$A$ metal block is exposed to beams of $X$-rays of different wavelengths. $X$-rays of which wavelength penetrate most?

In an $X$-ray tube, electrons emitted from a filament (cathode) carrying current $I$ hit a target (anode) at a distance $d$ from the cathode. The target is kept at a potential $V$ higher than the cathode, resulting in the emission of continuous and characteristic $X$-rays. If the filament current $I$ is decreased to $I/2$, the potential difference $V$ is increased to $2V$, and the separation distance $d$ is reduced to $d/2$, then:
$(A)$ The cut-off wavelength will reduce to half, and the wavelengths of the characteristic $X$-rays will remain the same.
$(B)$ The cut-off wavelength as well as the wavelengths of the characteristic $X$-rays will remain the same.
$(C)$ The cut-off wavelength will reduce to half, and the intensities of all the $X$-rays will decrease.
$(D)$ The cut-off wavelength will become two times larger, and the intensity of all the $X$-rays will decrease.

If a voltage applied to an $X$-ray tube is increased to $1.5$ times, the minimum wavelength $(\lambda_{\min})$ of an $X$-ray continuous spectrum shifts by $\Delta \lambda = 26 \, pm$. The initial voltage applied to the tube is:

In vacuum,an electron of energy $10 \ keV$ hits a tungsten target. The emitted radiation will be:

The structure of solid crystals is investigated by using

$X$-rays of wavelength $0.140 \,nm$ are scattered from a block of carbon. What will be the wavelengths of $X$-rays scattered at $90^{\circ}$ (in $\,nm$)?