Can you please give me the Business Mathematics previous year question papers of Osmania University of B.Com as it is very urgent for me?

As you want to get the Business Mathematics previous year question papers of Osmania University of B.Com so here is the information of the same for you:

1. A balloon, which always remains spherical, has a variable radius. Find the rate at which its volume is increasing with the radius, when it is 10 cm.

2. From the Table given below, find the average rate of change of Q with respect to t for the first thousand years.
t 0 1000 2000 3000 4000 5000 7000
Q 1000 681 463 315 214 146 68

3. From the Table given below, find the average rate of change of Q with respect to t for the thousand years following the four thousandth year;
t 0 1000 2000 3000 4000 5000 7000
Q 1000 681 463 315 214 146 68

4. From the Table given below, find the average rate of change of Q with respect to t for the total period of seven thousand years;
t 0 1000 2000 3000 4000 5000 7000
Q 1000 681 463 315 214 146 68

5. If the rate of change of y with respect to x is 5 and x is changing at 3 units per second, how fast is y changing?

6. A kite 80 feet high with 100 feet of cord starts moving away horizontally at the rate of 4 miles per hour. How fast is the cord being paid out?

7. A man is walking at the rate of 5 miles per hour towards the foot of a tower 60 feet high. At what rate is he approaching the top when he is 80 feet from the foot of the tower?

8. A man six feet long walks away from the foot of a lamp post 10 feet high, along a line and moves at the rate of 2 feet per second. Find the rate at which the shadow is increasing.

9. Divide the number 120 into two parts such that the product of one part and the square of the other is a maximum.

10. The telephone directorate finds that there is a net profit of Rs.15 per instrument if an exchange has 1000 subscribers or less. If there are over 1000 subscribers, the profits per instrument decrease by Re; .01 for each subscriber above that number. How many subscribers would give the maximum net profit?

11. The marginal cost of production of a firm is given by c’(x)=5+0.13x. The marginal revenue is given by R’(x)=18. The fixed cost is Rs.120. Find the profit function.

12. The population of town in decimal censes as given below. Estimate the population for 1895.
x: 1891 1901 1911 1921 1931
f(x) 46 66 81 93 101

13. Find y when x=8. x,y values are given below.
y: 0 5 10 15 20 25
X: 7 11 14 18 24 32

14. Find the annual net premium at the age of 25 from the following table.
Age (x) 20 24 28 32
Annual net premium f(x) 0.01427 0.01581 0.01772 0.01996

15. A function f(x) is given by the following table. Find (0.2) by a suitable formula.
x 0 1 2 3 4 5 6
f(x) 176 185 194 203 212 220 229

16. From the following table, estimate the number of students who obtained marks between 40 and 45.
Marks 30-40 40-50 50-60 60-70 70-80
No.of students 31 42 51 35 31

17. Find the value of f(1.6),if
X 1 1.4 1.8 2.2
f(x) 3.49 4.82 5.96 6.5

18. from the following table find f(0.7)approximately.
x 0.1 0.2 0.3 0.4 0.5 0.6
f(x) 2.68 3.04 3.38 3.68 3.96 4.21

19. Estimate the values of f(22) and f(42) from the following available date.
x 20 25 30 35 40 45
f(x) 354 332 291 260 231 204

20. Find the number of men getting wages between Rs. 10 and 15 from the following data.
Wages in Rs. 0-10 10-20 20-30 30-40
Frequency 9 30 35 42


21. A shop keeper sells not more that 30 pants of each colour. At least twice as many white one are sold as black ones. If the profit on each of the white be Rs.20 and that of black be 25. How many each kind be sold to give him maximum profit.

22. A sweet shop makes gift packets of sweets combines two special types of sweets A and B which weight 7 kg. At least 3 kg of A and no more that 5 kg of B should be used. The shop makes profit of Rs.15 on A and Rs.20 on B per kg. Determine the product of the mixture so as to get maximum profit.

23. A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to product a package of nuts while it takes 3 hours on machine A, 1 hour on machine B to produce a package of bolts. He earned a profit of Rs.50 per a packet of bolts. How many packets of each type should produce each day so as to maximize his profit, it he operates his machines for at least 12 hours a day.

24. Two persons A, B can stitch 3 shirts and 2 pants, 5 shirts and 2 pants per day respectively. And the daily wage of Rs.22.50 and Rs.23 per day. A ready made dress-seller wants 60 shirts and 32 pants at minimum labour cost. How many days should he utilize the service of each.

25. Assume a kg of meat contains 80 units of protein and 10 units of calcium while a litre of mile contains 15 units of protein and 60 units of calcium. If a person minimum requirements are 40 units of proteins and 30 units of calcium, what consumption of quantities of meat and milk will yield at least these minimum daily requirements.

26. A merchant deals with two items, dal and sugar. He could invest only Rs.15,000 and has a room for at most 80 bags. A bag of dal costs Rs.250 and a bag of sugar costs Rs.150. He gains Rs.15 on a bag of dal and Rs.12 on a bag of sugar. Assuming that he sells all quantities, how he should invest the money in order to get maximum profit.

27. A company manufactures two types of products, P1 and P2. Each product uses lathe and milling machine. The processing time per unit of P1 on the lathe is 5 hours and on the milling machine is 4 hours. The processing time per unit of P2 on the lathe is 10 hours and on the milling machine, 4 hours. The maximum number of hours available per week on the lathe and the milling machine are 60 hours and 40 hours, respectively. Also the profit per unit of selling P1 and P2 are Rs.6.00 and Rs.8.00, respectively. Formulate a linear programming model to determine the production volume of each of the products such that the total profit is maximized.

28. A company manufactures two different type of products: S and R . Each product requires processing on milling machine and drilling machine. But each type of machines has limited hours available per week. The net profit per unit of the products, resource requirements of the products and availability of resources are summarized as shown:
Machine type Processing time (in hours) Machine hours available per week
product S Product R
Milling machine 2 5 200
Drilling machine 4 2 240
Profit per unit (Rs) 250 400
Develop a linear programming model to determine the optimal production volume of each of the products such that the profit is maximized subject to the availability of machine hours.

29. A small manufacturer employs 5 skilled men and 10 semi-skilled men for making a product in two qualities: a deluxe model and an ordinary model. The production of a deluxe model requires 2 hour work by a skilled man and 2 hour work by a semi skilled man. The ordinary model requires 1 hours work by a skilled man and 3 hour work by a semi skilled man. According to worker union’s rules, no man can work more than 8 hours per day. The profit of the deluxe model is Rs.1000 per unit and that of the ordinary model is Rs. 800 per unit. Formulate a linear programming model f0or this manufacturing situation to determine the production volume of each model such that the total profit is maximized.

30. A company wants to engage casual labour to assemble its product daily. The company works for only one shift which consists of 8 hours and 6 days a week. The casual labour consists of two categories, viz. skilled and semi-skilled. The daily production per skilled labour is 80 assemblies and that of the semi-skilled labour is 60 assemblies. The rejection rate of the assemblies produced by the skilled labour is 5% and that of the semi-skilled labour is 10%. The loss to the company for rejecting an assembly is Rs.25. The daily wage per labour of the skilled and semi-sklled labour are Rs.240 and Rs.160, respectively. The required weekly production is 1,86,000 assemblies. The company wants to limit the number of semi-skilled labour per day to utmost 400. Develop a linear programming model to determine the optimal mix of the casual labour to be employed so that the total cost (total wage + total cost of rejections) is minimized.

31. Display the procedure for Northwest Corner cell method through a diagram.
32. Display the procedure for Least Cost Cell method through a diagram.
33. Display the procedure for Vogel’s Approximation Method through a diagram.

34. Determine an initial basic feasible solution to the following transportation problem using northwest corner cell method.
To 1 2 3 4 5 Availability
From 1 3 4 6 8 9 20
2 2 10 1 5 8 30
3 7 11 20 40 3 15
4 2 1 9 14 16 13
Demand 40 6 8 18 6

35. Find the initial basic feasible solution to the following transportation problem by Northwest corner cell method.
To 1 2 3 Supply
From 1 2 7 4 5
2 3 3 1 8
3 5 4 7 7
4 1 6 2 14
Demand 2 9 18

36. Find the initial basic feasible solution to the following transportation problem by Least cost cell method.

To 1 2 3 Supply
From 1 2 7 4 5
2 3 3 1 8
3 5 4 7 7
4 1 6 2 14
Demand 2 9 18

37. Consider the following trans-shipment problem with two sources and two destinations. The costs for shipment in rupees are given below:

Source S1 Source S2 Destination D1 Destination D2 Supply
Source S1 0 1 3 4 5
S2 1 0 2 4 25
Destination D1 3 2 0 1 -
D2 4 4 1 0 -
Demand - - 20 10
Determine the optimum shipping schedule.

38. Find the initial basic feasible solution of the following transportation problem by Vogel’s Approximation method:

Warehouse W1 W2 W3 W4 Capacity
Factory F1 10 30 50 10 7
F2 70 30 40 60 9
F3 40 8 70 20 18
Requirement 5 8 7 14 34

39. Determine an initial basic feasible solution to the following transportation problem using Northwest corner cell method.

Destination A1 A2 C1 D1 E1 Supply
Origin A 2 11 10 3 7 4
B 1 4 7 2 1 8
C 3 9 4 8 12 9
Demand 3 3 4 5 6


40. Determine an initial basic feasible solution to the following transportation problem using Vogel’s approximation method.
Destination A1 A2 C1 D1 E1 Supply
Origin A 2 11 10 3 7 4
B 1 4 7 2 1 8
C 3 9 4 8 12 9
Demand 3 3 4 5 6


41. The arrival rate of customers at the single window booking counter of a two wheeler agency follows Poisson distribution and the service time follow exponential (negative) distribution and hence, the service rate also follows Poisson distribution. The arrival rate and the service rate are 25 customers per hour and 35 customers per hour, respectively. Find the following:
(a) Utilization of the booking clerk
(b)Average number of waiting customers in the queue
(c) Average number of waiting customers in the system.

42. Vehicles pass through a toll gate at a rate of 90 per hour. The average time to pass through the gate is 36 seconds. The arrival rate and service rate follow Poisson distribution. There is a complaint that the vehicles wait for long duration. The authorities are willing to install one more gate to reduce the average time to pass through the toll gate to 30 seconds if the idle time of the toll gate is less than 10% and the average queue length at the gate is more that 5 vehicles. Check whether the installation of the second gate is justified.

43. The arrival rate of breakdown machines at a maintenance shop follows Poisson distribution with a mean of 4 per hour. The service rate of machines by a maintenance mechanic also follows Poisson distribution with a mean of 3 per hour. The downtime cost per hour of a breakdown machine is Rs.200. The labour rate per hour is Rs.50. Determine the optimal number of maintenance mechanics to be employed to repair the machines such that the total cost is minimized.

44. There are three clerks in the loan section of bank to process the initial queries of customers. The arrival rate of customers follows Poisson distribution and it is 20 per hour. The service rate also follows Poisson distribution and it is 9 customers per hour. Find the following:
(a) Average waiting number of customers in the queue as well as in the system.
(b) Average waiting time per customer in the queue as well as in the system.

45. There are four booking counters in a railway station. The arrival rate of customers follows Poisson distribution and it is 30 per hour. The service rate also follows Poisson distribution and it is 10 customers per hour. Find:
(a) Average waiting number of customers in the queue as well as in the system.
(b) Average waiting timer per customer in the queue as well as in the system.

46. There are three docks in a harbor. The arrival rate of ships follows Poisson distribution and it is 36 ships per month. The service rate (loading and unloading of containers) also follow Poisson distribution and it is 13 ships per month. The waiting space in the harbor can accommodate a maximum of 10 ships. Find the following:
(Average waiting number of ships ;in the queue as well as in the system.
(b) Average waiting timer per ship in the queue as well as in the system.

47. Vehicles are passing through a toll gate at the rate of 70 per hour. The average time to pass through the gate is 45 seconds. The arrival rate and service rate follow Poisson distribution. There is a complaint that the vehicles wait for long duration. The authorities are willing to install one more gate to reduce the average time to pass through the toll gate to 35 seconds if the idle time of the toll gate is less than 9% and the average queue length at the gate is more that 8 vehicles. Check whether the installation of the second gate is justifies.

48. The arrival rate of breakdown machines at a maintenance shop follows Poisson distribution with a mean of 6 per hour. The service rate of machines by a maintenance mechanic also follow Poisson distribution with a mean of 4 per hour. The downtime cost per hour of a breakdown machine is Rs.300. The labour hour rate is Rs.60. Determine the optimal number of maintenance mechanics to be employed to repair the machines such that the total cost is minimized.

49. Cars arrive at drive-in restaurant with a mean arrival rate of 30 cars per hour and the service rate of the cars is 22 per hour. The arrival rate and the service rate follow Poisson distribution. The number of parking space for cars is only 5. Find the standard results of this system.

50. A harbor has single dock to unload the containers from the incoming ships. The arrival rate of ships at the harbor follows Poisson distribution and the unloading time for the ships follow exponential (negative) distribution and hence, the service rate also follow Poisson distribution. The arrival rate and the service rate are 8 ships per week and 14 ships per week, respectively. Find:
(a) Average number of waiting ships in the queue and in the system.
(b) Average waiting time per ship in the queue and in the system.

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