Statement I: When ultraviolet light is incident on a photocell, its stopping potential is $V_0$ and the maximum kinetic energy of the photoelectrons is $K_{max}$. When the ultraviolet light is replaced by X-rays, both $V_0$ and $K_{max}$ increase.
Statement II: Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.
Answer: (C) Statement I is true, Statement II is false
X-rays have a higher frequency than ultraviolet, so $K_{max} = h\nu - \phi$ and $V_0$ both increase. Statement I is true.
The spread of speeds occurs even for monochromatic light: electrons deeper in the metal lose energy in collisions before escaping. It is not due to a range of frequencies, so Statement II is false.
Solution by Sreeraj P, M.Sc Physics