Polyethylene is prepared from calcium carbide as follows:
$CaC_2 + 2H_2O \to Ca(OH)_2 + C_2H_2$
$C_2H_2 + H_2 \to C_2H_4$
$nC_2H_4 \to (-CH_2-CH_2-)_n$
Calculate the amount of polyethylene produced from $64 \ kg$ of $CaC_2$. (in $kg$)

Assertion : $1, 3-$ Butadiene is the monomer for natural rubber.
Reason : Natural rubber is formed through anionic addition polymerization.

An organic compound $P$ with molecular formula $C_{9}H_{18}O_{2}$ decolorizes bromine water and also shows a positive iodoform test. $P$ on ozonolysis followed by treatment with $H_{2}O_{2}$ gives $Q$ and $R$. While compound $Q$ shows a positive iodoform test,compound $R$ does not. $Q$ and $R$ on oxidation with pyridinium chlorochromate $(PCC)$ followed by heating give $S$ and $T$,respectively. Both $S$ and $T$ show a positive iodoform test.
Complete copolymerization of $500$ moles of $Q$ and $500$ moles of $R$ gives one mole of a single acyclic copolymer $U$.
[Given,atomic mass: $H=1, C=12, O=16$ ]
$(1)$ Sum of the number of oxygen atoms in $S$ and $T$ is. . . . . .
$(2)$ The molecular weight of $U$ is
Give the answer for questions $(1)$ and $(2)$.

Match the polymers given in Column-$I$ with their commercial names given in Column-$II$.

Column-$I$	Column-$II$
$A$. Polyester of glycol and phthalic acid	$i$. Novolac
$B$. Copolymer of $1,3$-butadiene and styrene	$ii$. Glyptal
$C$. Phenol and formaldehyde resin	$iii$. Buna-$S$
$D$. Polyester of glycol and terephthalic acid	$iv$. Buna-$N$
$E$. Copolymer of $1,3$-butadiene and acrylonitrile	$v$. Dacron

Which of the following statements is correct for a spontaneous polymerization reaction?

Match the chemical substances in Column-$I$ with the type of polymers/type of bonds in Column-$II$.

Column-$I$	Column-$II$
$A$. Cellulose	$p$. Natural polymer
$B$. Nylon-$6,6$	$q$. Synthetic polymer
$C$. Protein	$r$. Amide linkage
$D$. Sucrose	$s$. Glycoside linkage