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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 B.Com. DEGREE EXAMINATION – COMMERCE SUPPLEMENTARY EXAMINATION – JUNE 2008 MT 3203 / 3200 - BUSINESS MATHEMATICS Date : 26-06-08 Time : 9.00 – 12.00 Dept. No. Max. : 100 Marks SECTION A Answer ALL Questions. (10 x 2 = 20) 1. Solve 16x+2 = 642x -1. 1 3 , 8 3. Differentiate (4x – 3)5 with respect to x. 2. Write the exponential form of (i) log 2 4. If total cost of output x is given by C = (ii) log 1000 = 4. 2x 35 + . Find the marginal cost when output is 3 units. 3 2 5. Evaluate (3x 3 + 7x 2 + 2x - 5) dx . 2 6. Evaluate xe-x dx . 0 7. Define a symmetric matrix. Give an example. 2 3 8. If A = 5 -4 , B = -7 0 1 6 9 -2 8 , C = -3 -1 5 3 -8 , then find 3A – B – 2C. 4 -9 9. In a Linear Programming Problem, define (a) objective function, (b) feasible solution. 10. Resolve into partial fractions: 1 . (1 - 3x) (2 + x) SECTION B Answer ANY FIVE Questions. (5 x 8 = 40) 11. The number of fishes (in hundreds) in a small commercial pond is approximated by F(t) = 27 – 15e0.8t , where t is in years. Find the number of fishes in 1 year, 2 years, 5 years and 10 years. 12. Solve log2 x – log2 (x - 1) = 1. 13. Find dy t t2 , when x = ,y= . dx 1+t 1+t 14. Evaluate (a) (4x + 3) dx 2x 2 + 3x + 5 , (b) x dx x2 + 1 . (4 + 4) 1 15. The marginal cost of production of a firm is given by C’(x) = 5 + 0.13x. The marginal revenue is R’(x) = 18. The fixed cost is Rs.120. Find the profit function. 2 16. If A = 1 2 1 1 , B = 4 5 0 -2 1 -3 4 3 0 and C = 1 3 1 0 -1 2 -4 , then prove that A(B+C) = AB +AC. 0 1 5 17. Solve graphically: Maximize z = 4x + 6y subject to the constraints: x + y 5 , x 2, y 4 , x 0, y 0. 2 3 4 18. Compute A , if A = 4 3 1 . 1 2 4 -1 SECTION C Answer ANY TWO Questions. 19. (a) If xy =ex-y, then prove that (2 x 20 = 40) dy log x = . dx (1 + log x) 2 (b) Differentiate log 3x 2 -7 with respect to x. (14 + 6) 20. (a) A certain manufacturing concern has the total cost function C = 15 + 9x – 6x2 + x3. Find when the total cost is minimum. (b) Find the equilibrium price and quantity, given the demand function and supply function Qd = 8p and Qs = p2 respectively. p2 21. (a) Integrate (14 + 6) 3x + 4 with respect to x. x +x-6 2 (b) Evaluate x 2 e x dx . (12 + 8) 22. Given the following transaction matrix, find the gross output to meet the final demand of 200 units of Agriculture and 800 units of Industry. | Producing | Sector | Purchasing Sector | Final | | demand | | Agriculture Industry | Agriculture 300 600 100 | | Industry 400 1200 400 | ******************** 2