Consider the following statements:
$(1)$ Bridgehead halides are inert towards both $S_{N^1}$ and $S_{N^2}$ reactions (until one of the ring size is an eight-membered ring).
$(2)$ The first step in both $S_{N^1}$ and $E_1$ reactions is the same.
$(3)$ $S_{N^2}$ reactions proceed with total retention of configuration.
$(4)$ $E_2$ eliminations are favored by the use of a solvent of low polarity and a high concentration of a strong base.
Which of the above statements are correct?

The correct order of increasing reactivity of $C-X$ bond towards nucleophile in the following compounds is:
$I$: Chlorobenzene (or aryl halide)
$II$: $2,4$-Dinitrochlorobenzene
$III$: $(CH_3)_3C-X$ ($3^o$ alkyl halide)
$IV$: $(CH_3)_2CH-X$ ($2^o$ alkyl halide)

Correct statements regarding alkyl halides ($R-X$) among the following are: A. Alcohol being less polar solvent as compared to water, alcoholic $KOH$ favours elimination reaction with $R-X$. B. Order of reactivity towards $S_N1$ mechanism is $C_6H_5-CH_2-Cl > C_6H_5-CHCl-C_6H_5$. C. Non substituted aryl halides exhibit properties similar to alkyl halides. D. Vinyl chloride is an example of haloalkene and allyl chloride is an example of haloalkyne. E. $R-Cl$ can be prepared by reacting $R-OH$ with $SOCl_2$ but $Ar-Cl$ cannot be prepared by reacting $Ar-OH$ with $SOCl_2$. Choose the correct answer from the options given below:

Match List-$I$ with List-$II$:

List-$I$ (Reaction)	List-$II$ (Name of reaction)
$A$. $2C_6H_5X + 2Na \xrightarrow{\text{Dry Ether}} C_6H_5-C_6H_5 + 2NaX$	$I$. Lucas reaction
$B$. $ArN_2^{+} X^{-} \xrightarrow[HCl]{Cu} ArCl + N_2 \uparrow + CuX$	$II$. Finkelstein reaction
$C$. $C_2H_5Br + NaI \xrightarrow{\text{Acetone}} C_2H_5I + NaBr$	$III$. Fittig reaction
$D$. $(CH_3)_3COH \xrightarrow[ZnCl_2]{HCl} (CH_3)_3CCl + H_2O$	$IV$. Gatterman reaction

Choose the correct answer from the options given below:

Product $(A)$ in this sequence is:

Which of the following graphs represents the correct graph for $S_N1$ reaction?