frac{17}{81} \right)^\frac{1}{4}\] ?

Using differential, find the approximate value of the \[\left( 33 \right)^\frac{1}{5}\] ?

Using differential, find the approximate value of the \[\sqrt{36 . 6}\] ?

Using differential, find the approximate value of the \[{25}^\frac{1}{3}\] ?

Using differential, find the approximate value of the \[\sqrt{49 . 5}\] ?

Using differential, find the approximate value of the \[\left( 3 . 968 \right)^\frac{3}{2}\] ?

Using differential, find the approximate value of the \[\left( 1 . 999 \right)^5\] ?

Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?

Find the approximate value of f (2.01), where f (*x*) = 4*x*^{2} + 5*x* + 2 ?

Find the approximate value of f (5.001), where f (x) = x^{3} − 7x^{2} + 15 ?

Find the approximate value of log_{10} 1005, given that log_{10} *e* = 0.4343 ?

If the radius of a sphere is measured as 9 cm with an error of 0.03 m, find the approximate error in calculating its surface area ?

Find the approximate change in the surface area of a cube of side *x* metres caused by decreasing the side by 1% ?

If the radius of a sphere is measured as 7 m with an error of 0.02 m, find the approximate error in calculating its volume ?

Find the approximate change in the value *V* of a cube of side *x* metres caused by increasing the side by 1% ?

#### Chapter 14: Differentials, Errors and Approximations solutions [Page 12]

For the function *y* = x^{2}, if x = 10 and ∆x = 0.1. Find ∆ y *?*

If *y* = log_{e} *x*, then find ∆*y* when *x* = 3 and ∆*x* = 0.03 ?

If the relative error in measuring the radius of a circular plane is α, find the relative error in measuring its area ?

If the percentage error in the radius of a sphere is α, find the percentage error in its volume ?

A piece of ice is in the form of a cube melts so that the percentage error in the edge of cube is *a*, then find the percentage error in its volume ?

#### Chapter 14: Differentials, Errors and Approximations solutions [Page 13]

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%

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

(a) 2*a*%

(b)\[\frac{a}{2} \%\]

(c) 3*a*%

(d) none of these

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

(a) k%

(b) 3k%

(c) 2k%

(d) k/3%

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

(a) α %

(b) 2α %

(c) 3α %

(d) none of these

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

(a) *k* %

(b) 2*k* %

(c) \[\frac{k}{2}\%\]

(d) 3*k* %

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

(a) 1.3968

(b) 1.3898

(c) 1.3893

(d) none of these

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

(a) 12000 π mm^{3}

(b) 800 π mm^{3}

(c) 80000 π mm^{3}

(d) 120 π mm^{3}

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

(a) λ %

(b) 2 λ %

(c) 3 λ %

(d) none of these

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 deminition of 1/2 % in the volume is

(a) \[\frac{1}{2} \%\]

(b) \[\frac{1}{4} \%\]

(c) \[\frac{1}{8} \%\]

(d) none of these

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

(a) 1 : 1

(b) 2 : 1

(c) 1 : n

(d) n : 1

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

(a) 2.0125

(b) 2.1

(c) 2.01

(d) none of these

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

(a) \[\frac{1}{14}\]

(b) 0.01

(c) \[\frac{1}{7}\]

(d) none of these

#### RD Sharma Mathematics Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session)

#### Textbook solutions for Class 12

## RD Sharma solutions for Class 12 Mathematics chapter 14 - Differentials, Errors and Approximations

RD Sharma solutions for Class 12 Maths chapter 14 (Differentials, Errors and Approximations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 12 Mathematics chapter 14 Differentials, Errors and Approximations are Maximum and Minimum Values of a Function in a Closed Interval, Maxima and Minima, Simple Problems on Applications of Derivatives, Graph of Maxima and Minima, Approximations, Tangents and Normals, Increasing and Decreasing Functions, Rate of Change of Bodies Or Quantities, Introduction to Applications of Derivatives.

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