Operations Research (MTH601)

1. Which of the following phases are performed to find the critical path in CPM?

   1. Forward and Backward (Early and Late finish program)
   2. Program Evaluation and Review
   3. Resource Scheduling and Allocation
   4. Precedence and succession

2. Under which of the following condition to solve an LP by using two phase method, we can't proceed for 2nd phase?

   1. Objective function of 1st phase has zero value.
   2. Objective function of 1st phase has positive value.

3. For an unbalanced Transportation problem, if the total demand is LESS than total supply then which of the following is true in order to balance the problem?

   1. A dummy sink would have to include with demand equal to the surplus
   2. A dummy source would have to include with supply equal to shortage
   3. One constraint will have evacuate
   4. One constraint will have to add

4. In a development project, if an activity (i, j) of duration three days finish earlier on the tenth day then which of the following will be its earler start day?

   1. Seventh day
   2. Third day
   3. First day
   4. Fifth day

5. In a Transportation Problem, the objective function 'Z' gives ________.

   1. Total Cost of transportation
   2. Total Time of transportation
   3. Total Profit of transportation
   4. Total inventory be supplied in transportation

6. While solving an LP by two phase meyhod, an objective function of 1st phase is always of ________.

   1. maximization
   2. minimization
   3. dependent on original objective function
   4. None of the given

7. For North West Corner method, in the first row and first column, resource and sink contain '5' and '7' units respectively; then after allocating the appropriate amount 'x11' in the cell (1, 1), we will move towards which of the following cell?

   1. (2, 2)
   2. (5, 2)
   3. (1, 2)
   4. (2, 1)

8. In Project Management, Program Evaluation and Review Technique (PERT) is based on ________ times.

   1. deterministic
   2. probabilistic
   3. stochastic
   4. Serial

9. In the phase of Early Start and Early Finish, to find the Critical Path in a network flow diagram, the computations are proceeded from ________ to the final event.

   1. bottom to top
   2. right to left
   3. left to right
   4. top to bottom

10. In a network flow diagram, two jobs 'a(i, k)' and 'b(j, k)' of durations '4' and '5' days repectively, enter an event 'k' then which of the following will be earliest start day of 'k' provided that (i, k) and (j, k) have started earlier at 3rd and 4th day respectively?

    1. 7th
    2. 8th
    3. 9th
    4. 6th

11. In North West Corner method, the first step sfter choosing the appropriate cell in 1st row, we allocate ________ so that the capacity of first row or first column is exhausted.

    1. as least as possible
    2. as much as possible
    3. non-negative quantity
    4. any arbitrary quantity

12. In a network flow diagram, events are just the points in ________ be represented by circles.

    1. xy-plane
    2. space only
    3. time only
    4. space-time

13. A set of nodes connected by lines which begin at the initial node of work and end at the terminal node is called ________ .

    1. Critical path
    2. Path
    3. Node
    4. Network

14. In a network flow diagram, the procedence relationship among the activities through ________ .

    1. project
    2. branch
    3. dummy
    4. nodes

15. By Simplex method, to maximize \(Z = 2x + 9y\) an LP problem, if 'z=0' for the initial iteration then for its next improved solution, which of the following would be the next entering variable?

    1. x>0
    2. y>0
    3. x<0
    4. y<0

16. For finding the maximum profit in an enterprise of selling two products such that 'freezing' the sale of one product and keep selling the other. The scenario is studied under ________.

    1. Un-boundedness
    2. Duality
    3. Degeneracy
    4. Artificial variable technique

17. In the initial iteration of Big M-method, the artificial variables appear in ________.

    1. Basis
    2. Non-basic variables set

18. If initial basic solution is ________, while solving an LP problem then no further iteration can be performed.

    1. degenerate
    2. non-degenerate
    3. feasible
    4. infeasible

19. Which one of the following is not an operations research problem solving steps?

    1. observation
    2. definition of the problems
    3. variable selections
    4. model construction

20. If an LP problem contains large number of constraints and a smaller number of variables then which of the following will reduce the computational burden in finding its solution?

    1. M-method
    2. Two phase method
    3. Graphical method
    4. Duality principle

21. In a network flow diagram, for an activity (i, j) of duration of three days, if its earliest start time is of two days then which of the following will be its early finish time?

    1. Six days
    2. One day
    3. One and half day
    4. Fifth days

22. Dummy activity is represented by ________ .

    1. doted line
    2. doted line with right to left arrow
    3. doted line with left to right arrow
    4. left to right arrow

23. Choose the correct one for the project times that are used in project management.

    1. Latest start time, Latest finish time, Earliest start time, Earliest finish time
    2. Latest start time, Latest finish time, Earliest start time, CPM
    3. Latest start time, Latest finish time, PERT, Earliest finish time
    4. PERT, CPM

24. In the Simplex method to solve an LP problem of maximization, if at the end of iteration, every entry of objective function row is positive then the given problem ________.

    1. needs further improvement
    2. has been maximized
    3. can not be optimized
    4. has no solution

25. In Project Management, Critical Path method is based on ________ times.

    1. deterministic
    2. probabilistic
    3. stochastic
    4. Serial

26. Which of the following is not a categories of the operation research (OR) techniques.

    1. Linear mathematical programming technique
    2. Feasible solution
    3. Inventory techniques
    4. Network techniques

27. In Simplex method to solve an LP problem, Gauss Jordan Elimination mrthod demands that all the key column entries should be zero except ________.

    1. 1st row entry
    2. key row (pivot) entry
    3. last row entry
    4. row with maximum ratio on RHS column

28. Which of the following will be an example of degenerate basic feasible solution for an LP problem?

    1. (2, 3-1)
    2. (0.2, 1)
    3. (2.1, 3)
    4. (-1.2, 0)

29. For an unbalanced Transportation problem, if the total demand is MORE than total supply then which of the following is true in order to balance the problem?

    1. One constraint will have evacuate
    2. One constraint will have to add
    3. A dummy sink would have to include with demand equal to the surplus
    4. A dummy source would have to include with supply equal to shortage

30. In two phase method process, first phase ________ the sum of artificial variables.

    1. minimize
    2. maximize
    3. maximize or minimize depending on the situation
    4. None of the given

31. In a project, a network diagram shows the procedure relations of inter related activities along with their corresponding activity ________ .

    1. times
    2. cost
    3. profit
    4. quantity

32. Dual of a Dual is ________.

    1. Primal
    2. Dual
    3. Primal-dual
    4. (Dual)^2

33. If for path 1-3-4 time is 5+3 = 8 days, for path 1-2-3-4 time is 6+7+3 = 16 days and for path 1-2-4 time is 6+6 = 12 days, then which of the followings is true.

    1. 1-3-4 is critical path
    2. 1-2-4 is critical path
    3. 1-2-3-4 is critical path
    4. 1-4 is critical path

34. In the phase of Early Start and Early Finish, to find the Critical Path in a network flow diagram, for the first node (event), we start with time ________.

    1. t = infinity
    2. t = 0
    3. t = a (arbitrary)
    4. with strict positive value

35. In two phase method if the minimum value of objective function in the first phase is greater than zero, then the solution of original problem ________.

    1. is uncertain
    2. exists
    3. does not exist
    4. None of the given

36. Duration of dummy activity is ________ .

    1. latest start time
    2. zero
    3. early start time
    4. 1

37. In two phase method, for the phase-I, if the objective function in terms of artificial variables is not minimized then the given problem has ________.

    1. Feasible solution
    2. Optimal solution
    3. Infeasible solution
    4. Degeneracy

38. The cost coefficient of artificial variable in Objective function is ________.

    1. 0
    2. M
    3. 1
    4. > than 1

39. In the Simplex method to solve an LP problem of minimization, if at the end of iteration, there is a positive coefficient in the objective row then the given problem ________.

    1. can not be optimized
    2. has no solution
    3. has been maximized
    4. needs further improvement

40. A balanced transportation model with '5' number of sources and '7' destinations has ________ number of constraint equations.

    1. 2
    2. 12
    3. 35
    4. 10

41. The task which is executed by the usage of resources and time is called ________ .

    1. node
    2. event
    3. Project
    4. activity

42. Which of the following is the objective of Project Management by using PERT and CPM menthods, for any project subject to resource constraints?

    1. To minize the project time
    2. To maximize the total project profit
    3. To minimize the total project cost
    4. To minimise the resource constraints

43. In a network flow diagram, a/an ________ is shown by dotted arrows and these consume no time or resources.

    1. activity
    2. branch
    3. dummy
    4. nodes

44. Which of the following order pair would minimize the objective function of the linear programming problem; \(z = x + 5y\) subject to \(x \ge 2, y \ge 0\) ?

    1. (2, 3)
    2. (2, 0)
    3. (0, 3)
    4. (0, 0)

45. While solving an LP problem by the Simplex method, in the standard table, the element at the intersection of key column and key row is called ________ element.

    1. Entering
    2. Leaving
    3. Slack
    4. Pivot

46. By Simplex method, to minimize \(Z = 2x + 9y\) an LP problem, if '\(z=A\gt0\)' for the initial iteration then for its next improved solution \( (0 \lt A \lt 100)\), which of the following would be the next entering variable?

    1. x<0
    2. y<0
    3. x>0
    4. y>0

47. In a network flow diagram, if any activity (i, j) starts earlier after two days and finish earlier on fifth day, then which of the following will be its completion time?

    1. Three days
    2. Five days
    3. Two days
    4. Ten days

48. The length of a path in a network is the total ________ it takes to traval along the path.

    1. length
    2. days
    3. time
    4. months

49. Which of the following difficulty may found while attempting an LP problem by M-method?

    1. It often loads to infeasible solution
    2. Computational error due to large value of M
    3. Degeneracy is inevitable
    4. Artificial do not leave the basis

50. There are ________ kinds of time calculations for a project.

    1. 1
    2. 2
    3. 3
    4. 4

51. Shortcoming of Big M method is that the value of M could be ________.

    1. very small
    2. very large
    3. negative
    4. positive

Select a course code for Objective Questions:

ACC311 ACC501 BIF101 BIF401 BIF501 BIO101 BIO201 BIO202 BIO203 BIO204 BIO301 BIO302 BIO303 BIO401 BIO503 BNK603 BT101 BT201 BT301 BT302 BT401 BT402 BT403 BT404 BT405 BT406 BT501 BT504 BT505 BT604 CHE201 CHE301 CS001 CS101 CS201 CS202 CS204 CS301 CS302 CS304 CS311 CS401 CS402 CS403 CS408 CS501 CS502 CS504 CS506 CS508 CS601 CS602 CS604 CS605 CS607 CS609 CS610 CS614 CS707 CS710 ECO401 ECO402 ECO403 ECO404 EDU302 EDU401 EDU402 EDU501 EDU601 ENG101 ENG201 ENG301 ENG501 FIN611 FIN624 FIN625 ISL201 IT430 MCM101 MCM301 MGMT623 MGT101 MGT211 MGT301 MGT401 MGT402 MGT501 MGT502 MGT503 MGT510 MGT601 MGT603 MKT501 MKT610 MKT630 MTH101 MTH202 MTH302 MTH501 MTH601 MTH634 PAK301 PHY101 PHY301 PSY101 PSY403 PSY502 PSY512 SOC101 SOC301 SOC401 STA301 STA630 STA641 ZOO102 ZOO401 ZOO501 ZOO502 ZOO503 ZOO504 ZOO505 ZOO506 ZOO510 ZOO630

Select a course code for Subjective Questions:

ACC311 CS001 CS101 CS201 CS301 CS607 CS701 CS702 CS703 CS704 CS707 CS708 CS710 CS711 CS718 CS721 CS724 ECO401 ECO403 ENG101 ENG301 MGT703 MTH501 STA301