| ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS) | ||||||||||||||||||
| END SEMESTER EXAMINATION – SEPT/OCT. 2015 | ||||||||||||||||||
| B.B.A. – I SEMESTER | ||||||||||||||||||
| M1 15AR104: BUSINESS MATHEMATICS AND STATISTICS | ||||||||||||||||||
| Duration: 3 Hours Max. Marks: 100 | ||||||||||||||||||
| SECTION – A | ||||||||||||||||||
| I) | Answer ALL the questions. Each carries 2 marks. (10×2=20) | |||||||||||||||||
| 1. | Statistics can be understood in two senses. Explain both with an example. | |||||||||||||||||
| 2. | Mention the laws of division and negative indices along with an example. | |||||||||||||||||
| 3. | State if the following are true or false:
i. (1000)0 = 0 ii. (4x)2 = 4x2 iii. x4 + x2 = x6 iv. (9/7)5 = 95/75 |
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| 4. | Explain four criterions on which data can be classified. | |||||||||||||||||
| 5. | What is an Annuity? Explain Annuity Due and Deferred Annuity. | |||||||||||||||||
| 6. | Solve: (5/2)x + 7/3 = (5/3)x – (1/3) | |||||||||||||||||
| 7. | A man sold an article for Rs. 161, gaining 1/6th of his outlay. Find the cost price of the article. | |||||||||||||||||
| 8. | What is coefficient of dispersion? What purpose does it serve? | |||||||||||||||||
| 9. | Find the coefficient of variation (standard deviation), if the sum of squares of the deviation of 10 observations taken from the mean 50 is 250. | |||||||||||||||||
| 10. | If A:B = 3:4, B:C = 5:9 and C:D = 16:15, find the ratio between A and D. | |||||||||||||||||
| SECTION – B | ||||||||||||||||||
| II) | Answer any FOUR questions. Each carries 5 marks. (4×5=20) | |||||||||||||||||
| 11. | i. A firm wishes to forecast sales data for the month of July on the basis of weighted average of the past data of four months. It assigns 0.10, 0.25, 0.25 and 0.4 weights to the actual sales data of past four months. Monthly sales for the months of March, April, May and June of a firm was found to be 350, 450, 400, 600 units. Forecast sales data for the month of July by using weighted average.
ii. Two quantities are in the ratio 3:4 and if 10 is subtracted from each of them, the remainders are in the ratio 1:3. What are the quantities? |
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| 12. | A stock broker firm has its head office in Mumbai and branch office in Delhi. For the year 2010, it supplied the following information:
Mumbai Delhi Number of transactions done 5470 1130 Average profit per transaction (Rs.) 300 200 From the above information calculate the average profit for the stock brokers per transaction by taking both the offices together. |
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| 13. | Municipal Corporation of Delhi collected the following amount of tax form roaming traders in a busy market:
Amount of Tax (Rs.): 25 50 75 100 200 300 No. of Traders: 135 120 90 60 55 40 From the above data of tax collections, calculate Q.D. and coefficient of Q.D. |
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| 14. | i. The average monthly income from interest for a housewife is Rs. 810 and the related median is Rs. 795. Calculate modal interest income.
ii. Find the amount in case the principal is Rs. 10,000 and the rate of compound interest is 5% p.a. for 2 yrs. if the compound interest is paid quarterly. |
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| 15. | “Positive correlation is found between the number of children born and exports over the last decade”, comment. Also explain the different types of correlation with examples. | |||||||||||||||||
| 16. | Ashok lent two equal sum of money to Rahul and Laxman. While Rahul agreed to pay interest @ 5% p.a., simple interest, Laxman will pay interest @ 6% p.a., simple interest. At the end of 10 yrs. Ashok received Rs. 1,000 more from Laxman towards interest. How much did Ashok lend to Rahul and Laxman each? | |||||||||||||||||
| SECTION – C | ||||||||||||||||||
| III) | Answer any THREE questions. Each carries 15 marks. (3×15=45) | |||||||||||||||||
| 17. | The following table shows the number of motor registrations in a certain territory for a term of 5 yrs. and the sale of motor tyres by a firm in the territory for the same period.
Find the regression equation to estimate the sale of tyres when the motor registration is known. Estimate sale of tyres when registration is 850. |
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| 18. | i. X,Y & Z start a business jointly. Twice the investment of X is equal to thrice the capital of Y and the capital of Y is four times the capital of Z. Find the share of X,Y & Z in an annual profit of Rs. 2,50,000. (5m)
ii. A survey was conducted in a city hospital and the amount spent by 150 patients is given in the following table. The median expenditure was found to be Rs. 909.52. Calculate the two missing frequencies. (10m)
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19. |
Share prices of two companies A Ltd. and B Ltd. are recorded as follows: A Ltd.: 12 13 15 14 14 14 13 17 B Ltd.: 113 114 113 115 117 114 112 114 Which company’s share prices are more variable? |
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| 20. | Following is the playing habit of certain students. Find Karl Pearson’s correlation. Also calculate probable error and point out whether ‘r’ is significant.
Age (years): 15 16 17 18 19 20 Percentage of no. of regular players: 80 75 60 40 30 15 |
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| 21. | i. A and B can complete a piece of work in 12 days, A and C in 15 days, B and C in 18 days. They work together for 5 days when A leaves. B and C continue the work for 7 days more, when B leaves. How long should it take for C to finish it? (8m)
ii. There are two numbers such that the sum of the first and three times the second is 53, while the difference between 4 times the first and twice the second is 2. Find the numbers. (7m) |
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| SECTION – D | ||||||||||||||||||
| IV) | Case Study (1×15=15) | |||||||||||||||||
| 22. | i. Following table shows the distance travelled in kilometers by executives of an IT company:
Calculate mode from the above figures by graphic method. (7m)
ii. A father wants to send his child for higher studies after 15 yrs. He expects the cost of higher studies then to be Rs. 1,00,000. How much should he save annually to have Rs. 1,00,000 after 15 years if the interest rate is 12% p.a.? (4m)
iii. A person bought an article and sold it at a profit of 20% on his purchase cost. Had he bought at 20% less, what would have been the profit percentage, if the selling price had been the same? (4m)
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