Effect of increasing base – UGC NET Question

With a fixed number of digit positions, a higher base allows each position to hold more distinct values. This expands the total number of combinations, thereby increasing the range of representable values. For example, three digits in base 2 yield 8 values, while three digits in base 10 yield 1000 values. Hence, increasing the base increases the representable range.

Option A:
Option A is correct because the total number of distinct patterns is base^digits, so raising the base while holding digits constant raises this power. This mathematical relationship directly implies an increased range.

Option B:
Option B, decreases, is the opposite of what actually happens. Decreasing the base reduces the number of choices per position and thus shrinks the range.

Option C:
Option C, keeps unchanged, would only be true if either the base or the number of digits did not change. Changing the base without altering digits affects the range.

Option D:
Option D, first increases then decreases, does not apply here because the formula base^digits grows monotonically as the base increases for a fixed positive number of digits.