Deemed University 2011 B.B.A University: Lingayas University Term: I Title of the : Business Mathematics-II - Question Paper

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Lingayas University

BBA-MBA (Integrated) 1^st Year (Term II)

Examination Feb 2011

Business Mathematics-II (BA - 1106)

[Time: 3 Hours] [Max. Marks: 100]

Before answering the question, candidate should ensure that they have been supplied the correct and complete question paper. No complaint in this regard, will be entertained after examination.

Note: Attempt five questions in all. All questions carry equal marks. Select two questions from Section A and two questions from Section B. Question no. 8 (Section C) is compulsory.

Section A

Q-1. (a) Total salary of A and B is equal. If A gets 65% allowance of his basic salary and B gets 80% of his basic salary, what is the basic salary of A, if the basic salary of B is Rs.1100? [10]

(b) Divide the number 26 into three parts such that their successive squares have equal differences and the sum of their squares is 300. [10]

Q-2. (a) Solve the equation: [10]

(b) Solve the equation: [10]

Q-3. (a) A principal of $10 is invested at 12% interest for 1 year. Determine the future value if the interest is compounded: (a) Annually (b) semi-annually (c) quarterly (d) monthly (e) weekly. [10]

(b) A man arranges to pay off his debt of Rs.990 by 40 month installments which form an AP. When 30 installments are paid he dies leaving Rs.300 of the debt unpaid. Find the value of the first three installments.

[10]

Section B

Q-4. Write short notes on the following:

(i) The Classical and Empirical Probability [6]

(ii) The addition rules of computing probability [7]

(iii) The multiplication rules of computing probability [7]

Q-5. (a) The Board of Directors of Escorts consists of eight men and four women. A four-member search committee is to be chosen at random to conduct a nation-wide search for a new company president.

(i) What is the probability that all four members of the search committee will be women? [5]

(ii) What is the probability all four members will be men? [5]

(b) Routine physical examinations are conducted annually as part of a health service program for Metro Rail employees. It was discovered that 8 percent of the employees need corrective shoes, 15 percent need major dental work, and 3 percent need both corrective shoes and major dental work.

(i) What is the probability that an employee selected at random will need either corrective shoes or major dental work? [5]

(ii) Show this situation in the form of a Venn diagram. [5]

Q-6. In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and standard deviation of the distribution. [20]

Q-7. A firm invested Rs.10 million in a new factory that has a net return of 500,000 per year. An investment of Rs.20 million would yield net income of Rs.2 million per year. What is the linear relationship between investment and annual income? What would be the annual return on an investment of Rs.15 million? [20]

Section C

Q-8. A sample of executives was surveyed about loyalty to their company. One of the questions was, If you were given an offer by another company equal to or slightly better than your present position, would you remain with the company or take the other position? The responses of the 200 executives in the survey were cross-classified with their length of service with the company.

	Length of Service
Loyalty	Less Than 1 year	1 -5 years	6-10 years	More than 10 years	Total
Would Remain	10	30	5	75	120
Would Not Remain	25	15	10	30	80
Total	35	45	15	105	200

 

What is the probability of randomly selecting an executive who is loyal to the company (would remain) and who has more than 10 years of service. Develop a tree diagram showing Loyalty and Length of Service with Conditional and Joint Probabilities. [20]