Sequentially arrange the reactions of observers and type of damage during an earthquake in the increasing order of earthquake intensity measured at Modified Mercalli Intensity (MMI) Scale.
A. Earthquake is felt quite noticeably indoors, especially on upper floors of buildings. Damage: No damage. Standing motor cars may rock slightly.
B. Everyone runs outdoors. Noticed by persons driving motor cars. Damage: Considerable damage in poorly built or badly designed structures.
C. Earthquake is not felt except by a few people under especially favorable circumstances. Damage: No damage.
D. Earthquake is felt by nearly everyone, many awakened. Damage: Some dishes, windows broken, few cracks in plaster, unstable objects overturned.
Step 1: Recall MMI scale progression.
- Very weak tremor felt only by a few → lowest order.
- Felt indoors but little/no damage → next.
- Felt by many with minor damage (plaster, objects fall) → moderate intensity.
- Severe shaking with structural damage → higher intensity.
Step 2: Arrange given events.
- C → least intensity (felt only by a few).
- A → moderate, noticeable indoors but no damage.
- D → stronger, felt by nearly everyone, minor damage.
- B → highest among given, severe shaking and structural damage.
Step 3: Conclusion.
Correct sequence: C, A, D, B.
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: