Step 1: Understanding penetration grade of bitumen.
Penetration test measures the hardness or softness of bitumen by measuring the depth (in tenths of a millimeter) to which a standard needle penetrates under standard test conditions.
Step 2: Apply given grade.
Bitumen grade 80/100 means that the penetration value lies between 80 and 100 tenths of a millimeter, i.e., between 8.0 mm and 10.0 mm.
Step 3: Match with given options.
Option (B) is correct: 80 mm to 100 mm (in tenths of a mm, i.e., penetration units).
Step 4: Conclusion.
Therefore, the penetration value of 80/100 grade bitumen is 80 to 100 (0.1 mm units), i.e., option (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: