The product formed when glycerol reacts with $PCl_5$ is -

Given below are two statements :
Statement $I$ :
In Lucas test,primary,secondary and tertiary alcohols are distinguished on the basis of their reactivity with conc. $HCl + ZnCl_{2}$,known as Lucas Reagent.
Statement $II$ :
Primary alcohols are most reactive and immediately produce turbidity at room temperature on reaction with Lucas Reagent.
In the light of the above statements,choose the most appropriate answer from the options given below :

When a Grignard reagent reacts with $(B)$,product $(D)$ is obtained. Reactant $(A)$ of the above reaction is:
$(A)$ $\xrightarrow{PBr_3} (C)$ $\xrightarrow{Mg, \text{ether}} \text{Grignard reagent}$
$(A) \xrightarrow{Na_2Cr_2O_7, H_2SO_4} (B)$
$\text{Grignard reagent} + (B) \to (D) \xrightarrow{H_3O^\oplus} (3,4-\text{dimethylhexan-3-ol})$

The compound $A$ when treated with ceric ammonium nitrate solution gives a yellow precipitate. The compound $A$ is

The correct order of the solubility of the different alcohols in water is

What product is formed when ethyl alcohol is oxidized with $K_2Cr_2O_7$?