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Question 1
ప్రశ్న 1
In an unconstrained Critical Path Method (CPM) network, what does a DETERMINISTIC activity duration mean for the standard forward- and backward-pass calculations?
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Explanation:
Deterministic CPM calculations use a defined duration for each network activity. The forward pass combines these durations with precedence logic to establish early times. The backward pass uses the same durations and the chosen project completion point to establish late times. This does not mean real construction durations are certain in practice. Risk and productivity may require subsequent estimates or schedule updates. A duration is not the same quantity as activity float.
వివరణ:
Question 2
ప్రశ్న 2
An activity in a zero-based CPM schedule has earliest start ES = 6 days and deterministic duration = 5 days. Times are continuous elapsed time points, so EF = ES + duration. What is its earliest finish EF?
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Explanation:
Earliest finish is calculated by adding activity duration to earliest start. The activity begins at project time 6. It occupies five continuous days under the stated convention. Its earliest finish is therefore 6 + 5 = 11 days. Inclusive day-label counting does not apply to these elapsed time points. The calculation assumes no additional lag or interruption.
వివరణ:
Question 3
ప్రశ్న 3
In an AON network, A takes 4 days and B takes 6 days; both begin at project time zero. C takes 3 days and may start only after BOTH A and B finish. All links are finish-to-start with zero lag. What is the earliest start ES of C?
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Explanation:
Activity A finishes at time 4 and B finishes at time 6. C has two immediate predecessors. It cannot begin until both of them are complete. The forward pass therefore uses the maximum predecessor earliest finish, max(4, 6). C can start at project time 6. Adding predecessor durations together would incorrectly assume sequential execution.
వివరణ:
Question 4
ప్రశ్న 4
A small CPM network consists of A = 3 days, then B = 5 days after A, then C = 4 days after B. The project begins at time zero and uses zero-lag finish-to-start links. What is the earliest finish EF of C?
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Explanation:
A starts at time zero and finishes at time 3. B starts at time 3 and finishes at time 8. C can start only after B finishes. Its four-day duration therefore takes it from time 8 to time 12. The earliest finish of C is 12 days. This chain has no parallel activities that could shorten the total.
వివరణ:
Question 5
ప్రశ్న 5
For the AON network A = 3 days and B = 7 days starting independently at time zero; C = 5 days after BOTH A and B; D = 4 days after C, what is the earliest start ES of D? All links are zero-lag finish-to-start.
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A finishes at time 3 and B finishes at time 7. Since C waits for both, its earliest start is time 7. C requires another five days, so it finishes at time 12. D follows C and can therefore start at time 12. The four-day duration of D would produce project completion at time 16. The question asks for the start of D rather than its finish.
వివరణ:
Question 6
ప్రశ్న 6
An AOA network has arrows 1→2 of 4 days, 1→3 of 6 days, 2→4 of 7 days and 3→4 of 3 days. Earliest time at event 1 is zero, and all activities have zero lag. What is the earliest occurrence time of event 4?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Event 2 occurs at time 4 through activity 1→2. Event 3 occurs at time 6 through activity 1→3. The route through event 2 reaches event 4 at time 4 + 7 = 11. The route through event 3 reaches it at time 6 + 3 = 9. A merge event can occur only after all incoming arrows finish. Its earliest occurrence time is max(11, 9) = 11 days.
వివరణ:
Question 7
ప్రశ్న 7
Two independent AON branches have A = 3 days followed by C = 4 days, and B = 5 days followed by D = 2 days. A and B both start at time zero, and project completion requires BOTH terminal activities C and D to finish. With unlimited resources and zero-lag finish-to-start links, what is the earliest project completion time?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The A-C branch requires 3 + 4 = 7 days. The B-D branch requires 5 + 2 = 7 days. Both branches may execute concurrently under the stated assumptions. The project is complete only when both terminal activities are finished. The earliest project finish is therefore max(7, 7) = 7 days. Two equally long branches can control completion simultaneously.
వివరణ:
Question 8
ప్రశ్న 8
In a zero-based CPM network with multiple terminal activities, no imposed external deadline and one project-completion milestone that requires ALL terminals, which initialization is correct for the standard backward pass?
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Explanation:
The forward pass identifies the earliest completion of the whole project. A common finish milestone requires all terminal branches to be finished. When no other deadline is imposed, this earliest project completion is the backward-pass finish boundary. Each terminal activity receives that common latest finish value. A shorter terminal branch can consequently acquire positive float. Using a separate completion date for each terminal would not calculate float against the common project finish.
వివరణ:
Question 9
ప్రశ్న 9
An AON project is a zero-lag sequence A = 4 days, B = 6 days and C = 3 days. Project time begins at zero, and the backward pass uses its earliest possible completion as the deadline. What is the latest finish LF of B?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The forward pass gives a total duration of 4 + 6 + 3 = 13 days. The final activity C must finish by project time 13. Since C takes three days, its latest start is 13 - 3 = 10. B must finish before C can start. Therefore B has LF = 10 days. Its latest start would be 10 - 6 = 4 days.
వివరణ:
Question 10
ప్రశ్న 10
For the zero-lag AON network A = 5 days and B = 8 days starting at time zero; C = 7 days after A; D = 3 days after B; and E = 2 days after BOTH C and D, calculate the latest start LS of D. Use the earliest project completion as the backward-pass deadline.
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The A-C branch reaches the merge at time 5 + 7 = 12. The B-D branch reaches the merge at time 8 + 3 = 11. E therefore starts at time 12 and finishes the project at time 14. Its latest start is also time 12 because it is the final activity. D must finish by time 12 and lasts three days. The latest start of D is 12 - 3 = 9 days.
వివరణ:
Question 11
ప్రశ్న 11
An AON network has A = 4 days; B = 5 days and C = 8 days both follow A; D = 2 days follows B; E = 1 day follows C; F = 3 days follows BOTH D and E. All relationships are zero-lag finish-to-start, and the earliest project finish sets the deadline. What is the latest finish LF of A?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The A-B-D-F path lasts 4 + 5 + 2 + 3 = 14 days. The A-C-E-F path lasts 4 + 8 + 1 + 3 = 16 days. The project therefore finishes at time 16. Backward calculation gives latest starts of B and C as times 6 and 4 respectively. A must finish by the smaller successor latest start, min(6, 4). Thus LF of A is 4 days.
వివరణ:
Question 12
ప్రశ్న 12
For the AON network A = 3 days and B = 2 days starting at time zero; C = 4 days after A; D = 6 days after B; E = 5 days after BOTH C and D; F = 2 days after E, what is the latest finish LF of C? Use zero-lag finish-to-start links and the earliest project finish as the deadline.
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
C finishes earliest at time 3 + 4 = 7. D finishes earliest at time 2 + 6 = 8. E starts earliest at time 8 and finishes at time 13. F then finishes the project at time 15. The backward pass puts E at latest start time 8, so its predecessor C must finish no later than time 8. Therefore LF of C is 8 days.
వివరణ:
Question 13
ప్రశ్న 13
An AON project has A = 3 and B = 5 days starting at time zero; C = 2 days after A; D = 4 days after B; E = 3 days after BOTH C and D; F = 2 days after E. Under a common earliest-finish deadline and zero-lag finish-to-start links, what is the latest start LS of A?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The A-C branch reaches E at time 3 + 2 = 5. The B-D branch reaches E at time 5 + 4 = 9. E lasts three days and F lasts two, so the project finishes at time 14. Working backward, E has latest start 9 and C must finish by time 9. C has latest start 9 - 2 = 7, so A must finish by time 7. The latest start of A is 7 - 3 = 4 days.
వివరణ:
Question 14
ప్రశ్న 14
AON activity data are A = 4 days and B = 5 days (both start at time zero); C = 3 days after A; D = 2 days after B; and E = 4 days after BOTH C and D. All links are zero-lag finish-to-start. What is earliest start ES of E?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A completes at time 4 and C subsequently finishes at time 4 + 3 = 7. B completes at time 5 and D finishes at time 5 + 2 = 7. E must wait for both C and D. Its earliest start is therefore max(7, 7) = 7 days. Both incoming paths govern the merge at the same time. E would finish at time 11 after its four-day duration.
వివరణ:
Question 15
ప్రశ్న 15
For the zero-lag AON network A = 6 days and B = 3 days (both start at time zero); C = 4 days after A; D = 5 days after A; E = 2 days after BOTH B and C; F = 3 days after BOTH D and E, find the latest start LS of D using the earliest project completion as the deadline.
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A-C finishes at time 6 + 4 = 10, whereas B finishes at time 3. E therefore runs from time 10 to time 12. D runs earliest from time 6 to time 11. F must wait for E and D, so it starts at time 12 and finishes at time 15. Backward calculation sets LF of D to the latest start of F, which is 12. Since D lasts five days, its latest start is 12 - 5 = 7 days.
వివరణ:
Question 16
ప్రశ్న 16
An AON network consists of A = 5 days and B = 4 days starting independently; C = 3 days after A; D = 6 days after A; E = 4 days after BOTH B and C; F = 2 days after BOTH D and E. With zero-lag finish-to-start links and no imposed deadline, what is the latest finish LF of D?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
C finishes at time 5 + 3 = 8, while B finishes at time 4. E therefore runs from time 8 to time 12. D runs earliest from time 5 to time 11. F begins at time 12 and finishes the project at time 14. Its latest start under the common finish deadline is time 12. D directly precedes F, so its latest finish is 12 days.
వివరణ:
Question 17
ప్రశ్న 17
AON data are A = 4 days and B = 8 days as initial activities; C = 3 days after A; D = 5 days after B; E = 2 days after BOTH C and D; and F = 4 days after E. All links are zero-lag finish-to-start. What is the latest start LS of C when the earliest project finish is the deadline?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The A-C branch reaches the merge at time 4 + 3 = 7. The B-D branch reaches it at time 8 + 5 = 13. E runs from time 13 to 15, followed by F until time 19. The backward pass gives E latest start 13. Therefore C may finish as late as time 13 without delaying E. Subtracting C duration of three days gives LS of C = 10 days.
వివరణ:
Question 18
ప్రశ్న 18
AON activities A = 2 days and B = 5 days start at time zero; C = 6 days after A; D = 3 days after B; E = 4 days after BOTH C and D. What is the earliest project completion time under zero-lag finish-to-start relationships and unrestricted resources?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The A-C path reaches E at time 2 + 6 = 8. The B-D path also reaches E at time 5 + 3 = 8. Since both predecessors finish at time 8, E may start then. E requires an additional four days. The earliest project completion is therefore time 8 + 4 = 12. Both incoming branches are equally long and control the start of E.
వివరణ:
Question 19
ప్రశ్న 19
For the AON network A = 6 days and B = 4 days starting independently; C = 7 days follows A; D = 5 days follows B; E = 3 days follows BOTH C and D, determine the latest start LS of B using the calculated earliest project finish. All links are zero-lag finish-to-start.
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The A-C branch completes its prerequisites for E at time 6 + 7 = 13. The B-D branch reaches E at time 4 + 5 = 9. E therefore runs from time 13 to project completion at time 16. The latest finish of D is the latest start of E, namely time 13. D can start as late as time 13 - 5 = 8. B must finish by time 8, so its latest start is 8 - 4 = 4 days.
వివరణ:
Question 20
ప్రశ్న 20
In a zero-lag AON network, A = 2 days and B = 3 days start at time zero; C = 5 days follows BOTH A and B; D = 4 days follows C. The backward pass is referenced to the earliest project finish. What is latest finish LF of A?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A finishes at time 2 while B finishes at time 3. C waits for both and begins at time 3. C lasts five days and D lasts four, producing a project finish at time 12. Working backward gives C latest start at time 3. A must finish by this latest start of C, so LF of A is 3 days. The extra one day is schedule flexibility on A relative to B.
వివరణ:
Question 21
ప్రశ్న 21
AON activities A = 3 days and B = 7 days start independently; C = 2 days follows A; D = 4 days follows B; E = 3 days follows BOTH C and D; F = 1 day follows E. Under zero-lag finish-to-start links, determine latest start LS of E using the earliest project finish as deadline.
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The A-C branch reaches E at time 3 + 2 = 5. The B-D branch reaches it at time 7 + 4 = 11. E therefore begins earliest at time 11 and finishes at time 14. F then occupies one day and finishes the project at time 15. With no additional deadline, F latest starts at time 14. E latest finishes at time 14 and thus latest starts at 14 - 3 = 11 days.
వివరణ:
Question 22
ప్రశ్న 22
AON data are A = 2 days and B = 5 days starting at zero; C = 3 days follows A; D = 6 days follows B; E = 4 days follows BOTH C and D. With zero-lag finish-to-start links and project completion set to its earliest possible time, what is latest start LS of A?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The A-C branch reaches E at time 2 + 3 = 5. The B-D branch reaches E at time 5 + 6 = 11. E begins at time 11 and project completion is time 15. On the backward pass, C must finish by the latest start of E, time 11. C lasts three days and may start as late as time 8. A must therefore finish by time 8, giving latest start 8 - 2 = 6 days.
వివరణ:
Question 23
ప్రశ్న 23
For an AON network A = 4 days; B = 2 days and C = 6 days both follow A; D = 3 days follows BOTH B and C; E = 5 days follows D, what is the latest finish LF of B? Use zero-lag finish-to-start links and the earliest project finish as the backward-pass deadline.
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A finishes at time 4. B finishes earliest at time 4 + 2 = 6 and C at time 4 + 6 = 10. D therefore begins at time 10 and finishes at time 13. E subsequently finishes the project at time 18. D has latest start 10 because it controls the project finish. B is a predecessor of D and may finish as late as time 10, so its LF is 10 days.
వివరణ:
Question 24
ప్రశ్న 24
An AOA project consists of arrows 1→2 (5 days), 1→3 (4 days), 2→4 (6 days), 3→4 (9 days), and 4→5 (3 days). Event 1 occurs at time zero; all activity relationships are zero lag. Using the earliest completion of event 5 as the backward-pass terminal time, what is the LATEST occurrence time of event 2?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The path through event 2 lasts 5 + 6 + 3 = 14 days. The path through event 3 lasts 4 + 9 + 3 = 16 days, so event 5 occurs earliest at time 16. Event 4 must occur no later than time 16 - 3 = 13. Activity 2→4 requires six days. Thus event 2 must occur no later than 13 - 6 = 7 days. The latest event-2 occurrence time is 7 days.
వివరణ:
Question 25
ప్రశ్న 25
An AOA network has arrows 1→2 (3 days), 2→4 (5 days), 2→5 (7 days), 4→6 (4 days) and 5→6 (1 day). Event 1 occurs at time zero, and event 6 is the common project finish. What is the LATEST occurrence time of event 2 when the backward pass uses the earliest possible project finish?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The path through event 4 lasts 3 + 5 + 4 = 12 days. The path through event 5 lasts 3 + 7 + 1 = 11 days. Thus the project earliest completion and event-6 latest time are both 12 days. Event 4 has latest time 12 - 4 = 8, and event 5 has latest time 12 - 1 = 11. Event 2 must satisfy both outgoing arrows, so its latest time is min(8 - 5, 11 - 7). This gives min(3, 4) = 3 days.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: B. A specified duration is used for each activity when calculating early and late times, subject to later approved schedule updates. సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: D. 11 days. సమాధానం: D.
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Question 3 ప్రశ్న 3Answer: A. 6 days. సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: C. 12 days. సమాధానం: C.
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Question 5 ప్రశ్న 5Answer: B. 12 days. సమాధానం: B.
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Question 6 ప్రశ్న 6Answer: D. 11 days. సమాధానం: D.
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Question 7 ప్రశ్న 7Answer: A. 7 days. సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: C. Set the LF of every terminal activity equal to the common project earliest completion time determined by the forward pass. సమాధానం: C.
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Question 9 ప్రశ్న 9Answer: B. 10 days. సమాధానం: B.
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Question 10 ప్రశ్న 10Answer: D. 9 days. సమాధానం: D.
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Question 11 ప్రశ్న 11Answer: C. 4 days. సమాధానం: C.
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Question 12 ప్రశ్న 12Answer: A. 8 days. సమాధానం: A.
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Question 13 ప్రశ్న 13Answer: B. 4 days. సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: B. 7 days. సమాధానం: B.
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Question 15 ప్రశ్న 15Answer: A. 7 days. సమాధానం: A.
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Question 16 ప్రశ్న 16Answer: C. 12 days. సమాధానం: C.
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Question 17 ప్రశ్న 17Answer: D. 10 days. సమాధానం: D.
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Question 18 ప్రశ్న 18Answer: B. 12 days. సమాధానం: B.
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Question 19 ప్రశ్న 19Answer: A. 4 days. సమాధానం: A.
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Question 20 ప్రశ్న 20Answer: C. 3 days. సమాధానం: C.
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Question 21 ప్రశ్న 21Answer: D. 11 days. సమాధానం: D.
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Question 22 ప్రశ్న 22Answer: B. 6 days. సమాధానం: B.
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Question 23 ప్రశ్న 23Answer: C. 10 days. సమాధానం: C.
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Question 24 ప్రశ్న 24Answer: D. 7 days. సమాధానం: D.
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Question 25 ప్రశ్న 25Answer: A. 3 days. సమాధానం: A.