Q1: What is the selectivity index, if the grade of tailings & concentrate is the same ?

ANS:C - 1

The selectivity index (SI) is a measure of the efficiency of a separation process, such as mineral beneficiation. It compares the grade of the valuable component in the concentrate to the grade of the same component in the tailings. The selectivity index is defined as: SI=Grade of Concentrate−Grade of FeedGrade of Tailings−Grade of Feed\text{SI} = \frac{\text{Grade of Concentrate} - \text{Grade of Feed}}{\text{Grade of Tailings} - \text{Grade of Feed}}SI=Grade of Tailings−Grade of FeedGrade of Concentrate−Grade of Feed​ When the grade of the tailings is the same as the grade of the concentrate, it implies that no separation has occurred, and the process is ineffective. In such a case, the numerator in the formula becomes zero: SI=Grade of Concentrate−Grade of FeedGrade of Tailings−Grade of Feed=Grade of Tailings−Grade of FeedGrade of Tailings−Grade of Feed=00\text{SI} = \frac{\text{Grade of Concentrate} - \text{Grade of Feed}}{\text{Grade of Tailings} - \text{Grade of Feed}} = \frac{\text{Grade of Tailings} - \text{Grade of Feed}}{\text{Grade of Tailings} - \text{Grade of Feed}} = \frac{0}{0}SI=Grade of Tailings−Grade of FeedGrade of Concentrate−Grade of Feed​=Grade of Tailings−Grade of FeedGrade of Tailings−Grade of Feed​=00​ This is an indeterminate form, but practically, it indicates that the separation process has no selectivity. In most practical scenarios, this situation is interpreted as the selectivity index being 1 when there's no discrimination between the concentrate and tailings, but if the grade in the concentrate is exactly the same as in the tailings, the correct theoretical answer is: SI=1\text{SI} = 1SI=1 However, without effective separation, if considering the practical context, the selectivity index would be closer to 0. So, given the options:

1. 0
2. ∞
3. 1
4. 0.5