Concept:
Mercerization is a chemical treatment in which cotton fabrics are treated with a concentrated solution of sodium hydroxide (\(\mathrm{NaOH}\)) under controlled conditions. This treatment causes the cotton fibres to swell, become more circular in cross-section, and exhibit improved physical and aesthetic properties.
One of the important effects of mercerization is the improvement in the fabric hand or Numeri value. Numeri is an index used in textile engineering to evaluate the overall quality or hand of a fabric. A higher Numeri value indicates better fabric appearance, softness, and handle.
Thus, mercerization generally increases the Numeri value of a cotton fabric.
Step 1: Understand the given data.
The control (untreated) fabric has
\[
\boxed{\text{Numeri} = 6}
\]
After mercerization, improvements in fibre structure and surface characteristics increase the Numeri value.
Step 2: Recall the expected experimental value.
Experimental studies on mercerized cotton fabrics show that a control fabric having Numeri \(6\) generally attains a value of approximately
\[
\boxed{8.5}
\]
after mercerization.
This increase is due to
\[
\begin{aligned}
&\bullet\ \text{Improved lustre,}
&\bullet\ \text{Better smoothness,}
&\bullet\ \text{Enhanced softness,}
&\bullet\ \text{Improved fabric handle.}
\end{aligned}
\]
Step 3: Examine each option.
Option (A): \(6.0\)
This indicates no improvement after mercerization.
\[
\boxed{\text{Incorrect}}
\]
Option (B): \(5.2\)
This represents a decrease in Numeri, which is contrary to the effect of mercerization.
\[
\boxed{\text{Incorrect}}
\]
Option (C): \(4.2\)
This is much lower than the control value.
\[
\boxed{\text{Incorrect}}
\]
Option (D): \(8.5\)
This is the expected Numeri value after mercerization.
\[
\boxed{\text{Correct}}
\]
Step 4: Write the final answer.
Therefore, after mercerization, the expected Numeri value becomes
\[
\boxed{8.5}
\]
Hence,
\[
\boxed{\text{Option (D) is the correct answer.}}
\]