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REVISION- BUSINESS MATHEMATICS AND

STATISTICS - RBTWO MARKS QUESTIONS:

1. What is meant by degrees of freedom?

2. When does the arithmetic mean lose its significance?

3. Differentiate between a census and a survey?

4. Illustrate symmetrical and asymmetrical distributions.

5. Find the 5th term and the sum of the first 8 terms of an AP 1,10,19,.....

6. Explain “level of significance”

7. What is the significance of a null hypothesis

8. Distinguish between ‘maxima’ and minima

9. List out the characteristics of statistics

10. What are the limitations of binomial distribution?

11. What is decision making under uncertainty?

12. What are the advantages of stratified random sampling?

13. What is standard error?14. What is index number

15. What is correlation

16. What is regression

17. What is dispersion? What is the purpose of a measure of dispersion?

18. What is Skewness? What are the different measures of skewness?

19. How will you interpret the sign and magnitude of a correlation coefficient?

20. List the chief properties of a normal distribution.

21. What is a sign test? When is it used?

22. In which context is the Mann Whitney Test used?

23. What is kurtosis? Explain the three different curves under kurtosis?

24. What is binomial distribution? What are its business applications?

25. Give one example for each of the following: i) Linear function ii) Geometric Progression.26. What is meant by the regret criterion?

27. Find the sum of the first 10 terms of an A.P 1,4,7,10.....

28. Find the sum of the first 12 terms of an A.P 1,3,5,7........

29. Find three numbers in A.P whose sum is 21 and product is 280?

30. What term of the following A.P 3 + 6 + 9 + 12....... is 90.

31. The fourth term of a G.P is ½ and the seventh term is 4/27. Find the 12th term.

32. The 3rd term of a G.P is ¾ and the seventh term is 4/27. Find the fourth term

33. Find the sum of the series 3+7+11..... to 40 terms.

34. How many terms of a G.P 4,2,1 amount to 127/16?

35. The first term and the last term of a G.P are 4 and 324. The sum of the series is 384.

Find the CR.

36. What is the importance of statistics in managerial decision making?

37. What are averages? How are they useful?

38. What is Sampling? Jan 05

39. What is Chi square test? Where and for what it is used?

40. What are the components of Time series

41. What is correlation? Mention its significance

42. What is sum of squares and mean of squares

43. What is the significance of testing a hypothesis

44. What is Poisson distribution

45. What is Sign Test

46. What are Index Numbers

47. What is Binomial Distribution48. What is cluster Sampling

49. Define Integration

BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE



Eight Marks Questions and Twelve Marks

Theory Questions

1. Why is statistics called imposing mathematics

2. What do you mean by sampling errors? Explain the types of sampling errors?

3. Is it important for the chosen samples to be representative of the population. Using thevarious methods of sampling, explain how representativeness can be achieved

4. Eloborate on how a decision tree and the payoff-EMV concepts are useful in

managerial decision making.

5. Explain the applications of statistics in managerial decision making. Also discuss the

limitations of statistics.

6. What is Sampling? Why is it important? Discuss the methods of Sampling?

7. Explain the procedure of setting up and testing a hypothesis? [Jan 05,06]

8. What is decision tree? What are the steps in decision tree analysis? [Sep 01, Jan-07]

9. Explain addition, subtraction and multiplication of matrices with examples.

10. What is a statistical average? State the properties of a good average.

11. Explain the method of moving averages in calculating the trend. What are the meritsand limitations of this method.

12. Explain the procedure of setting up and testing a hypothesis.

13. What is business forecasting? Explain the various techniques of forecasting. Explain

the major steps in forecasting. What are the limitations of forecasting?

14. What is correlation? Distinguish between positive and negative correlation. What is

the significance of coefficient correlation?

15.Explain and point out the difference between one tailed and two tailed tests.

16. Explain business forecasting and its various methods. How is it useful to a business

manager?

17. Explain Chi square analysis with an example

18. Explain Annova with an example

19. Explain the terms “level of significance” and degrees of freedom used in Chi Square

test.

20. How is regression and its applicability in business different from correlation and its

applicability

21. Explain the Time Reversal Test and Factor Reversal Test with help of suitable

examples.

22. Distinguish between correlation and regression analysis.

23. Distinguish between Karl Pearson’s and Bowley’s measure of skewness. Which one

of these would you prefer and why?

24.




REVISION- BUSINESS MATHEMATICS AND

STATISTICS - RB1. The following are the annual profits in thousands of rupees, in a certain business:

Year 2001 2002 2003 2004 2005 2006 2007Profits

(Rs 000)

60 72 75 65 80 85 95

i) Use the method of Least square to fit a straight line to the above data

ii) Also make an estimate of the profits for the year 2009 [Jan 2011]

2. Fit the straight line trend by the method of least squares for the following data.

Forecast the production figures for the coming year. A graph is not necessary

[Jan2010]

3. Fit a straight line trend by the method of least square to the following data and the

project the production for the next two years (A graph is not required)

[Jan 2009]

3. ABC Ltd gives the following information relating to the sales of refrigerators in the past

ten years: [Jan 2008]

Fit a straight line trend by the method of least squares and estimate the sales of 2009

4. Fit a straight line trend for the following data: [Jan 2007]


Year 200

3

200

4

200

5

200

6

200

7

2008

Production in ‘000 metrictons 140 146 142 145 150 160

Year 200

2

200

3

200

4

200

5

2006

Production in ‘000 metric

tons

45 45 47 48 52

Year 199

8

199

9

200

0

200

1

200

2

200

3

200

4

200

5

200

6

2007

Refrigerators sold

in thousands

8 10 11 11 18 15 19 19 22 24

Year 199

1

199

2

199

3

199

4

1995

Sale of sugars in ‘000 metric tons 80 90 92 93 94



5. Fit a straight line trend by the method of least squares to the data given below and project

the probable sales for the next two years (A graph is not required) [Jan 2006]

6. Calculate Karl Pearson’s and Bowley’s coefficient of Skewness for the marks obtained by

students of 2 institutions [Jan 2010]

7. For a group of 20 items Σ x =

1452, Σ x2 = 144280 and mode = 63.7. Find the Pearsonian’s coefficient of Skewness.

[Jan 2009]

8. Illustrate skewness with diagram given Q1 = 18, Q3 = 35, Mode = 21, Mean = 18, Find

the coefficient of skewness [Jan 2011]

9. Find the coefficient of correlation with the help of Karl Pearson’s Method [Jan 2011]

X 4

3

4

4

4

6

4

0

4

4

4

2

4

5

4

2

3

8

4

0

4

2

57

Y 2

9

3

1

1

9

1

8

1

9

2

7

2

7

2

9

4

1

3

0

2

6

10

10. Find the coefficient of correlation for the following data: [Jan 2010]

X 1

9

2

1

2

3

2

5

32

Y 6

5

6

6

6

5

6

8

75

11. Find the Karl Pearson’s coefficient of correlation, the probable error and comment on the

significance of correlation for the following data: [Jan 2008]

12.Calculate the

coefficient of correlation

and the probable error and comment on the significance of correlation for the following data:

[Jan 2009]

X 6 7 7 9 1

0

12

Y 18

16

17

19

19

21


Year 199

9

200

0

200

1

200

2

200

3

2004

Sales in thousands of Rupees 164 180 186 187 190 192

Measure Institution A Institution B

Mean 65 66

Median 61 62

Standard

Deviation

10 13

Third Quartile 87 102

First Quartile 78 30

Advertising expenses 1

5

1

8

1

9

2

0

2

2

2

4

25

Sales in ‘000 Rs 2

4

2

6

2

6

2

7

2

8

2

8

30



13. Obtain the regression equations for the following data: [Jan 2007]

X 3

0

5

0

2

0

80 1

0

2

0

2

0

40

Y 5

0

8

0

3

0

11

0

2

0

2

0

4

0

50

14. An investment company speculates about the relationship between the family incomeand their allocation for investment. A survey of 8 randomly selected families gives the

following data: [Jan 2010]

a) Develop the regression equations to describe this data. b) Estimate the probable income of a family who allocates 22 percent for investment

c) What could be the percentage of income allocated to investment by a family

earning Rs 27,500 per month?

15. Determine the regression equation X on Y and Y on X for the following data:[Jan

2011]

X 1

2

1

4

1

6

2

0

32

Y 3

4

4

0

3

8

4

2

50

16. The following data gives the experience of lathe operations in a factory and the

number of lathe operators in a factory and the number of units of production turned out per

day.

[Jan 05/06]

Lathe Operator 1 2 3 4 5 6 7

Experience in yrs(X) 1

4

1

0

1

6

2 1 8 3

Units of

Production(Y)

8

4

8

0

8

7

6

0

5

4

7

8

56

Calculate the regression lines and

i) Estimate the probable units of production of a lathe operator with an experience of 15 yrsii) Estimate the years of experience of a lathe operator with a daily production of 96 units

17. A manufacturing company purchases plastic buckets which are normally distributed

with a mean diameter of 9 inches and a variance of 3 inches. In a total production of 12,000

buckets how many are expected to be

a) Greater than 12 inches in diameter?

b) Less than 7 inches in diameter?

c) Between 8 inches and 10 inches in diameter? [Jan 2010]

18. The mean and standard deviation of marks obtained by the candidates in a

competitive examination are 50 and 15 respectively it 1200 candidates appear for the

examination. Find:

[Jan 2009]a)The number of candidates who are expected to score more than 70


Annual income in 000s 1

8

2

1

1

9

3

4

2

3

3

0

3

6

38

Percent allocation for investment 2

8

3

6

3

2

4

0

3

5

5

5

6

0

64



b)The expected number of candidates who score between 60 and 75 marks.

c) The number of candidates who may score between 35 and 55 marks

d) The number of candidates who score less than 40 marks.

19. An aptitude test for selecting Management Trainees was conducted on 5000

candidates. The average score was 56 and the standard deviation was 24. Assuming normal

distribution for the scores. Find: [Jan 2008]

i) The number of candidates whose scores exceeded 85

ii) Candidates who scored between 65 and 70.

iii) Candidates who scored less than 50

iv) Candidates who scored 60

20. The average monthly sales of 5000 firms are normally distributed. It mean and

standard deviation are Rs 36,000 and Rs 10,000 respectively. Find:

i) The number of firms the sales of which are over Rs 40,000.

ii) Percentage of firms the sale of which will be between Rs 38,500 and 41,000

iii) The number of firms the sales of which will be between Rs 30,000 and Rs 40,000

iv) The number of firms the sales of which are less than Rs 30,000 [Mar 2011] 21. The screws produced by a certain machine were checked by examining number of

defectives in a sample of 12. The following table shows the distribution of 128 samples

according to the number of defective items they contained

No of

defectives

in a

sample of

12

0 1 2 3 4 5 6 7 Total

No of

samples

7 6 19 35 30 23 7 1 128

Fit a Binomial distribution and find the expected frequencies if the chance of the

machine defective is ½. [Jan 2007]

22.A box contains 50 coins numbered from 1 to 50. One coin is drawn at random. Find

the probability that the number on the coin drawn will be a multiple of a) 3 or 9 b) 5

or 7

23. (a) In an AP of 3,9,15,.... find the (i)sum of the first 14 terms and (ii) the twelth term?

(b) P and Q play for a prize of Rs1,00,000. P is to throw a dice first and is to win if he

throws 1. If he fails, Qis to throw and is to win if he throws 1 or 2. If he fails, P is to

throw again and is to win if he throws 1,2 or 3. Find their respective expectations.[Jan11]

24. A sample of 100 dry battery cells tested to find the length of life produced the

following results: µ = 12 hrs, σ = 3 hrs. Assuming that the data are normally distributed.

What percentage of battery cells are expected to have life. I) more than 15 hrs ii) less than

6 hrs iii) Between 10 and 14 hrs [Mar 02]

Given Z 2.5 2.0 1.0 0.67

Area 0.493

8

0.477

2

0.341

3

0.2487

25.In an intelligence test administered to 500 students, the average score was 42 and

standard deviation was 24. Find [Jan 06]a) The number of students whose score exceeded 50




b) The number of students who got a score between 30 and 40

c) The number of students who got a score above 60

26.1000 light bulbs with a mean life of 120 days are installed in a firm. Their length of

life is normally distributed with a standard deviation of 20 days. How many bulbs will

expire in less than 90 days [Mar 03]

27.An MBA graduate is selected for interview in 3 different firms. For the first post,there are 5 candidate, for the second post, there are 10 candidates and for the third

post, there are 9 candidates, what are his chances of getting at least one post?

[Jan 05]

28. Ten percent of the tools produced in a certain manufacturing process turn out to be

defective. Find the probability that in a sample of 10 tools chosen at random, exactly

two will be defective by using (i) Binomial Distribution (ii) the poisson distribution

29. The number of machines malfunctions per shift at a factory is recorded for 180 shifts

and the following data are obtained:

No of

malfunctions

0 1 2 3 4 5 6

No of shifts 8

2

4

2

3

1

1

2

8 3 2

What is a reasonable probability model for this type of data? [Mar 03]

30.Five students P,Q,R ,S and T are given a problem to solve The probabilities are P- 1/3

Q – 1/5, R- 1/6 , S- 1/8 and T – 1/9 of solving the problem. What is the probability

that the problem will be solved. [Jan 2009]

31.A machinery will function only if all its three components P, Q and R are working.

The probability of P failing during one year is 0.15 that of Q falling is 0.05 and that of

R failing is 0.10. What is the probability that the equipment will fail before the end of

the year. [Mar 04]

32.In a post office three clerks are assigned to process incoming mail. The first clerk

process 40%, second 35% and the third 25% of the mail. The first clerk has an error

rate of 0.04, the second has 0.06 and the third has 0.03. A mail selected at random

from a day’s output is found to have an error. The post Master wishes to know the

probability that the mail was processed by the first, second or third clerk respectively.

[Jan 07]

33.A candidate has to be selected for a managerial post with the following

characteristics: [Jan 08]

An MBA degree (probability of getting such a candidate is one in hundred)

Excellent communication (probability is one in fifty)Knowledge of a foreign language (probability is one in eighty)

Experience of working as a manager (probability of getting such a candidate is one

in 20). Find the probability of getting one required candidate.




34.If the opening stock matrix O=

8 361

5321

1 136

, purchase matrix P =

6453

2319

4132

the

sales matrix S =

4623

735 1

9248

. Find the closing stock matrix C

[Jan 10]

35.If A =

857

2 43

9 16

and B =

754

362

193

find 2 A + 3B [Jan 08]

36.If the revenues of a firm are given by matrix?

=

30

100

2575

7550 R

and the costs are

given by the matrix.

15

35

1045

2525

. Find the profit matrix P.

37.If A =

54

32

=

17

3 B . Find X and such that AX = B.

38.Find the inverse of a matrix A =

−−

−

111

232

422





751

062

123


−

−

872

051

436

41.If the opening stock matrix is

24

53, the closing stock matrix is

23

32the sales

unit matrix is

43

34

the sales price per unit is Rs 2 per unit, find the purchases

matrix.

42.If the cost C = 8 x3 + 6 x2+ 3x find the a) average cost b) the marginal cost if the

Quantity produced is 300 units. If the price per unit for sales is as 750, what is the

profit or loss in the sale.

43.Find the maximum and minimum values of the function y = x4 - 8 x2 + 12.

44.If the total cost function C = 4Q - Q2+ 2 Q3 find the average cost function and

marginal cost function. If Q = total quantity.

45.The total cost of x units is y rupees where y = x27.5x0.2-3000

2

3

+ x

and all units

made are sold at Rs 10 per unit. At what two points does marginal cost equals

marginal revenue.

46.From the following information determine the units to be manufactured in order to

earn maximum profits: Tc = 0.0008 X2 + 3.4 X + 25,000 and TR = 0.001 X2 + 25 X

47.A firm produces a single product and it can market as many units as it is able to produce at a price of Rs 1.75. Its plant and equipment can produce as many as 5000

units a day. The total fixed cost is its 2,000 daily. Unit variable cost is Rs 0.50. How

many units per day must be produced in order that the firm breaks even?

48. What is sampling? When is sampling done? Discuss the different methods of

sampling and their applicability in business.

49. A sample of 200 people with particular disease was selected. Out of these, 100 were

given a drug and the others were not given any drug. The results are as follows

Test whether the drug is effective or not [Jan 07]

Number of People

Drug No drug

Cured 65 55

Not Cured 35 45

50.2000 families of a city were selected at random to test belief that families with higher

income bought the sedan-type of car and families with lower income bought the small

car. Given the following results, Use chi square test to find out if it is true: [Jan 06]

Income Sedan type of

car

Small Car Total

High 594 606 1200

Low 262 538 800

Total 856 1144 2000




51.Using Chi-square analysis, determine the incidence of accidents caused by technically

skilled and unskilled personnel. [Jan 05]

Personnel Accidents No accidents Total

Skilled 10 90 100

Unskilled 15 65 80Total 25 155 180

52.Using Chi-square Analysis, determine the incidence of Job-related conflicts caused by

trained and untrained personnel. [Mar- 04]

Personnel Conflict

s

No conflicts Total

Trained 20 180 200

Untrained 30 130 160

Total 50 310 360

53. The expenditure of 1000 families is given as under:

Expenditure in Rs 40-

59

60-

79

80-

99

100-

119

120-139

No of customers 50 X1 500 X2 50

The median and mean for the distribution are both Rs 87.50. Calculate the missing

frequencies

54. Given the following frequency distribution of sales in a departmental store compute

(i) the median, and ii) The quartile deviation. What is the range of sales which contains the

middle of 50% of the receipts?

Sales in rupees 50-99 100-

149

150-159 200-249 250-299 300-

349

Total

No of customers 9 21 42 17 6 5 100

55.Calculate the consumer price Index by the method of (a) Aggregate expenditure and

(b) Family budget for the given data: [Mar 2011]

Commodity Quantity in

2009

Price in 2009 Price in 2010

A 100 8 12.00

B 25 6 7.5

C 10 5 5.25

D 20 48 52.00

E 25 15 16.50F 30 9 27.00

56.Using the following show that Fisher’s Index satisfies time reversal and factor

reversal test. [ Jan 09]


Items 200

5

2007

Price Quantity Price Quantity

P 5 6 6 7

Q 7 12 6 13

R 6 15 8 15

S 8 10 8 12



57.Construct Laspeyre’s , Paasche’s and Fisher’s Index for the following data:[Jan 07]

58.Calculate Fischer’s ideal index from the following data and prove that it satisfies the

time reversal and factor reversal tests:

[Jan 05]

59. Calculate

Fischer’s ideal index from the following data and prove that it satisfies the time

reversal and factor reversal tests: [Jan 06]

TWELVE MARKS

QUESTIONS:

1. Infer whether there is a significant variation in the preference for sweet or salty snacks

in different cities from the following data elicited with the sample. [Jan 10]

Bangalore Mumbai Chennai Kolkota

Sweet Snacks 624 987 523 842

Salty Snacks 365 482 650 9622. A study was carried out on the advertising methods of a brand of product. The unit

sales achieved by five stores were recorded as under: [Jan 09]

Calculate the F-ratio, using the Annova and 5% level of significance. Establish

Whether a) four methods of advertisement produce different effects on the sales

volumes b) there is a significant difference between the sales in the different stores.


Items 1987 1988

Price Quantity Price Quantity

A 2 8 4 6

B 5 10 6 5C 4 14 5 10

D 2 19 2 13

Items 2001 2002

Price Expenditure Price Expenditure

A 10 55 14 80

B 12 65 16 50

C 8 40 10 60

D 16 80 18 70

E 14 70 12 95

A B C D E

P0 30 32 30 31 32

Q0 95 11

5

12

0

12

5

125

P1 22 24 25 27 28

Q1 21

5

22

0

21

9

22

2

224

Store A Store B Store C Store D Store E

Method I 78 85 82 88 79

Method II 93 87 85 85 85

Method III 81 92 77 83 81

Method IV 79 83 71 78 78



3. Four judges of a soft skills assessment test gave the following marks to six candidates.

Using ANOVA test whether there is a significant differences in [Jan 08]

a) The performance of the six candidates b)The judgement of the four judges

4. The following represent the number of units of production per day turned out by 4

different workers using different types of machines [Jan 07]

Machine Type

WORKERS A B C D E

1 4 5 3 7 6

2 6 8 6 5 43 7 6 7 8 8

4 3 5 4 8 2

On the basis of this information, can it be concluded that

a) The mean productivity is the same for different machines

b) The worker’s don’t differ with regard to productivity?

6. Using the Chi Square test, analyse the following data to determine whether the

preference pattern of consumers for cell phones is dependent on income levels

Cell Phones Low Medium High Total

Nokia 65 90 100 255

Motorola 35 40 80 155

Erricson 50 60 220 330

Total 150 190 400 740

7. A clinical trial gave the following results for a certain experiment conducted in using

a new treatment for curing cold. Using the Chi square test determine whether the

new treatment was attractive or not. [Jan 10]

7. KMF wishes to test whether the preference pattern of Bangalore consumers for

different kinds of milk is dependent on income levels. A random sample of 1200

consumers gives the following data. Use the Chi-square test and determine whether the preference patterns are independent of income levels. [Jan 08]


Judges A B C D E F

1 11 12 11 12 13 13

2 13 13 11 13 12 12

3 3 12 12 14 13 12

4 14 15 13 16 14 12

Treatment Favourable

Response

No Response Total

New 265 185 450

Conventional 375 115 490Total 640 300 940



8. A business man from Chennai wishes to sell his products in Bangalore he can set up a

showroom in the city or can sell through a wholesaler, setting up a showroom in the

city will entail costs of Rs 6,00,000 with a 55% probability success. If the showroom

succeeds he can gain a net profit of Rs 10,00,000 per year. If it fails he can either

shutdown the showroom or rent it out for an annual rent of Rs 3,60,000(for the rest

of the year). The probability that he gets rent for the showroom is 40%.

If he sells through a wholesaler he incurs Rs 3,00,000 initial costs. The chances of

selling successfully are 45% with a net profit of Rs 5,50,000 per year.a) Advice the businessman on the best decision

b) How is the decision tree analysis useful in business decision [Mar 04]

9. A businessman has two options to sell his products. He can set up a showroom in the

city or can sell from his factory outlet. Setting up a showroom will cost Rs 3,00,000

with a 60% probability of success. If the showroom succeeds, he can close the

showroom or rent it out for an annual rent of Rs 2,40,000( for the rest of the year).

The probability of getting rent is 80%. [Jan05]

If he sells from the factory outlet, he has to incur Rs 50,000 as renovating charges.

The chances of successful selling here is 40% with a net profit of Rs 4,00,000 per

year

a) What would you advice the businessman to do b) Advise the businessman on how a decision tree helps him to make a decision.

10. An investor has 3 options to invest, but he can invest in only one option at a time. He

can invest either in a departmental stores, a cold storage or in an maintenance shop.

If he invests in a departmental store and succeeds he can invest in the cold storage

and if he succeeds he can invest in the car maintenance shop. If he invests in the cold

storage and succeeds he can invest in the car maintenance shop and if he succeeds he

can invest in the departmental store.

If he invests in the car maintenance shop succeeds he can invest in the cold storage

and if he succeeds he can invest in the departmental stores. Based on the data given

below, draw a decision tree and advice the investor on the best decision to take.[Jan 06]


INCOME Types of Milk Preferred

Low Fat Medium Fat High Fat

Low 100 225 25

Medium 125 75 150

High 75 150 275



Probability of

success

Investment Loss on failure

Departmental

Store

0.65 8,00,000 45,000

Cold storage 0.60 7,50,000 40,000

Maintenance shop 0.70 7,40,000 3,50,000

11.A manufacturer is faced with 2 alternatives about his products: [Jan 08]

a) Modify then existing product

b) Produce and market a new product

The first stage choice leads to further chooses only when the demand turns out to be

low. Details of this second stage are:

I stage Choice II stage

Alternative

Final Demand Probability Pay off in

LakhsA Reduce price Low 0.3 0.4

High 0.7 1.7

Increase price Low 0.8 0.6

High 0.2 2.25

B Reduce Price Low 0.2 0.5

High 0.8 1.25

Increase Price Low 1.0 0.8

High 0 2.0

Construct a decision tree and pay of table and advice the manufacturer on the best

course of action.

12.A businessman makes two independent investments A and B available to him but he

lacks the capital to undertake both of them simultaneously. He can choose to take A

first and then stop or if A is successful then take B or vice versa. The probability of

success on A is 0.7, while for B it is 0.4. Both investments require an initial capital

outlay of Rs 20,000 and both return nothing if the venture is unsuccessful. Sucessful

completion of A will return Rs 30,000 (over cost) whereas successful completion of

B will return Rs 50,000 (over cost). Draw the decision tree and determine the best

strategy. [Jan 09]

13. A restaurateur has 3 projects in hand. He can only take up one project at a time. The

first project is to take up a fast food corner at an investment of Rs 6,00,000 where the


Alternative Initial Demand

Probability Pay off on

High Low High

A 0.6 0.4 5 lakhs

B 0.5 0.5 7 lakhs



chances of success will be 0.75 with cash inflow of Rs 9,00,000. Failure means cash

inflow of Rs 1,50,000 in salvage furniture and utensils.

The second project is to open expresso coffee shop with an investment of Rs 8,00,000

where there will be definite success with an inflow of Rs 9,00,000.

The third project is to start a Darshini with an investment of Rs 10,00,000. The chance

of success are 0.6 with an inflow of Rs 12,00,000. Failure means an inflow of Rs3,00,000 in salvage material. If there is a success the restaurateur will decide to start a

fast food kiosk with an investment of Rs 4,00,000 whereby he can expect high

demand with 0.8 probability and Rs 5,00,000 inflow, medium demand with 0.15

probability and cash flow Rs 4,00,000, low demand with a cash inflow of Rs 1,00,000

All the amounts have been adjusted to current value. You are expected to draw a

decision and a payoff table and thereby advise the restaurateur about the best course

of action [Jan 10]

14. Construct index numbers of price from the following data by applying

a. Laspeyre’s b. Paasche’s c. Bowleye’s d. Marshal Edgeworth’s Method [Jan 08]

Also find the Fisher’s price index and test it for the factor reversal and time reversal

tests

Commodity Po Qo P1 Q1

A 12 18 14 16

B 15 20 16 15

C 14 24 15 20

D 13 29 12 23

E 11 28 13 21

15. The total cost of production of a firm is given by the following functions

C = 200135 + x . Find [Mar-03]

a) The total cost for an output of 65 units.

b) The average cost for an output of 100 unis

c) The marginal cost for an output of 50 units

d) If the quantity sold is 150 units, at what price should the firm sell so as to break-

even.

14. The market supply function of a commodity is q = 80 + 4P where q denotes the

quantity supplied and P denotes the market price. The unit production cost is Rs 1.50.

The government feels that a total profit of Rs 240 is desirable. What is the price that

the farmer has to receive so that he can realise this profit. [Mar 07]

15. The total cost of production of a firm is given by the following functionsC = 0.8X +14. Find [Sept-03]

a) Total cost an output of 10 units

b) The average cost of an output of 8 units


d) If the quantity sold is 14 units at what price should the firm sell so as to breakeven?

16. The total cost of production of a firm is given by the function C= 12x2-6x+4

a) The total cost for an output of 15 units

b) The average cost for an output of 12 units


d) The profit function for x units and price per unit of Rs 4

e) The profit for 24 units as per the profit function. [Mar-04]

17. The total cost of production of a firm is given by the function C= 10x2-5x+3




a) The total cost for an output of 8 units

b) The average cost for an output of 20 units


d) The profit function for x units and price per unit of Rs 6

e) The profit for 25 units as per the profit function. [Jan05]

18. The cost function is given as C= 6 x3 + 4x2 +2. Find is x = Rs 8a) The average cost function and the average cost

b) The marginal cost function and the marginal cost

c) The revenue function if the price per unit is Rs 250 and the revenue

d) The profit function and the profit. [Jan06]

19. A firm produces a single product and it can market as many units as possible to

produce as many as 5000 units a day. The total fixed cost is Rs 2,000 daily. Unit

variable cost is Rs 0.50. How many units per day must be produced in order that the

firm breaks even [Jan 06]

20. If the cost curve C = 8 x3 + 6x2 + 3x find

a) the average cost b) the marginal cost if the quantity produced is 300 units. If the

price per unit for sales is as 2750, what is the profit or loss in the sale? [Jan 10] 21. City residents were surveyed recently to determine the readership of newspapers

available 50% of the residents read the morning newspaper 60% read the evening

newspaper and 20% read both newspapers. Find the probability that a resident

selected reads either the morning or evening paper. [Jan 07]

22. Following are the marks obtained by two students “A” and “B” in 10 tests of 100

marks each.

Tests 1 2 3 4 5 6 7 8 9 10

A 44 80 76 48 52 72 72 51 60 54

B 48 75 54 60 63 69 72 51 57 66

Find who is better in studies and if consistency is the criterion for awarding a prize,who should get the prize?


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