Given below are two statements :

Statement $I$ : Gallium is used in the manufacturing of thermometers.

Statement $II$ : A thermometer containing gallium is useful for measuring the freezing point ( $256 \mathrm{~K}$ ) of brine solution.

In the light of the above statement, choose the correct answer from the options given below :

In the following sets of reactants which two sets best exhibit the amphoteric characters of $Al_2O_3. xH_2O$ ?

Set $1$: $Al_2O_3 .xH_2O\, (s)$ and $OH^-(aq)$

Set $2$: $Al_2O_3 .xH_2O\, (s)$ and $H_2O\,(l)$

Set $3$: $Al_2O_3 .xH_2O\, (s)$ and $H^+(aq)$

Set $4$: $Al_2O_3 .xH_2O\, (s)$ and $NH_3(aq)$

Hoop's process is used for the purification of the metal

Give suitable laboratory preparation for diborane.

The correct statements from the following are :

$(A)$ The decreasing order of atomic radii of group $13$ elements is $\mathrm{Tl}>\mathrm{In}>\mathrm{Ga}>\mathrm{Al}>\mathrm{B}$.

$(B)$ Down the group $13$ electronegativity decreases from top to bottom.

$(C)$ $\mathrm{Al}$ dissolves in dil. $\mathrm{HCl}$ and liberate $\mathrm{H}_2$ but conc. $\mathrm{HNO}_3$ renders Al passive by forming a protective oxide layer on the surface.

$(D)$ All elements of group 13 exhibits highly stable +1 oxidation state.

$(E)$ Hybridisation of $\mathrm{Al}$ in $\left[\mathrm{Al}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}$ ion is $\mathrm{sp}^3 \mathrm{~d}^2$.

Choose the correct answer from the options given below: