January 2010

1 Semester (Autonomous)

Time 3 Hours)                                                                                                     (Max. Marks 90

Note- Answer any two questions from Section A and any three questions from Section B. Each question of Section A is of 15 marks and each questions of Section B is of 20 marks.

(Section A)

1.      What do you mean by continuity of a function? Explain various types of discontinuity.

2.      Define Matrix and its types, Also explain how matrix is useful in Business problem solving?

3.      With the help of suitable example, explain Input/output Analysis.

(Section B)

4.      (a)     Examine the continuity of following function at x = 0 : (b)     Evaluate- 5.      (a)  (b)     The total cost of a plant is given by-

C (x) = 0.005x3 - 0.02x2 - 30x + 3000

where C (x) is the total cost associated with the total output x. Determine the average and marginal cost of the production.

6.      (a)     If sum of three numbers in geometric progression is 31 and sum of their squares is 651. Find the numbers:

(b)     Solve- (c)     Define Total Cost and Marginal Cost.

7.      Solve the following system of Linear equations by Matrix Inverse Method-

5x - 6y + 4z= 15

7x + 4y - 3z = 19

2x + y + 6z = 46

8.      (a)     Show that x5 - 5x4 + 5x3 -1, has a maximum when x =1, and minimum when x= 3, and neither when x = 0.

(b)     Explain Consumer Surplus and Producer Surplus.

*****