Step 1: Recall the definitions.
- Liquid Limit (LL): The water content at which soil changes from plastic state to liquid state.
- Plastic Limit (PL): The water content at which soil changes from semi-solid state to plastic state.
- Shrinkage Limit (SL): The water content at which further loss of moisture does not result in decrease of soil volume.
Step 2: Relationship among the limits.
By definition:
\[
\text{LL} > \text{PL} > \text{SL}.
\]
Step 3: Conclusion.
Therefore, the correct relation is LL $>$ PL $>$ SL.
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:
In a constant head permeameter, having cross-sectional area of $20 \, \text{cm}^2$, when the flow was taking place under a hydraulic gradient of $0.5$, the amount of water collected is $1200 \, \text{cm}^3$ in $60 \, \text{sec}$. The permeability of the soil is:
If the effective stress strength parameters are $C' = -10 \, \text{kPa}$ and $\phi' = 30^\circ$, the shear strength on a plane, within the saturated soil mass at a point where total normal stress is $300 \, \text{kPa}$ and pore water pressure is $150 \, \text{kPa}$, will be:
From a flow-net, which of the following information can be obtained?
A. Rate of flow
B. Pore water pressure
C. Exit gradient
D. Permeability
Choose the most appropriate answer from the options given below: