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RD Sharma Class 12 Exercise 12 FBQ Derivative as a rate measure Solutions Maths - Download PDF Free Online

RD Sharma Class 12 Exercise 12 FBQ Derivative as a rate measure Solutions Maths - Download PDF Free Online

Updated on Jan 20, 2022 07:14 PM IST

RD Sharma is a highly favoured book for Mathematics and is arguably one of the most reliable coursebooks for students in class 12. The book contains complete solved questions of the entire CBSE class 12 maths syllabus and is useful in finding any required information on all concepts. This great advantage of using RD Sharma solutions has enabled students to have an advanced knowledge of maths. Mathematics is a subject that is feared by many students. In class 12, the syllabus gets tougher while the stakes are raised high. In this situation, it becomes necessary for students to have a proper guide that will help them solve the book and improve their knowledge. The book is super useful in all kinds of doubt-clearing and the Class 12 RD Sharma chapter 12 exercise FBQ solution in particular is an exceptional specimen of the series.

This Story also Contains
  1. RD Sharma Class 12 Solutions Chapter 12 FBQ Derivative as a Rate Measure - Other Exercise
  2. Derivative as a Rate Measurer Excercise: FBQ
  3. Derivatives as a rate measure exercise fill in the blanks question 5
  4. RD Sharma Chapter-Wise Solutions:

Also Read - RD Sharma Solution for Class 9 to 12 Maths

RD Sharma Class 12 Solutions Chapter 12 FBQ Derivative as a Rate Measure - Other Exercise

Background wave

Derivative as a Rate Measurer Excercise: FBQ

Derivatives as a rate measure exercise fill in the blanks question 1

Answer: 125
Hint: Here, we use the basic concept of dydx and dzdx
Given: x2+16 with respect to [xx1] at x=3
Solution: Let y=x2+16
z=x(x1)
dydx=x(x2+16)12
dzdx=[{(x1)x}{(x1)2}]
dydx=x(x2+16)12 and (dzdx)=1(x1)2
Hence,
dydx=[(dydx)(dzdx)]
dydx=[x(x2+16)]121/(x1)2
dydzx=3=[3×15/14]=(35)×4
=125

Derivatives as a rate measure exercise fill in the blanks question 2

Answer: r
Hint: Here, we use the of surface area S=4πr2
Given: drdt=2cm/s
Solution: dsdt=8πrdrdt
dsdt=8πr×2
dsdt=16πr
Rate of change of surface area radius of sphere.

Derivatives as a rate measure exercise fill in the blanks question 3

Answer: 102or14.14cm2/s
Hint: Here, we use the length of diagonal dsdt=0.5cm/s and l=2a
Given:dldt=0.5cm/s,Area = 400
Solution: d(2a)dt=0.5
dadt=0.52
a2=400
So, a = 20
da2dt=2×20×0.52=>2×102
=102cm2/sec

Derivatives as a rate measure exercise fill in the blanks question 4

Answer: 1cm3/cm2
Hint: Here, we use the volume of surface area of a cone V=43πr3
Given: Radius is 2 cm
Solution: V=43πr3
dVdr=3×43πr2
S=4πr2
dSdr=2×4πr
=8πr
dVdS=dVdr×drdS
=>r2=1atr=2
So,1cm3/cm2 is the answer.

Derivatives as a rate measure exercise fill in the blanks question 5

Answer: θ=π3
Hint: Here, we use the concept of θ angle
Given: Let θ,dθdt=d(sinθ)dt
Solution: Let θ increase twice as fast as it’s sine
dθdt=2d(sinθ)dt
dθdt=2cosθdθdt
1=2cosθ
cosθ=12
θ=π3

Derivatives as a rate measure exercise fill in the blanks question 6

Answer: 103cm2/s
Hint: Let the side of cm equilateral triangle be xcm
Given: dxdt=2cm2/s
Area of equilateral triangle A=34x2 .......(i)
Solution: Differentiating equation (i) with respect to x we get
dAdt=34×2x×dxdt
=3x2dxdt
When x=10
dAdt=1032×2=103cm2/s

Derivatives as a rate measure exercise fill in the blanks question 7

Answer: 130πft/min
Hint: Here we use the formula of volume, V=43πr3
Given:dVdt=30cm3/sec
Solution: V=43πr3
dVdt=4πr2(drdt)
drdt=[dVdt]/4πr2
drdt=[30[4×π×15×15]]
=130πft/min

Derivatives as a rate measure exercise fill in the blanks question 8

Answer:s
Hint: Here we use the concept and formula of acceleration and velocity
Given: S=aet+(bet)
Solution: Acceleration =d2s/dt2
S=aet+(bet)
dSdt=aet+bet(1)
=aetbet
d2Sdt2=aet+bet
a=aet+bet=s
So, a=s

Derivatives as a rate measure exercise fill in the blanks question 9

Answer: 1513cm/s
Hint: Here we use the concept of acceleration and velocity
Given: V=5x(x2/6)
Solution: So,
dVdt=5×dxdtx3×dxdt
dxdt=dVdt5(x3)
When x=2 anddVdt=5cm3/sec
dxdt=5523=1513cm/s

Derivatives as a rate measure exercise fill in the blanks question 10

Answer: 2πft/minute
Hint: Here we use the formula of volume of vertical cylindrical tank
Given: Radius=2 ft as the r of 8 cubic ft/min
Solution: V=πr2h
dVdt=4π(dhdt)
(dhdt)=(14π)(dVdt)
dVdt=(14π)×8
=2πft/minute

Derivatives as a rate measure exercise fill in the blanks question 11

Answer: dCdtπcm/sec
Hint: Here we use the circumference of circle,C=2πr
Given: The radius of a circle is increasing at the rate of 0.5 cm/sec
Solution: C=2πr
dCdt=2πdrdt
=2π×0.5 [drdt=0.5]
dCdt=πcm/sec

Derivatives as a rate measure exercise fill in the blanks question 12

Answer:dAdt=12πcm2/sec
Hint: Here we use the formula of area of circle (A) with radius r is given by
Given:A=πr2
Solution: dAdt=d(πr2)dt×drdt=2πrdrdt .......[by chain rule]
It is given that
drdt=3cm/s
dAdt=2πr(3)=6πr
Thus, when r=2 cm
dAdt=6π(2)=12πcm2/s

The RD Sharma class 12th exercise FBQ is important to practice as these questions may appear in boards. All questions of the FBQ exercise will be solved in the RD Sharma solutions book and students can use these to tackle the chapter. This chapter deals with concepts such as finding the radius of a cube, calculating the volume of the hub, measuring the rate of change of area with respect to radius, etc.

The RD Sharma class 12 solution of Derivative as a rate measure exercise FBQ has been made by handpicked experts who are great tutors of maths. They know some certain methods of calculations which will aid students to solve questions better and understand all the concepts clearly. The RD Sharma class 12th exercise FBQ are also topnotch and incredibly accurate. Since practice is the only way students can learn maths, the book can be included in one's daily home study session to improve their chances of scoring well. Using RD Sharma class 12 chapter 12 exercise FBQ, will also help with various school assignments, homework, and terminal exams.

The concepts discussed in RD Sharma Class 12 Solutions Chapter 12 exercise FBQs will even help you solve NCERT questions as now you will have a better knowledge on all the concepts. Parents can be instructed to use these books to conduct mock tests for their children at home.

RD Sharma Class 12th exercise FBQ has 12 questions and It includes the following concepts

  • Definition of derivative as a rate measurer.

  • Rate of increase of the perimeter, circumference of any figure

  • Rate of Change in Marginal cost and Marginal Revenue.

  • Application based question on derivative as a rate measurer

Benefits of picking RD Sharma class 12th exercise FBQ Solutions from Career360 include:

  • Downloadable free copies of the book available at Career360.

  • All exercise questions are covered so it's a one-stop solution to all your maths problems.

  • These solutions are simple but solved with detailed steps.

  • Sometimes common questions from the book appear in board exams.

  • More reliable than expensive tuition and study materials.

RD Sharma solutions for maths has seen a lot of success stories and had a fair share of toppers recommending the book. It cannot be disputed that RD Sharma class 12th exercise FBQ is the best possible guide for all students that is also easily available and completely free of cost.

RD Sharma Chapter-Wise Solutions:

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FBQ sections are an important part of the exam paper and students absolutely need to study them to have a clear understanding of all chapters. FBQs are also a great way to revise before exams as it covers all concepts taught in class.

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There are 12 questions in Class 12 RD Sharma Chapter 12, FBQs. All questions are based on the whole syllabus of the chapter.

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