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Second Semester B.Com Degree Examination, May 2010

BCOM (Complementary)

Course No. 2: 2C02 COM: QUANTITATIVE TECHNIQUES

Time: 3 Hours Total Wt: 30, WGP: 120

Instruction: Use of simple calculators and statistical table permitted.

PART- A

This part consist of two bunches of questions carrying equal weightage of one. Each bunch consists of four objective types of questions. Answer all questions:

I. 1. If the probability of event A is equal to the conditional probability of A given B, (A/B), it means

a) A and B are dependent events

b) A and B are independent events

c) A and B are joint events

2. Bernoulli distribution is another name for

a) Poisson distribution

b) Normal distribution

c) Binominal distribution

3. The correlation co-efficient should always be

a) More than one

b) Less than zero

c) Between -1 and +1 (both inclusive)

4. Regression equation of Y on X is used when we want to predict

a) Value of Y for a given value of X

b) Value of X for a given value of Y

c) Both of the above (W=1)(WGP = 4)

II. 5. If P(A)=0.5, P(B)=0.6 and P(A∩B)=0.2, P(A∩B) is equal to

a) 0.1

b) 0.9

c) 0.3

d) 0.5

6. If n=6, q=⅓ and p=⅔ for a binomial distribution, the mean is equal to

a) 4

b) 6

c) 3

d) 5

7. If ∑ xy = 60, ∑ y2 = 90 assuming x and y are deviations from actual means, r will be equal to

a) 0.72

b) 0.28

c) 0.3

d) 0.8

8. The number of permutations possible, out of 5 different objects taking two at a time will be

a) 30

b) 60

c) 20

d) 10

(W = 1)(WGP = 4)

PART – B

Answer any eight questions in one or two sentences each. Each question carries a weightage of one:

9. What is meant by ‘cyclical variation’?

10. Give any two assumptions of linear programming problem.

11. What is a discrete frequency distribution?

12. Give an example of ‘mutually exclusive’ events.

13. What is the ‘line of best fit’?

14. List any two methods of calculating correlation.

15. What is the ‘key element’ in a simplex table?

16. What is standard normal variate?

17. Define operations research.

18. List two methods to analyse time series trends. (W=8x1=8) (WGP=8x4x1=32)

PART – C

Answer any six questions. Answer not to exceed one page. Each question carries a weightage of two:

19. Explain any four features of operations research.

20. What are the properties of normal distribution? (any 8)

21. How will you interpret a scatter diagram?

22. What are the different types of correlation?

23. From the following data, find the regression equation of x and y.

x: 5 6 7 3 2

y: 4 5 8 2 1

24. There are 6 boys and 4 girls. A committee of 6 is to be formed. In how many ways can this be done if the committee has to contain at least two girls.

25. A firm engaged in producing two models X1 and X2 performs 3 operations painting, assembly and testing. Relevant data are as follows:

Hours required for each unit

Model Selling Price Assembly Painting Testing

X1 Rs. 50 1.0 0.2 0.0

X2 Rs. 80 1.5 0.2 0.1

Total number of hours available per week are assembly=600, painting=100, testing=30. The firm wishes to maximize total revenue. Write up the linear programming model.

26. 4 coins are tossed at a time, 208 times. Number of heads observed at each throw is recorded and the results are as follows:

No. of heads at a throw: 0 1 2 3 4 total

Frequency: 5 48 112 35 8 208 (W=6x2=12)

Fit a binomial distribution to the given data. (WGP=6x4x2=48)

PART – D

Answer any two. Each question carries a weightage of four.

27. What are the limitations of O.R.?

28. The ranking of 10 individuals at the start and at finish of a training course are as follows:

Rank before: 1 6 3 9 5 2 7 10 8 4

Rank after: 6 8 3 2 7 10 5 9 4 1

Calculate Spearman’s rank correlation coefficient.

29. Given P(B1) = P(B2) = P(B3) = 1/3. P(A/B1) = 1/2 P(A/B2) = ¼ P(A/B3)= 1/5.

Calculate P(B2/A). (W=2x4=8) (WGP=2x4x4=32)

__________________

Second Semester B.Com Degree Examination, May 2010

BCOM (Complementary)

Course No. 2: 2C02 COM: QUANTITATIVE TECHNIQUES

Time: 3 Hours Total Wt: 30, WGP: 120

Instruction: Use of simple calculators and statistical table permitted.

PART- A

This part consist of two bunches of questions carrying equal weightage of one. Each bunch consists of four objective types of questions. Answer all questions:

I. 1. If the probability of event A is equal to the conditional probability of A given B, (A/B), it means

a) A and B are dependent events

b) A and B are independent events

c) A and B are joint events

2. Bernoulli distribution is another name for

a) Poisson distribution

b) Normal distribution

c) Binominal distribution

3. The correlation co-efficient should always be

a) More than one

b) Less than zero

c) Between -1 and +1 (both inclusive)

4. Regression equation of Y on X is used when we want to predict

a) Value of Y for a given value of X

b) Value of X for a given value of Y

c) Both of the above (W=1)(WGP = 4)

II. 5. If P(A)=0.5, P(B)=0.6 and P(A∩B)=0.2, P(A∩B) is equal to

a) 0.1

b) 0.9

c) 0.3

d) 0.5

6. If n=6, q=⅓ and p=⅔ for a binomial distribution, the mean is equal to

a) 4

b) 6

c) 3

d) 5

7. If ∑ xy = 60, ∑ y2 = 90 assuming x and y are deviations from actual means, r will be equal to

a) 0.72

b) 0.28

c) 0.3

d) 0.8

8. The number of permutations possible, out of 5 different objects taking two at a time will be

a) 30

b) 60

c) 20

d) 10

(W = 1)(WGP = 4)

PART – B

Answer any eight questions in one or two sentences each. Each question carries a weightage of one:

9. What is meant by ‘cyclical variation’?

10. Give any two assumptions of linear programming problem.

11. What is a discrete frequency distribution?

12. Give an example of ‘mutually exclusive’ events.

13. What is the ‘line of best fit’?

14. List any two methods of calculating correlation.

15. What is the ‘key element’ in a simplex table?

16. What is standard normal variate?

17. Define operations research.

18. List two methods to analyse time series trends. (W=8x1=8) (WGP=8x4x1=32)

PART – C

Answer any six questions. Answer not to exceed one page. Each question carries a weightage of two:

19. Explain any four features of operations research.

20. What are the properties of normal distribution? (any 8)

21. How will you interpret a scatter diagram?

22. What are the different types of correlation?

23. From the following data, find the regression equation of x and y.

x: 5 6 7 3 2

y: 4 5 8 2 1

24. There are 6 boys and 4 girls. A committee of 6 is to be formed. In how many ways can this be done if the committee has to contain at least two girls.

25. A firm engaged in producing two models X1 and X2 performs 3 operations painting, assembly and testing. Relevant data are as follows:

Hours required for each unit

Model Selling Price Assembly Painting Testing

X1 Rs. 50 1.0 0.2 0.0

X2 Rs. 80 1.5 0.2 0.1

Total number of hours available per week are assembly=600, painting=100, testing=30. The firm wishes to maximize total revenue. Write up the linear programming model.

26. 4 coins are tossed at a time, 208 times. Number of heads observed at each throw is recorded and the results are as follows:

No. of heads at a throw: 0 1 2 3 4 total

Frequency: 5 48 112 35 8 208 (W=6x2=12)

Fit a binomial distribution to the given data. (WGP=6x4x2=48)

PART – D

Answer any two. Each question carries a weightage of four.

27. What are the limitations of O.R.?

28. The ranking of 10 individuals at the start and at finish of a training course are as follows:

Rank before: 1 6 3 9 5 2 7 10 8 4

Rank after: 6 8 3 2 7 10 5 9 4 1

Calculate Spearman’s rank correlation coefficient.

29. Given P(B1) = P(B2) = P(B3) = 1/3. P(A/B1) = 1/2 P(A/B2) = ¼ P(A/B3)= 1/5.

Calculate P(B2/A). (W=2x4=8) (WGP=2x4x4=32)

__________________

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