[Solved] Critical Path MCQ [Free PDF] - Objective Question Answer for Critical Path Quiz - Download Now! (2024)

1. CPM is concerned with activities.
2. CPM is suitable for non - repetitive projects.
3. CPM cannot be analysed statistically.
4. CPM establishes a relationship between time and cost.

Concept:

Critical Path Method (CPM):

• The critical path method (CPM) is a technique where you identify tasks that are necessary for project completion and determine scheduling flexibilities. A critical path in project management is thelongest sequence of activitiesthat must be finished on time in order for the entire project to be complete. Any delays in critical tasks will delay the rest of the project.
• CPM revolves around discovering the most important tasks in the project timeline, identifying task dependencies, and calculating task durations.
• CPM was developed in the late 1950s as a method to resolve the issue of increased costs due to inefficient scheduling. Since then, CPM has become popular for planning projects and prioritizing tasks.

Program (Project)Evaluationand Review Technique (PERT):

• Program Evaluation and Review Technique (PERT) is a method used to examine the tasks in a schedule and determine a Critical Path Method variation (CPM). It analyzes the time required to complete each task and its associated dependencies to determine the minimum time to complete a project.
• It estimates the shortest possible time each activity will take, the most likely length of time, and the longest time that might be taken if the activity takes longer than expected. The US Navy developed the method in 1957 on the Polaris nuclear submarine project.

Additional Information

Difference between PERT and CPM

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1. Normal float
2. Maximum float
3. Minimum float
4. Zero float
5. None of these

The activities with zero slack of head event and zero slack for the tail event, are called as critical activities.

The activities with zerofloat are called critical activities. The sequence of critical activities in a network is called the critical path.

So,the critical path, by definition, has a zero total float or delay. And the delay of one activity prolongs the duration of completion of the project.

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1. 3
2. 9
3. 81
4. 27
5. 54

Concept:

In CPM:

The standard deviation of critical path:

σ_cp=\(\sqrt {Sum\;of\;variance\;along\;critical\;path} \)

σ_cp =\(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

Where,σ₁,σ₂, ....,σ₈,σ₉are the standard deviation of each activity on the critical path

Calculation:

Given:

σ1,σ2, ....,σ8,σ9= 3

σcp=\(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

σ_cp =\(\sqrt {3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2} \)

σ_cp =\(\sqrt {9 \times 9} \)= 9

∴ the standard deviation of the critical path is9.

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1. 3
2. 9
3. 81
4. 27

Concept:

In CPM:

The standard deviation of the critical path:

σcp=\(\sqrt {Sum\;of\;variance\;along\;critical\;path} \)

σcp=\(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

Where,σ1,σ2, ....,σ8,σ9are the standard deviation of each activity on the critical path

Calculation:

Given:

σ1,σ2, ....,σ8,σ9= 3

σcp=\(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

σcp=\(\sqrt {3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2} \)

σcp=\(\sqrt {9 \times 9} \)= 9

∴ the standard deviation of the critical path is9.

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1. P-R-U-V
2. P-R-T-U
3. Q-S-T-U
4. Q-S-U-W

Explanation:

The project activities, precedence relationships are given below:

From the diagram we can conclude that the critical path isQ-S-U-W.

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Critical Path Question 6

1. 3
2. 9
3. 81
4. 27

Critical Path Question 6 Detailed Solution

Concept:

In CPM:

The standard deviation of critical path:

σ_cp=\(\sqrt {Sum\;of\;variance\;along\;critical\;path} \)

σ_cp =\(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

Where,σ₁,σ₂, ....,σ₈,σ₉are the standard deviation of each activity on the critical path

Calculation:

Given:

σ1,σ2, ....,σ8,σ9= 3

σcp=\(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

σ_cp =\(\sqrt {3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2} \)

σ_cp =\(\sqrt {9 \times 9} \)= 9

∴ the standard deviation of the critical path is9.

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Critical Path Question 7

1. small project only
2. large project only
3. both small and large projects equally
4. neither small nor large projects

Critical Path Question 7 Detailed Solution

Explanation:

Critical Path:

Acritical pathis a sequence of interdependent activities or tasks that must be finished before the project can be finished. It is thelongest path (i.e. path with the longest duration) from project start to finish.

Critical Path Method:

• Thecritical path method (CPM)is a project modeling technique that’s used by project managers to find importantdeadlinesand deliver a project on time.
• In a project, the critical path is thelongest distancebetween the start and the finish, including all the tasks and their duration.
• Once a critical path is determined, you’ll have aclear pictureof the project’s actual schedule.
• To find this, project managers use theCPM algorithmto find theleast amountof time necessary to complete each task with the least amount of slack.
• For small projects, managers are often able to memorize and to coordinate all of the various tasks necessary for their completion.
• For larger projects, however, with numerous activities occurring simultaneously, remembering and coordinating these activities can prove much more difficult. CPM and related tools allow managers to determine which particular tasks most affect the total time of the project and enable managers to better schedule each task so that deadlines are met at the least possible cost

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Critical Path Question 8

1. maximum float
2. minimum float
3. zero float
4. negative float

Critical Path Question 8 Detailed Solution

Explanation:

Critical activity:

Critical activities are those activities whose float is zero and they lie on the critical path.

Float:

Relax or delay provided to any activity is known as float.

Floats are of three types. They are as follows:

Total Float (TF):

The maximum delay or relax provided to any activity without affecting the project duration.

TF = L_j – E_i – d_ij

Free Float (FF):

Relax or delay provided to any activity without affecting the Earliest Start Time (EST) of the successor activity.

FF = E_j – E_i – d_ij

Independent Float:

Relax or delay provided to any activity without affecting the Earliest Start Time (EST) of successor activity as well as Latest Finish Time (LFT) of the predecessor activity.

IF = E_j – L_i - d_ij

Relation among float TF ≥ FF ≥ IF

Critical Path:

• The longest path in the network diagram is called Critical Path.
• The length of the Critical Path determines the minimum duration required for the completion of the project.

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Critical Path Question 9

1. negative
2. positive fraction
3. positive
4. zero

Critical Path Question 9 Detailed Solution

Explanation:

Critical Path:

• Thelongest pathin the network diagram is called theCritical Path.
• Thelengthof the Critical Path determines theminimum durationrequired for the completion of the project.

Critical activity:

• Critical activitiesare those activitiesthat lie on critical path.
• The float of activities that lie on the critical path is zero.

Float:

• Relax or delay provided to any activity is known as float.

Floats are of three types. They are as follows:

Total Float (TF):

The maximum delay or relax provided to any activity without affecting the project duration.

TF = Lj– Ei– dij

Free Float (FF):

Relax or delay provided to any activity without affecting theEarliest Start Time (EST)of the successor activity.

FF = Ej– Ei– dij

Independent Float:

Relax or delay provided to any activity without affecting the Earliest Start Time(EST)of successoractivity as well as Latest Finish Time(LFT)of the predecessoractivity.

IF = Ej– Li- dij

Relation among floatTF ≥ FF ≥ IF

On the Critical path, total, free, and independent float are all equal and zero.

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Critical Path Question 10

1. P-R-U-V
2. P-R-T-U
3. Q-S-T-U
4. Q-S-U-W

Critical Path Question 10 Detailed Solution

Explanation:

The project activities, precedence relationships are given below:

From the diagram we can conclude that the critical path isQ-S-U-W.

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Critical Path Question 11

1. 17
2. 21
3. 23
4. 25

Critical Path Question 11 Detailed Solution

We are asked to calculate the time along critical path. For complete analysis of critical path we need to do forward pass and backward pass computation. In this question only time is asked, and we know that the time along the critical path is maximum of all the paths in our network so we will directly evaluate the maximum time along any path and mark the answer to save time. Also forward and backward pass computation is necessary if we are asked to find critical path or float related parameters.

In this question “<” & “>” symbols are used to just describe the precedence relationship.

i.e. A < B means A occurs before B.

⇒ On constructing the network diagram with the given precedence relationship.

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Critical Path Question 12

Critical Path Question 12 Detailed Solution

The minimum project completion time is 30 days.

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Critical Path Question 13

1. 3
2. 9
3. 81
4. 27

Critical Path Question 13 Detailed Solution

Concept:

In CPM:

The standard deviation of the critical path:

σcp=\(\sqrt {Sum\;of\;variance\;along\;critical\;path} \)

σcp=\(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

Where,σ1,σ2, ....,σ8,σ9are the standard deviation of each activity on the critical path

Calculation:

Given:

σ1,σ2, ....,σ8,σ9= 3

σcp=\(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

σcp=\(\sqrt {3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2} \)

σcp=\(\sqrt {9 \times 9} \)= 9

∴ the standard deviation of the critical path is9.

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Critical Path Question 14

1. zero slack
2. maximum slack
3. minimum slack
4. negative slack

Critical Path Question 14 Detailed Solution

Explanation:

Critical Path

• Critical path activities are the project tasks that must start and finish on time according toschedule.
• A delay in any critical path activity will delay the completion of the scheduled project.

Float or Slack in critical activity

• Slackor float refers to the amount of timethat various related tasks can be delayed without pushing the schedule.
• Float is a measure of schedule flexibility.
• The critical path, by definition, has no slack. But other tasks not on the critical path may have a built-in float.
• If the Start date and Finishdate for an activity are the same as the schedule, the activity is said to have zero floats.
• Activities that have zero floats must start on time to prevent the schedule from slipping.
• Critical activities can also have a negative float.
• Negative float occurs when an activityfinishes beforethe scheduled date.

Additional Information

Critical Path Method (CPM):

It is commonly used for those projects which are repetitive in nature and where one has prior experience of handling similar projects. Its is a deterministic model and places emphasis on time and cost for activities of a project.

• A project can be defined as a set of large numbers of activities or jobs that are performed in a certain sequence determined.
• A network is a graphical representation of a project, depicting the float as well as the sequence of well-defined activities and events.
• An activity is any portion of a project which consumes time or resources and has a definable beginning and end.
• Event is the beginning and ending point of activity or group of activities.

B-D-E-H is the critical path inthe diagram below.

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Critical Path Question 15

Critical Path Question 15 Detailed Solution

Concept:

Draw project network and find critical path of network.

Calculation:

Various paths in this network are,

1 – 2 – 5 – 6 → 14 weeks

1 – 2 – 4 – 5 – 6 → 12 weeks

1 – 3 – 4 – 5 – 6 → 10 weeks

Hence, critical path is 1 – 2 – 5 – 6 with duration of 14 weeks.

Now, duration of activity S can be increased by 2 weeks atmost.

So, maximum duration of activity S without delaying completion of project is 6 weeks.

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