## mba-1-sem-mathematics-and-statistics-for-managers-march-2011

mba-1-sem-mathematics-and-statistics-for-managers-march-2011

March 2011

1 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 section. All questions carry equal marks.

I.       (a)     With the help of Venn diagram show that (A È B)C = A C Ç B C and (A Ç B)C              =  A C È B C.

(b)     Define trigonometric functions and prove that sini2x + cos2x = 1.

2.      (a)     Define continuity of a function f (x) at x = a and give an example.

(b)     Evaluate : 3.      (a)     Find derivative of y =(2-sin x) (ex+x3+2) with respect to x.

(b)     Evaluate ∫x2 sinx3 dx.

4.      (a)     Solve the system of equations by Matrix Method :

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

(b)     Let the market supply function of an item be q = 80 + 10p, where q denotes the quantity supplied and p denotes the market price. The unit cost of production is Rs. 5. It Is felt that the total profit should be Rs. 800. What market price has to be fixed for the item, so as to achieve this profit?

5.      (a)     Explain the scope and limitations of Statistics in Managerial Decision Making.

(b)     What are the various methods of collecting primary data? Briefly explain any two such methods pointing out their merits and demerits.

6.      (a)     A coin is tossed six times. Find out probability of getting 5 or more heads.

(b)     Discuss Binomial frequency theoretical distribution and find its characteristics and applications.

7.      (a)     Define and differentiate the terms Correlation and Regression for given data.

(b)     Compute two regression equations for X and Y from given data:

X   50        60        50        60        80        50        80        40        70

Y   30        60        40        50        60        30        70        50        60

8.      (a)     Explain the utility of time series analysis depending on different components of time series.

(b)     Calculate 3-yearly, 4-yearly and 5-yearly moving average of production in given figure and draw the trend :

Years                     96     97     98        99        2000      01       02       03     04       05

Production ' X'      21     30     36        42        46          50       56       63     70       74