$C_6H_6O$ (phenol) $\xrightarrow[\text{3}H_2\text{ (High temp and pressure)}]{Ni} (A)$ $\xrightarrow{Cu} (B)$ $\xrightarrow{NH_2OH} (C)$ $\xrightarrow{H^{+}} (D)$ $\xrightarrow{HO^{-}} (E)$
Product $(E)$ is

Which of the following statements are correct?
$a$. Natural rubber becomes soft and sticky at high temperature.
$b$. Neoprene is a polymer of $2-$chloro$-1,3-$butadiene.
$c$. Nylon $6,6$ is a polyamide fibre.
$d$. Buna$-S$ is an example of a homopolymer.

The mass average molecular mass and number average molecular mass of a polymer are respectively $40,000$ and $30,000$. The polydispersity index of the polymer will be:

Given below are two statements,one is Assertion $(A)$ and the other is Reason $(R).$
Assertion $(A):$ Natural rubber is a linear polymer of isoprene called cis-polyisoprene with elastic properties.
Reason $(R):$ The cis-polyisoprene molecules consist of various chains held together by strong polar interactions with a coiled structure.
In the light of the above statements,choose the correct one from the options given below:

The polymer having an amide linkage is

Which among the following statements is $NOT$ true for neoprene?