Base and available digit symbols – UGC NET Question

In a positional number system of base r, each digit position can take one of r distinct symbols. These symbols are typically 0 through r-1, giving a total of r different digits. This property allows each position to represent r possibilities, and the number of combinations grows as powers of r. Therefore, the system always uses r distinct digit symbols, making option C correct.

Option A:
Option A, r-1, would omit a required symbol (one remainder class), contradicting base-r definition.

Option B:
Option B, r², confuses digit symbols with two-digit combinations; symbols are only r.

Option C:
Option C is correct: digits available are 0 to r-1, total r symbols.

Option D:
Option D, r+1, would imply an extra symbol, effectively changing the base.