The short-circuit kVA is calculated using the formula:
\[
\text{Short circuit kVA} = \frac{\text{Rated kVA}}{\text{Percent reactance}}
\]
Given:
- Rated kVA = 100 kVA,
- Reactance = 10%.
Substituting the values:
\[
\text{Short circuit kVA} = \frac{100}{0.1} = 1000 \, \text{kVA}
\]
Thus, the short-circuit kVA of the generator is 1000 kVA, which corresponds to option (3).