January 2010

I Semester

Time 3 Hours)                                                                                                    (Max. Marks 60

Note- Attempt any five questions with a minimum of two questions from each section. All questions carry equal marks.

(Section A)

1.      (a)     In an industry of 100 firms, 54 practice Symbiotic Marketing, 15 employ Symbiotic Marketing and 66 adopt Morph Marketing. The number of firms adopting Symbiotic Marketing and Symbiotic Marketing is 33, Symbiotic-Marketing and Morph Marketing is 30; Symbiotic Marketing and Morph Marketing is 39. If the number of firms practicing the three styles of marketing is 24, find the number of firms :

(i)         Employing Symbiotic-Marketing only,

(iii)       Practicing Morph-Marketing only and

(iv)       Not resorting to any of these three.

(b)     (i)         Evaluate :

(ii)        A wholesale vegetable seller has the following price schedule : Rs. 5 per kilogram for 20 kilograms or less, Rs. 4 per kilogram for more than 20 kilograms and not more than 40 kilograms, Rs. 3.50 per kilogram for more than 40 kilograms. Express the price p as a function of the quantity x. Discuss the continuity of p at x = 20 and x = 40.

2.      (a)     A manufacturer can sell x items per day at a price p rupees each, where .The cost of production for x items is 500 + 13x + 0.2x2. Find how much he should produce to have a maximum profit, assuming that all items produced can be sold? What is the maximum profit?

(b)     A company manufactures two types of TV sets, which are assembled and finished in two workshops W, and W2. Each type takes 20 hours and 10 hours for assembly and 5 hours and 3 hours for finishing in the respective workshops. If total number of hours available are 450 and 230 in workshops W1 and W2 respectively, calculate the number of units of each type be produced, using matrix method only.

3.      (a)     Solve the system of equations using Cramer's Rule:

2x + 4y - z = 9

3x + y + 2z =7

+ 3y - 3z = 4

(b)     Evaluate each of the integrals-

4.      (a)     (i)               If f (x) = 2x2 - 5x + 4, for what value of x is 2f (x) = f(2x)?

(ii)

(b)     Define the following terms-

(i)               Linear function                       (ii)        Quadratic function

(iii)             Exponential function              (iv)       Logarithmic function.

(Section B)

5.      (a)     The value of the arithmetic mean and standard deviation of the following frequency distribution of a continuous variable derived from the use of working origin and scale are Rs. 107 and 13.1 respectively. Determine the actual classes-

Step deviation d     :          -3         -2         -1         0          +1        +2

Frequency, f           :          1          3          4          7          3          2

(b)     The data for the promotion and academic qualification of a company Is given below-

(i)         Calculate the conditional probability of promotion after en MBA has been identified.

(ii)        Calculate the conditional probability that it is an MBA when a promoted employee has been chosen.

(iii)       Find the probability that a promoted employee was an MBA.

6.      (a)     The lifetimes of certain kinds of electronic devices have a mean of 300 hours and standard deviation of 25 hours. Assuming that the distribution of these lifetimes, which are measured to the nearest hour, can be approximated closely with a normal curve.

(i)         Find the probability that any one of these electronic devices will have a lifetime of more than 350 hours.

(ii)        What percentage will have lifetimes of 300 hours or less?

(iii)       What percentage will have lifetimes from 220 or 260 hours?

(b)     A movie producer is bringing out a new movie. In order to develop an advertising strategy, he wants to determine whether the movie will appeal most to a particular age group or whether it will appeal equally to all age groups. The producer takes a random sample attending the preview of the new movie, and obtains the following results-

What Inference will you draw from this data?

7.      (a)     The following data relate to age of employees and the number of days they reported sick in month-

Calculate karl Pearson's Coefficient of Correlation and Interpret it.

(b)     The following table gives the aptitude test scores and productivity indices of 10 workers selected at random-

Estimate the productivity index of a worker whose test score is 92 using a regression equation.

8.      A tea company appoints four salesmen, A, B, C and D, and observes their sales in three seasons- summer, winter and monsoon. The figures (in lakhs) are given iri the following table-

 Season Salesman Total A B C D Summer 36 36 21 35 128 Winter 28 29 31 32 120 Monsoon 26 28 29 29 112 Total 90 93 81 96 360

(a)     Do the salesmen significantly differ in performance?

(b)     Is there significant difference between the seasons?

9.      (a)     What do you understand by Time Series Analysis? Explain the Exponential smoothing Method.

(b)     What are the steps involved in decision theory approach? What are different types of decision-making environments? Explain any two.