Identify product $B$ in the following reaction sequence:
$(CH_3)_2C=C(CH_3)_2$ $\xrightarrow{X_2, H_2O} A$ $\xrightarrow{OH^{-}} B$

Match the chemical conversions in List-$I$ with the appropriate reagents in List-$II$ and select the correct answer using the code given below the lists:
List-$I$:
$P$. $tert$-butyl chloride $\rightarrow$ isobutylene
$Q$. Sodium $tert$-butoxide $\rightarrow$ $tert$-butyl ethyl ether
$R$. $1$-methylcyclopentene $\rightarrow$ $1$-methylcyclopentanol
$S$. $1$-methylcyclopentene $\rightarrow$ $2$-methylcyclopentanol (trans-isomer)
List-$II$:
$1$. $(i) \ Hg(OAc)_2; (ii) \ NaBH_4$
$2$. $NaOEt$
$3$. $EtBr$
$4$. $(i) \ BH_3; (ii) \ H_2O_2/NaOH$
Codes: $P \quad Q \quad R \quad S$

What is the increasing order of reactivity of the following alkyl halides in the Williamson synthesis?
$I. \, CH_2 = CHCH_2Cl$
$II. \, CH_3CH_2CH_2Br$
$III. \, (CH_3)_3CCH_2Br$
$IV. \, CH_3CH_2CH_2Cl$

Match List-$I$ with List-$II$.
Choose the correct answer from the options given below:

Match the structures in Column-$I$ with their common names in Column-$II$ and $\text{IUPAC}$ names in Column-$III$.

Column-$I$	Column-$II$	Column-$III$
$(A) \ HO-CH_2-CH_2OH$	$(1) \ \text{sec-Butyl alcohol}$	$(i) \ \text{Ethane-1,2-diol}$
$(B) \ CH_3-CH(OH)-CH_2CH_3$	$(2) \ \text{Isopropyl alcohol}$	$(ii) \ \text{2,2-Dimethylpropan-1-ol}$
$(C) \ CH_3-CH(OH)-CH_3$	$(3) \ \text{Ethylene glycol}$	$(iii) \ \text{Butan-2-ol}$
$(D) \ (CH_3)_3C-CH_2OH$	$(4) \ \text{Neopentyl alcohol}$	$(iv) \ \text{Propan-2-ol}$

Dichlorocarbene is formed by chloroform and alcoholic $KOH$. Which reaction involves this carbene?