Water logging is caused due to:
A. Inadequate drainage facilities
B. Over irrigation
C. Presence of permeable strata
D. Seepage of water through the canals
Choose the most appropriate answer from the options given below:
Step 1: Understand causes of water logging.
Water logging occurs when excess water accumulates in the soil, raising the water table and reducing aeration.
Step 2: Analyze each option.
- (A) Inadequate drainage facilities: True, as poor drainage causes accumulation of water.
- (B) Over irrigation: True, applying more water than required raises the water table.
- (C) Presence of permeable strata: True, as water percolates downward and accumulates in subsurface.
- (D) Seepage of water through canals: True, contributes to water logging in nearby areas.
Step 3: Conclusion.
All four factors contribute $\Rightarrow$ Correct answer is (3).
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: