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RD Sharma Class 12 Exercise CSBQ Maxima And Minima Solutions Maths - Download PDF Free Online

RD Sharma Class 12 Exercise CSBQ Maxima And Minima Solutions Maths - Download PDF Free Online

Edited By Lovekush kumar saini | Updated on Jan 21, 2022 02:48 PM IST

The Class 12 RD Sharma chapter 17 exercise CSBQ solution plays a major role in making the students understand the mathematical concepts to a great extent. The class 12 students suffer due to lack of proper guidance to learn mathematics. The presence of the RD Sharma class 12th exercise CSBQ eradicates that emptiness and gives a strong support system to the students.

This Story also Contains
  1. RD Sharma Class 12 Solutions Chapter 17 CSBQ Maxima and Minima - Other Exercise
  2. Maxima and Minima Excercise: CSBQ
  3. RD Sharma Chapter-wise Solutions

Also read - RD Sharma Solutions For Class 9 to 12 Maths

RD Sharma Class 12 Solutions Chapter 17 CSBQ Maxima and Minima - Other Exercise

Maxima and Minima Excercise: CSBQ

Maxima and Minima Exercise Case Study Based Questions Question 1(i)

Answer: 2x+πy=200.
Hint: perimeter = sum of all sides.
Solution:
Give the perimeter of the region=200m
x+12×2πr+x+12×2πr=200
2x+2πr=200

Putting

2x+2π(y2)=200
2x+πy=200.

Maxima and Minima Exercise Case Study Based Questions Question 1(ii)

Answer: 2π(100xx2)
Hint: Area of rectangle = length × breadth
Solution:
Area =Area of rectangle
=x×y
$\ since, 2x+ \pi y =200$
$\ \pi y =200-2x$
y=1π(2002x)
Area = x×1π(2002x)
Area = 1π(200x2x2)
=2π(100xx2)

Maxima and Minima Exercise Case Study Based Questions question 1(iii)

Answer: 5000πm2
Hint: use maxima minima concept.
Solution:
Now, A=2π(100xx2)
To find maximum value of A we find
dAdx
We must show f’(x) = 0 for finding maxima and minima
dAdx=2π(1002x)
dAdx=0
2π(1002x)=0
100=2x
x=50
Putting x value in A
A=2π(100xx2)
=2π(100×50(50)2)
=2 T(50002500)
A.=2π(2500)=5000 m2π

Maxima and Minima Exercise Case Study Based Questions Question 1(iv)

Answer:x=0
Hint: use concept of maxima and minima.
Solution:
Total Area = =Area of rectangle+2× Area of semicircle.
=A+2×12πr2
=A+πr2
Putting
r=y2
=A+π(y/2)2
=A+πy24

Putting A value,

=2π(100xx2)+πy24
Putting
y=1π(2002x)
=2π(100xx2)+π4(1π(2002x))2
=2π(100xx2)+π4×1π2(2002x)2
=2π(100xx2)+π4×1π222×(100x)2
=200xπ2x2π+1002π+x2π200xπ
=x2π+1002π
Total Area =x2π+1002π

Let Total Area =Z
$z=\frac{-x^{2}}{\pi}+\frac{10000}{\pi} $
 dzdx=2xπ
dzdx=0
2xπ=0
x=0

Maxima and Minima Excercise Case Study Based Questions Question 1(v)

Answer:5000 m2π
Hint: use concept of maxima and minima.
Solution:
Total area Z=x2π+10000π
Putting,
x=0
Z=1002π
Z=10000πm2
Also Maximum area, A=5000πm2
Thus,
Difference between areas =10000π5000π
=5000 m2π

Maxima and Minima Excercise Case Study Based Questions Question 2(i)

Answer: 0.04
Solution:
Let A: Vinay process the form
Let B: Sonia process the form
Let A: Iqbal process the form
We need to find
The conditional probability that an error is committed in processing given that Sonia processed the form is P(EB)
Since, Sonia’s error rate 0.04
P(EB)=0.04
P(E/B)=0.04

Maxima and Minima Excercise Case Study Based Questions Question 2(iii)

Answer: 0.04F
Solution:
The total probability of committing an error = Probability Vinay processes the form × Vinay’s error rate + Probability Sonia processes the form × Sonia’s error rate + Probability Iqbal processes the form × Iqbal’s error rate
=50%×0.06+20%×0.04+30%×0.03
=510×0.06+210×0.04+310×0.03
=0.030+0.008+0.009
=0.047

Maxima and Minima Exercise Case Study Based Questions Question 2(iv)

Answer: 3047
Solution:
We first find the probability that an error is committed in processing given that Vinay processed the form P(AE)
Now,
P(AE)=P(A)P(EA)p(A)p(EA)+P(B)P(EB)+P(C)P(EC)
=5510×0.06+210×0.44+310×0.03
=5×0.065×0.06+2×0.04+3×0.03
=0.300.30+0.08+0.19
=0.300.47
=3047
Probability form has an error but was not processed by Vinay,
=1P(AE)
=13047
=1747

Maxima and Minima Exercise Case Study Based Questions Question 2(v)

Answer: 1
Solution:
i=13P(EiA)=p(E1A)+P2(E2A)+p(E3A)
=P(E1)P(AE1)P(E1)P(AE1)+P(E2)P(AE2)+P(E3)P(AE3)+P(E2)P(AE2)P(E1)P(AE1)+P(E2)P(AE2)+P(E3)P(AE3)+
P(E3)P(AE3)P(E1)P(AE1)+P(E2)P(AE2)+P(E3)P(AE3)
=1

Maxima and Minima Exercise Case Study Based Questions Question 3(i)

Answer: R=Rs(500x)(300+x)
Hint: use the concept of revenue.
Solution:
Total Revenue R = No. of Subscribers × Rate
=(500x)×(300+x)
Where x is the Rs for increasing one subscriber.

Maxima and Minima Excercise Case Study Based Questions Question 3(ii)

Answer:AR=Rs(500x1)(300+x)
Hint: use concept of revenue.
Solution:
Normal Revenue is
R=(500x)(300+x)
The average revenue of the company when annual subscription is increased by Rs x per subscibers
Average revenue
=(500xx)(300+x)=Rs(500x1)(300+x)

Maxima and Minima Excercise Case Study Based Questions Question 3(iii)

Answer: 2002x
Hint: use concept of maxima and minima.
Solution:
R(x)=(500x)(300+x)
R(x)=x2+200x+150000
Differentiating with respect to x,
R(x)=2x+200
 Hence =2002x

Maxima and Minima Excercise Case Study Based Questions Question 3(iv)

Answer:Rs400
Hint: use concept of maxima and minima.
Solution:
R=(500x)(300+x)
R=(300+x)+500x
=2002x
R=0
2002x=0
x=100.
R=2<0 Maximum. 
 Rate =300+100=400Rs

Maxima and Minima Excercise Case Study Based Questions Question 3(v)

Answer: 160,000
Hint: use concept of maxima and minima.
Solution:
Given that there are 5000 subscribers and each subscriber pays 3000 Rs as rent per year
Let us assume that x rupees are increased in the rent.
So the total cost received by the company C is
C=(3000+x)(5000x)C=15000000+2000xx2
Differentiate it with respect to x, We get
dcdx=20002x
20002x=0
x=1000
So the maximum cost required by the company is 4000×4000=160,000

Maxmima and Minima Exercise Case Study Questions Question 4(i)

Answer: 2x+2y+πx=10
Hint: use the formula of perimeter.
Solution:
Perimeter of the window = 10 m
Let 2x, y represents width and height
Length +2× breadth + circumference of semicircle = 10
2x+2y+π(2x2)=10
2x+2y+πx=10

Maxmima and Minima Exercise Case Study Questions Question 4(ii)

Answer: 10x(π+2)x2
Hint: use the formulas of area and perimeter.
Solution:
Perimeter of the window is given, by
P=2x+2y+πx
p=2x+4y+πx (p=10 m)
2x+4y+πx=10
y=10πx2x4(1)
 Area =(2x)(2y)+πx22
[∴Area of the window = Area of the Rectangle + Area of the Semicircle]
A=4xy+πx22   (2)
y value in (2) 
A=4x(10πx2x4)+πx22
=10xπx22x2+πx22
=10x2x2πx22
=10x4x2+πx22
=10x(2x2+πx2)
 A=10xx2(π+2)

Maxmima and Minima Exercise Case Study Questions Question 4(iii)

Answer:10x(π+42)x2
Hint: use the basic concept.
Solution:
 Area =(2x)(2y)+πx22
=4x(10πx2x4)+πx22
A=10x2x2πx22
=10x4x2+πx22
A=10xx2(π+42)

Maxmima and Minima Exercise Case Study Questions Question 4(iv)

Answer: 20π+4,10π+4
Hint: use concept of maxima and minima.
Solution:
Let x, y be the length and breadth of the rectangle ABCD, Let x2 be the radius of semicircle with center at O
Perimeter = 10 m
x+2y+πx2=10
2x+4y+πx=20
$4 y=20-(\pi+2) x $
 y=20(π+2)x4
A=xy+12π(x2)2
=x[20(π+2)x4]+[x2π8]
A=1/4[20x(π+2)x2]+[πx28]
dAdx=14[202(π+2)x]+πx4
dAdx=0
14[202(π+2)x]+πx4=0.
202πx4x+πx=0
20(π+4)x=0
x=20π+4
And,
$y=\frac{20-(\pi+2)\left(\frac{20}{\pi+4}\right)}{4} $
 =20π+8020π404(π+4)
y=10π+4

Maxmima and Minima Exercise Case Study Questions Question 4(v)

Answer:50π+4
Hint: use formula of area of semicircle.
Solution:
Area of maximum length throughout the window = radius of Semicircle (x)2+ breadth of rectangle 
=(20π+42)+10π+4
=40π+4+10π+4=50π+4

Maxima and Minima Exercise Case Study Based Questions Question 5(i)

Answer:  1800xy 
Hint: use concept.
Solution:
X is length, y is breadth
Area = l × b
A=xy, For one square meter the cost is 1800
So, A=1800xy

Maxima and Minima Exercise Case Study Based Questions Question 5(ii)

Answer:
Hint: perimeter of rectangle =2(l×b)
Solution:
The cost of construction of the vertical wall is like Perimeter
Perimeter =2(l×b)
=2(x+y)
For one square meter the cost is 1800
Then the cost of a vertical wall is
=2×1800(x+y)
=3600(x+y)

Maxima and Minima Exercise Case Study Based Questions Question 5(iii)

Answer:3600(14x2)
Hint: volume =l×b×h
Solution:
Let c be the total cost of the tank
C(x) = Cost of base + Cost of sides
=1800xy+3600(x+y)(1)
As w know,
Length if the tank =x
Breadth of the tank =y
Depth of the tank =h
=2 m
Volume of the tank =8 m3
1=xb=yh=2v=8m2

Volume=l×b×h

8=2×x×yy=4x(2)

Sub y value in (1)
C(x)=1800×(4x)+3600(x+4)
7200+3600(x+4x1)
c(x)=0+3600(1+(1)4x11)
=3600(14x2)
=3600(14x2)

Maxima and Minima Exercise Case Study Based Questions Question 5(iv)

Answer:x=2
Hint: use the concept of maxima and minima.
Solution:
As we know,
C(x)=3600(14x2)
Putting c(x)=0
3600(14x2)=0.
14x2=0
x24x2=0
x24=0
(x2)(x+2)=0
x=2
c(x)=3600(04(2)x21)
=3600(04(2)x3
=3600(8x3)
=28800x3
=28800x3
Putting x=2
c(2)=28800>0(2)3c(2)>0
So minimum is x=2

Maxima and Minima Exercise Case Study Based Questions Question 5(v)

Answer: 21600
Hint: use basic concepts.
Solution:
Least cost of construction is = C (2)
C(2)=7200+3600(x+4x1)
=7200+3600(2+42)
=7200+3600(4+42)
=7200+3600(4)
=7200+14400
=21,600

Maxima and Minima Excercise Case Study Based Questions question 6(i)

Answer: 2x+πy=14
Hint: use formula of perimeter.
Solution:
Wire of Length is =28m
Side of the Square =x
Circle of Radius =y
Sum of perimeter of a circle is =28m
2π (Radius) +4( side )=28
2πy+4x=28
2(πy+2x)=28
2x+πy=14

Maxima and Minima Excercise Case Study Based Questions Question 6(ii)

Answer: 1π[(π+4)x256x+196]
Hint: use formulas.
Solution:
 Area =π( raduis )2+( side )2
A=πy2+x2(1)
We know that
2x+πy=14
πy=142x
y=142xπ
Substituting value of y in (1) π(142xπ)2+x242
A=π(142xπ)2+x216
=1π(142x)2+x216
=1π(1422(14)(2x)+(2x)2)+x216.
=1π[19656x+4x2]+x216
=1π[(π+4)x256x+196]

Maxima and Minima Excercise Case Study Based Questions Question 6(iii)

Answer:28π4+π
Hint: use the concept of maxima and minima.
Solution:
Side of the Square =28x4
Area of the square =[28x4]2
Thus Total Area =x24π[28x4]2
dddx=2x4π+216(28x)(1)
dddx=x2π28x8
dAdx=0
x2π28x8=0
4x=28ππx
4x+πx=28π
x[4+π]=28π
x=28π4+π

Maxima and Minima Excercise Case Study Based Questions Question 6(iv)

Answer: 14ππ+4
Hint: use basics.
Solution:
2x+πy=14
As we know,
x=28π4+π
=2(28π4+π)+πy=14
(56π4+π)+πy=14
56π4+π=14πy
14+56π4+π=πy
56π14π+56π=πy(4+π).
14ππ+4=y
14ππ+4=y

Maxima and Minima Excercise Case Study Based Questions Question 6(v)

Answer:196π2π(π+4)
Hint: use basic concepts and concepts of maxima and minima.
Solution:
A=π(142x4)2+x242
=π(142x4)2+x216
=π(196+4x256x)16+x216
Put x=1
A=π(196)2π(π+4)
=196π2π(π+4)

Maxmima and Minima Exercise Case Study Questions Question 7(i)

Answer:120x225600
Hint: use distance formula.
Solution:
GA=GB=x
Let G be the position of the godown at a distance x each from A and B
CD=20021602
=120
GD=x21602
GC=DCDG
=120x21602
=120x225600

Maxmima and Minima Exercise Case Study Questions Question 7(ii)

Answer:2xx225600
Hint: use basic concepts.
Solution:
We know,
y=GA+GB+GC
Then,
y=2x+120x21602
dydx=212x21602
dydx=2xx225600

Maxmima and Minima Exercise Case Study Questions Question 7(iii)

Answer:25600(x225600)3/2
Hint: use the concept of maxima and minima.
Solution:
dydx=2xx225600
d2ydx2=[1(x225600)+x12(x225600)322x]
=[25600(x225600)3/2]

Maxmima and Minima Exercise Case Study Questions Question 7(iv)

Answer: x=3203
Hint: use the concept of maxima and minima.
Solution:
d2ydx2=[25600(x225600)5/2]
dydx=212(x2100)22x=0
For max or min

2x=1x2(160)2(1)
d2ydx2=[2xx28x3] by (1)=6x

y is minimum when x=3203

Maxmima and Minima Exercise Case Study Questions question 7(v)

Answer: 40(43+3)
Hint: use basic concept.
Solution:
GA+GB+GC=?
 GB=GA=x
2x=1x21602
x=2x160
x=320/v3
GA+GB+GC=120+1603
=40(43+3)

Maxima and Minima Exercise Case Study Based Questions Question 8(i)

Answer: x2+y2=400
Hint: use pythagoras theorem.
Solution:
Length =2x
Breadth =2y

AB2+BC2=AC2
(2x)2+(2y)2=(40)2
4x2+4y2=1600
x2+y2=400

Maxima and Minima Exercise Case Study Based Questions Question 8(ii)

Answer: A=4x400x2
Hint: use the formula of area of rectangle.
Solution:
Area =l×b

A=2x×2y
As we know,
x2+y2=400
y2=400x2
y=400x2
 A=2x×2400x2
 A=4x400x2

Maxima and Minima Exercise Case Study Based Questions Question 8(iii)

Answer: 8(200x2)400x2
Hint: use the concept of maxima and minima.
Solution:
x2+y2=400 
y2=400x2
 A=1×b
A=2x×2400x2
=4x400x2
dAdx=44004x2+4((2x2)2400x2)
dAdx=8(200x2)40xx2

Maxima and Minima Exercise Case Study Based Questions Question 8(iv)

Answer:800 m2
Hint: use the concept of maxima and minima.
Solution:
As we know,
dAdx=0
dAdx=8(200+x2)400x2
dAdx=0
f(200+x2)=0
1600+8x2=0
8x2=1600

x2=1600

x=±400
x=400 for x
 for, 2x=2×400=800 m2
Thus is the maximum area of the garden.

Maxima and Minima Exercise Case Study Based Questions Question 8(v)

Answer:400(π2)m2
Hint: use basic cgfy concept.
Solution:
Other part is converted into circle
=x(π2)
=400(π2)m2

The Sharma class 12th exercise CSBQ is essential for the students who face difficulties in learning the mathematical concepts. A teacher or a tutor cannot assist a student any time whenever they have doubts. Having a copy of the RD Sharma Class 12th exercise CSBQ book gives the students a clarity regarding their doubts. Therefore, no one would feel perplexed while doing their homework or assignments.

The chapter 17 in the class 12 mathematics syllabus has five exercises in total. The CSBQ part consists of 40 questions to be answered by the students. It is obvious that the teachers will not help them with finding the answers for all these questions. The homework can be completed by the students using the RD Sharma Class 12th Exercise CSBQ Solution.

Some of the topics that this portion covers are finding the maximum and minimum values of a function, finding the properties of maxima and minima, solving the higher-order derivative test, definition of maximum and minimum, point of inflection and point of inflexion. The RD Sharma Class 12 Solutions Chapter 17 Exercise CSBQ will be an effective reference material in solving the doubts regarding all these topics.

Benefits of using the RD Sharma Class 12th Exercise CSBQ in exam preparation:

  • All the solutions are given by an expert team who have contributed their knowledge for the welfare for the students. The revised set of solutions gives the assurance that they are accurate and have no mistakes in it.

  • The questions in the sample papers and the solutions present in the RD Sharma Class 12 Chapter 12 Exercise CSBQ are changed according to the updates made in the NCERT syllabus books.

  • Even though this single solution reference material can make great changes in a student’s life, it need not be purchased by spending thousands of rupees. All the RD Sharma books in the Career 360 website can be obtained without paying even a single buck.

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Frequently Asked Questions (FAQs)

1. Which reference book would a class 12 handling teacher recommend to her students?

Most of the teachers suggest the RD Sharma Class 12 Chapter 17 solutions book to their students.

2. Do the RD Sharma books follow the NCERT pattern?

The RD Sharma books are framed according to the NCERT pattern in a way that the CBSE students can gain knowledge from it. 

3. What makes the RD Sharma books essential for a class 12 student?

Along with the solutions for all the questions given in the textbook, the RD Sharma books contain various sample papers and additional questions for the students to practice well before their exams. This makes it very useful for the class 12 students.

4. Which is the best online site that contains the RD Sharma reference books?

The Career 360 website contains the entire set of RD Sharma reference materials where everyone can access and download the books. 

5. How many CSBQ from this chapter does the RD Sharma solution book covers?

There are 40 CSBQ in this chapter for which all the solutions are provided in the RD Sharma Class 12 Chapter 17 Solutions material. 

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