$A$ potential difference of $20 \ kV$ is applied across an $X-ray$ tube. The minimum wavelength of $X-rays$ generated (in $\mathring{A}$) is

$A$ parallel plate capacitor with a dielectric slab of dielectric constant $K$ between its plates has a capacitance $C$ and is charged to a potential $V$. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system is:

Consider the following statements:
$(a)$ $R_2SiO$ is the repeating unit of linear silicones.
$(b)$ $RSiCl_3$ on hydrolysis followed by dehydration gives linear silicones.
$(c)$ Silicones can be used as heat insulators.
$(d)$ Silica is soluble in $HF$.
The correct statement$(s)$ is/are:

If $A = \begin{bmatrix} \alpha & 0 \\ 1 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}$,then the value of $\alpha$ for which $A^2 = B$ is

The number of unpaired electrons in an $O_2$ molecule is

The number of common tangents to the two circles $x^2+y^2-8x+2y=0$ and $x^2+y^2-2x-16y+25=0$ is: