# LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 ```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
(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
(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
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.
p2
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
|
|
Final
|
|
demand
|
| Agriculture
Industry
| Agriculture
300
600
100
|
| Industry
400
1200
400
|
********************
2
```