February 2010

Master of Business Administration (MBA) Examination

I Semester

Mathematics and Statistics for Managers

Time 3 Hours)                                                                                                     (Max. Marks 80

Note: Attempt any five questions with a minimum of two questions from each part. All questions cane equal marks.

Part I : Business Mathematics

1.         (a)        Let the market supply function of an item be q = 160 + 8p,  where q denotes the quantity supplied and p denotes the market price. The unit cost of production is Rs. 4. It is felt that.the total profit should be Rs. 500. What market price has to be fixed for the Item so as to achieve this profit?

            (b)        Write a note on Logarithmic function. Discuss its characteristics,

2          (a)        Give an information definition of the limit of a function and  discuss its properties.

                        (b)        Evaluate :


3.         (a)        The demand function for &particular commodity is y = 15 exp (¬x/3) for 0 < × < 8, where y is the price per unit and x is the number of units demanded. Determine the price and quantity for which the revenue is maximum.

            (b)        Find the derivative of  with respect to x.

4.         (a)        Find the present value of an annuity consisting of 41 monthly payments of Rs. 100 each, the first being made at the end of 2 years and money is worth 6% compounded monthly.

            (b)        Using matrix inversion method, solve the following system of equations :

                        2x - y + 3z = 1, x + y + z = 2, and x - y + z = 4.


(Part II : Business Statistics)


5.         (a)        The chances that doctor A will diagnose a disease X correctly is 60% The chances that a patient will die by his treatment after correct diagnosis is 40% and chances of death by wrong diagnosis is 70%. A patient of doctor A, who had disease X, died. What is the probability that his disease was diagnosed correctly?

            (b)        In 256 sets of twelve tosses of a coin, in how many cases may one, expect eight heads and four tails?

6.         (a)        The coefficient of rank correlation between marks in Mathematics and Statistics by a certain group of students is 0.8. If the sum of the squares of the difference in ranks is given to be 33, find the number of students in the group.

            (b)        The equations of two regression lines obtained in a Correlation Analysis are as follows

                        3X + 12Y = 19,     3Y + 9X = 46

            Obtain :

(i)            The value of the correlation between X and Y,

(ii)           mean values of X and Y, and

(iii)          the ratio of the Coefficient of Variability of X to that of Y.

7,         (a)        Write a note on measuring Seasonal Variations.

(b)        Write a-note on measuring Cyclic Variations.

8.         (a)        Write a note on Statistical Desision Theory under Risk.

            (b)        Write a note on role of Statistics in Management Decisions.