Among the following wavelengths, one is absent while the rest are...

In a Coolidge tube, the emitted X-rays have a continuous spectrum with a well-defined minimum wavelength, known as the cutoff wavelength \lambda_\min, given by \lambda_\min = \dfrac{hc}{eV}, where $V$ is the accelerating voltage.

All wavelengths greater than or equal to \lambda_\min are present in the continuous X-ray spectrum, while wavelengths shorter than \lambda_\min are absent.

If only one of the given wavelengths is absent while the rest are present, the absent wavelength must be the shortest one among the given options. If a longer wavelength were absent, all wavelengths shorter than it would also have to be absent.

Among the given options of $25 \text{ pm}$, $50 \text{ pm}$, $75 \text{ pm}$, and $100 \text{ pm}$, the shortest wavelength is $25 \text{ pm}$.

Therefore, $25 \text{ pm}$ is the absent wavelength.