Question 1 |

A PERT network has 9 activities on its critical path. The standard deviation of each activity on the critical path is 3. The standard deviation of the critical path is

3 | |

9 | |

27 | |

81 |

Question 1 Explanation:

In CPM,

\begin{array}{l} \sigma=\sqrt{\text { sum of variance along critical path }} \\ \sigma=\sqrt{\sigma^{2}+\sigma^{2}+\ldots .+\sigma^{2}} \\ \sigma=\sqrt{9 \sigma^{2}}=\sqrt{9 \times 9}=9 \end{array}

\begin{array}{l} \sigma=\sqrt{\text { sum of variance along critical path }} \\ \sigma=\sqrt{\sigma^{2}+\sigma^{2}+\ldots .+\sigma^{2}} \\ \sigma=\sqrt{9 \sigma^{2}}=\sqrt{9 \times 9}=9 \end{array}

Question 2 |

Activities A, B, C and D form the critical path for a project with a PERT network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) distribution, and are independent of each other.

\begin{array}{|l|c|c|c|c|}\hline \text{Activity} & \text{A} & \text{B} & \text{C} & \text{D} \\ \hline \text{Mean (days)} & \text{6} & \text{11} & \text{8} & \text{15} \\ \hline \text{Variance (days$^{2})$} & \text{4} & \text{9} & \text{4} & \text{9}\\ \hline \end{array}

The probability that the project will be completed within 40 days is _____ (round off to two decimal places).

(Note: Probability is a number between 0 and 1).

\begin{array}{|l|c|c|c|c|}\hline \text{Activity} & \text{A} & \text{B} & \text{C} & \text{D} \\ \hline \text{Mean (days)} & \text{6} & \text{11} & \text{8} & \text{15} \\ \hline \text{Variance (days$^{2})$} & \text{4} & \text{9} & \text{4} & \text{9}\\ \hline \end{array}

The probability that the project will be completed within 40 days is _____ (round off to two decimal places).

(Note: Probability is a number between 0 and 1).

0.25 | |

0.5 | |

0.65 | |

0.85 |

Question 2 Explanation:

PERT-CPM

\begin{aligned} T_{S} &=40 \text { days, } T_{E}=6+11+8+15 \\ T_{E} &=40 \text { days, } \\ 2 &=\frac{T_{S}-T_{E}}{\sigma}=0 \rightarrow 50 \% \end{aligned}

Probability of completing project in expected time is always 0.5.

Question 3 |

Consider the following network of activities, with each activity named A-L, illustrated
in the nodes of the network

The number of hours required for each activity is shown alongside the nodes. The slack on the activity L, is ________ hours.

The number of hours required for each activity is shown alongside the nodes. The slack on the activity L, is ________ hours.

1 | |

2 | |

3 | |

4 |

Question 3 Explanation:

Time along path A-B-C-F-I-J-K = 42 hours

Time along path A-B-C-E-H-L = 31 hours

Time along path A-B-C-D-G-H-L = 40 hours

Slack for L = 42 - 40 = 2 hours

Time along path A-B-C-E-H-L = 31 hours

Time along path A-B-C-D-G-H-L = 40 hours

Slack for L = 42 - 40 = 2 hours

Question 4 |

The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship "X \lt Y \lt Z" means that X is predecessor of activities Y and Z. The time to complete the activities along the critical path is ______ weeks.

17 | |

21 | |

23 | |

25 |

Question 4 Explanation:

Critical path duration = 23 weeks

Question 5 |

The arc lengths of a directed graph of a project are as shown in the figure. The shortest path
length from node 1 to node 6 is _______.

7 | |

9 | |

11 | |

14 |

Question 5 Explanation:

Shortest path is

Shortest length = 7

It is the problem of shortest path which will be 7.

In this question do not confuse with critical path. Examinar ask shortest path. Critical path is the longest path which is not asked in this question.

Shortest length = 7

It is the problem of shortest path which will be 7.

In this question do not confuse with critical path. Examinar ask shortest path. Critical path is the longest path which is not asked in this question.

Question 6 |

Processing times (including setup times) and due dates for six jobs waiting to be processed at a work centre are given in the table. The average tardiness (in days) using shortest processing time rule is ___________ (correct to two decimal places).

4.26 | |

5.65 | |

6.33 | |

8.46 |

Question 6 Explanation:

By SPT Rule

Total tardiness = 38

Average tardiness per job =\frac{\text { Total tardiness }}{\text { No. of Jobs }}=\frac{38}{6}=6.33\text{days}

Total tardiness = 38

Average tardiness per job =\frac{\text { Total tardiness }}{\text { No. of Jobs }}=\frac{38}{6}=6.33\text{days}

Question 7 |

A project starts with activity A and ends with activity F. The precedence relation and durations of the activities are as per the following table:

The minimum project completion time (in days) is _______.

The minimum project completion time (in days) is _______.

19 | |

30 | |

39 | |

48 |

Question 7 Explanation:

There are two path,

\begin{aligned} A-B-D-F=30 \text { days } \\ A-C-E-F=24 \text { days } \end{aligned}

Critical path A-B-D-F and of 30 days and it is also minimum time required to complete project.

Question 8 |

The standard deviation of linear dimensions P and Q are 3 m and 4 m, respectively. When assembled, the standard deviation (in m) of the resulting linear dimension (P+Q) is ________

5 | |

6 | |

4 | |

3 |

Question 8 Explanation:

According to Root Sum Square or RSS model

\sigma_{a}=\sqrt{\sum_{i=1}^{n} \sigma_{i}^{2}}

where, \sigma_{a}= assembly tolerance standard deviation

\sigma_{i}=i^{\text {th }} component tolerance standard deviation

Here \sigma_{P}=3 \mu \mathrm{m} and \sigma_{Q}=4 \mu \mathrm{m}

\sigma_{a}=\sqrt{\sigma_{P}^{2}+\sigma_{Q}^{2}}=\sqrt{3^{2}+4^{2}}=5 \mu \mathrm{m}

\sigma_{a}=\sqrt{\sum_{i=1}^{n} \sigma_{i}^{2}}

where, \sigma_{a}= assembly tolerance standard deviation

\sigma_{i}=i^{\text {th }} component tolerance standard deviation

Here \sigma_{P}=3 \mu \mathrm{m} and \sigma_{Q}=4 \mu \mathrm{m}

\sigma_{a}=\sqrt{\sigma_{P}^{2}+\sigma_{Q}^{2}}=\sqrt{3^{2}+4^{2}}=5 \mu \mathrm{m}

Question 9 |

A sample of 15 data is follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data is

4 | |

13 | |

17 | |

20 |

Question 9 Explanation:

Mode means highest number of observations
or occurrence of data most of the time as data
17, occurs four times, i.e., highest time. So
mode is 17.

Question 10 |

In PERT chart, the activity time distribution is

Normal | |

Binomial | |

Poisson | |

Beta |

Question 10 Explanation:

Activity time distribution is beta.

There are 10 questions to complete.