Which of the following statements (pertaining to CPM network analysis) are correct?
A. It is an event-oriented method.
B. It is an activity-oriented method.
C. Time and cost are controlling factors.
D. Time alone is the controlling factor.
Choose the most appropriate answer from the options given below:
Step 1: Difference between PERT and CPM.
- PERT (Program Evaluation and Review Technique) is an event-oriented method, focusing on uncertainties in project time.
- CPM (Critical Path Method) is an activity-oriented method, focusing on planning, scheduling, and control of time and cost.
Step 2: Checking each statement.
- (A) Event-oriented → This is true for PERT, not CPM. Hence, incorrect.
- (B) Activity-oriented → Correct for CPM.
- (C) Time and cost are controlling factors → Correct, CPM deals with cost and time optimization.
- (D) Time alone is the controlling factor → Incorrect, because CPM considers both time and cost.
Step 3: Conclusion.
The correct statements are B and C only.
The solution(s) of the ordinary differential equation $y'' + y = 0$, is:
(A) $\cos x$
(B) $\sin x$
(C) $1 + \cos x$
(D) $1 + \sin x$
Choose the most appropriate answer from the options given below:
For the matrix, $A = \begin{bmatrix} -4 & 0 \\ -1.6 & 4 \end{bmatrix}$, the eigenvalues ($\lambda$) and eigenvectors ($X$) respectively are:
The value of $\iint_S \vec{F} \cdot \vec{N} \, ds$ where $\vec{F} = 2x^2y \hat{i} - y^2 \hat{j} + 4xz^2 \hat{k}$ and $S$ is the closed surface of the region in the first octant bounded by the cylinder $y^2 + z^2 = 9$ and the planes $x = 0, x = 2, y = 0, z = 0$, is:
The value of the integral $\displaystyle \oint_C \frac{z^3 - 6}{2z - i} \, dz$, where $C: |z| \leq 1$, is:
The time estimates obtained from four contractors (P, Q, R and S) for executing a particular job are as under:
\[\begin{array}{|c|c|c|c|} \hline \textbf{Contractor} & \textbf{Optimistic time, $t_o$} & \textbf{Most likely time, $t_m$} & \textbf{Pessimistic time, $t_p$} \\ \hline \text{P} & 5 & 10 & 13 \\ \hline \text{Q} & 6 & 9 & 12 \\ \hline \text{R} & 5 & 10 & 14 \\ \hline \text{S} & 4 & 10 & 13 \\ \hline \end{array}\]
Which of these contractors is more certain about completing the job in time?