If the operating potential of an $X-$ray tube is $50 \text{ kV}$,the velocity of $X-$rays coming out of it is

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.

The characteristic $X$-rays depend on .........

The wavelength of an $X$-ray beam is $10 \, \mathring{A}$. The mass of a fictitious particle having the same energy as that of the $X$-ray photons is $\frac{x}{3} h \, \text{kg}$. The value of $x$ is ....... . ($h =$ Planck's constant)

For the production of characteristic $K_{\gamma}$ $X$-ray,the electron transition is:

The shortest wavelength of $X-$rays emitted from an $X-$ray tube depends upon