LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – MATHEMATICS

SECOND SEMESTER – APRIL 2012

MT 2901 – MATHEMATICAL METHODS

 

 

Date : 28-04-2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION A

Answer any five questions                                                                                   (5 x 4 = 20)

1. Find the equation of the line through the point and parallel to the line through the points  and .
2. Suppose the fixed cost of production for a commodity is $20000; the variable cost is $15 per unit and the commodity sells for $20 per unit. What is the break-even quantity?
3. If the marginal revenue function is , determine the revenue and demand functions.
4. Evaluate if  when .
5. Find the general solution of the differential equation .
6. If , find and .
7. If and , show that .

SECTION B

Answer any four questions                                                                               (4 x 10 = 40)

8. Find the equation of the line that passes through the intersection of the lines and  and is perpendicular to the line .
9. (i) Find the equation of the curve which has a slope of zero at the point , has a point of inflection at  and for which .

(ii) Evaluate      .                                                                                (6+4)

10. Evaluate  using partial fractions.
11. (i) Show that is a solution of  where c is an arbitrary constant and find a particular solution that satisfies the condition  when .

(ii) Solve the equation .                                                                (6+4)

12. Solve the difference equation , if and also calculate , ,  and .
13. If , . Find the least squares estimates for the regression equation .

SECTION C

Answer any two questions                                                                                 (2 x 20 = 40)

14. (i) What relation (parallel, perpendicular, coincident or intersecting) does the line have to the following lines?

• (b)  (c)

(d)  (e)  (f) .

(ii) Find the equation of the line which is parallel to the line through the points (5,6) and (7,8) and also passes through the intersection of the line having slope -2 through the point (-4,-6) and the line having slope 3 through the point (2,2).

(12+8)

15. (i) The quantity demanded and the corresponding price, under pure competition, are determined by the demand and supply functions and , respectively. Determine the corresponding consumer’s surplus and producer’s surplus. (ii) Evaluate (a)  (b)                                                                                                                                                                  (10+10)
16. (i) Solve the equation .

(ii) State the type, order and degree of the following equations

• ; (b) .

(iii) Show that  is a solution of  and find a particular solution if ,,

(6+4+10)

17. (i) Write the difference equation in terms of lagged values of .

(ii) If , find .

(iii) If ,   and  then show that  .                                                                                                         (8+4+8)

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