The correct answer is option 'B' - fineness modulus.

Fineness modulus is an index number that represents the relative sizes of both coarse and fine aggregates in a concrete mix. It is a measure of the coarseness or fineness of the aggregate particles and is used to determine the proportioning of the aggregates in a concrete mix design.

Explanation:

1. Definition of fineness modulus:
- Fineness modulus is a single value that is used to describe the grading of aggregates. It is calculated by adding the cumulative percentages of aggregate retained on each of the standard sieves and dividing the sum by 100.
- The formula for calculating the fineness modulus is: FM = (Cumulative percentage retained / 100)

2. Importance of fineness modulus:
- The fineness modulus is an important parameter in concrete mix design as it helps in determining the proportion of fine and coarse aggregates in the mix.
- It provides an indication of the particle size distribution of the aggregates, which in turn affects the workability, strength, and durability of the concrete.
- Different types of concrete require different fineness moduli to achieve the desired properties.

3. Proportioning of aggregates:
- The fineness modulus is used to proportion the aggregates in a concrete mix. The proportion of fine and coarse aggregates is determined based on the desired fineness modulus for the specific application.
- For example, in high-strength concrete mixes, a lower fineness modulus is preferred, which means a higher proportion of fine aggregates is used.
- On the other hand, in normal strength concrete mixes, a higher fineness modulus is often used, allowing for a higher proportion of coarse aggregates.

4. Grading of aggregates:
- The fineness modulus is closely related to the grading of aggregates. It provides information about the distribution of particle sizes in the aggregate mixture.
- A low fineness modulus indicates a fine-grained aggregate with particles predominantly in the smaller size range, while a high fineness modulus indicates a coarse-grained aggregate with particles predominantly in the larger size range.
- The grading of aggregates affects the workability, strength, and durability of concrete. Well-graded aggregates with a balanced distribution of particle sizes are generally preferred in concrete mix design.

In conclusion, the fineness modulus is an index number that expresses the relative sizes of both coarse and fine aggregates in a concrete mix. It is an important parameter used in proportioning the aggregates and determining the grading of the aggregate mixture.