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(C) Statement $A$ is true: The characteristic $X-$ray spectrum is produced due to electronic transitions between energy levels of the target atoms. Si

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Both $A$ and $B$ are true.

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(C) Statement $A$ is true: The characteristic $X-$ray spectrum is produced due to electronic transitions between energy levels of the target atoms. Since these energy levels $(E_K, E_L, \dots)$ are specific to the atomic number $(Z)$ of the element,the wavelengths $\lambda = \frac{hc}{E_K - E_L}$ depend on the nature of the target material.Statement $B$ is true: The short wavelength limit (cut-off wavelength) of the continuous $X-$ray spectrum is given by $\lambda_{min} = \frac{hc}{eV}$,where $V$ is the accelerating potential difference. Thus,$\lambda_{min} \propto \frac{1}{V}$,meaning it varies inversely with the potential difference applied to the $X-$ray tube.Therefore,both statements are true.

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