Arrange the following in order of $C-Br$ bond strength in a polar solvent. The structures are as follows:
$(I)$ $1$-methylcyclohexa-$2,4$-dienyl bromide
$(II)$ cyclohexa-$2,4$-dienyl bromide
$(III)$ $1$-methylcyclopenta-$2,4$-dienyl bromide
$(IV)$ cyclopenta-$2,4$-dienyl bromide

An 'Assertion' $(A)$ and a 'Reason' $(R)$ are given below. Choose the correct answer from the following options.
Assertion $(A)$: Vinyl halides do not undergo nucleophilic substitution easily.
Reason $(R)$: Even though the intermediate carbocation is stabilized by loosely held $p-$ electrons,the cleavage is difficult because of strong bonding.

Examine the following statements pertaining to an $S_N2$ reaction:
$(1)$ The rate of reaction is independent of the concentration of the nucleophile.
$(2)$ The nucleophile attacks the $C$ atom on the side of the molecule opposite to the group being displaced.
$(3)$ The reaction proceeds with simultaneous bond formation and bond rupture/cleavage.
Amongst the following,which of the above are true?

In the following pairs of halogen compounds,which compound undergoes faster $S_N1$ reaction?
$(i)$ $2$-chloro-$2$-methylpropane and $3$-chloropentane
(ii) $2$-chloroheptane and $1$-chlorohexane

For a given alkyl group,the densities of the halides follow the order:

The reaction of $2-$bromopentane with sodium ethoxide in ethanol yields ........