Consider an electron in the $n=3$ orbit of a hydrogen-like atom with atomic number $Z$. At absolute temperature $T$, a neutron having thermal energy $k_{\mathrm{B}} T$ has the same de Broglie wavelength as that of this electron. If this temperature is given by $T=\frac{Z^2 h^2}{\alpha \pi^2 a_0^2 m_{\mathrm{N}} k_{\mathrm{B}}}$, (where $h$ is the Planck's constant, $k_B$ is the Boltzmann constant, $m_{\mathrm{N}}$ is the mass of the neutron and $a_0$ is the first Bohr radius of hydrogen atom) then the value of $\alpha$ is ______.

List-I shows four configurations, each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of magnitude $p$, oriented as marked by arrows in the figures. In all the configurations the dipoles are fixed such that they are at a distance $2 r$ apart along the $x$ direction. The midpoint of the line joining the two dipoles is $X$. The possible resultant electric fields $\vec{E}$ at $X$ are given in List-II.

Choose the option that describes the correct match between the entries in List-I to those in List-II.

List–I	List–II
(P)	(1) $$ \vec{E}=0 $$
(Q)	(2) $\displaystyle \vec{E} = -\,\frac{p}{2\pi\epsilon_0\,r^3}\,\hat{\jmath}$
(R)	(3) $\displaystyle \vec{E} = -\,\frac{p}{4\pi\epsilon_0\,r^3}\,(\hat{\imath} - \hat{\jmath})$
(S)	(4) $\displaystyle \vec{E} = \frac{p}{4\pi\epsilon_0\,r^3}\,(2\hat{\imath} - \hat{\jmath})$
	(5) $\displaystyle \vec{E} = \frac{p}{\pi\epsilon_0\,r^3}\,\hat{\imath}$

A circuit with an electrical load having impedance $Z$ is connected with an AC source as shown in the diagram. The source voltage varies in time as $V(t)=300 \sin (400 t) \mathrm{V}$, where $t$ is time in s . List-I shows various options for the load. The possible currents $i(t)$ in the circuit as a function of time are given in List-II.

Choose the option that describes the correct match between the entries in List-I to those in ListII.

List–I	List–II
(P)	(1)
(Q)	(2)
(R)	(3)
(S)	(4)
	(5)

List-I shows various functional dependencies of energy $(E)$ on the atomic number $(Z)$. Energies associated with certain phenomena are given in List-II.

Choose the option that describes the correct match between the entries in List-I to those in List-II.

List–I	List–II
(P) $E \propto Z^2$	(1) energy of characteristic x-rays
(Q) $E \propto (Z - 1)^2$	(2) electrostatic part of the nuclear binding energy for stable nuclei with mass numbers in the range 30 to 170
(R) $E \propto Z(Z - 1)$	(3) energy of continuous x-rays
(S) $E$ is practically independent of $Z$	(4) average nuclear binding energy per nucleon for stable nuclei with mass number in the range 30 to 170
	(5) energy of radiation due to electronic transitions from hydrogen-like atoms