Identify the products of the given reactions.

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(C) In Reaction-$1$,the $-OTs$ group and the $-NMe_2$ group are in a cis-configuration. The nucleophilic attack by $CH_3COO^-$ occurs via an $S_N2$ me

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$A$ single product is obtained in both the reactions.

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(C) In Reaction-$1$,the $-OTs$ group and the $-NMe_2$ group are in a cis-configuration. The nucleophilic attack by $CH_3COO^-$ occurs via an $S_N2$ mechanism,resulting in inversion of configuration at the carbon atom bearing the $-OTs$ group. Since the starting material is chiral,the product is a single enantiomer.In Reaction-$2$,the $-OTs$ group and the $-NMe_2$ group are in a trans-configuration. The lone pair on the nitrogen atom of the $-NMe_2$ group participates in Neighboring Group Participation $(NGP)$,forming a cyclic aziridinium ion intermediate. This intermediate is then opened by the acetate nucleophile. Due to the symmetry and the nature of the $NGP$-assisted pathway,this reaction also leads to a specific stereochemical outcome,typically resulting in a single product (or a specific pair of enantiomers depending on the starting material's chirality). Given the options,the most accurate description is that a single product is obtained in both reactions due to the stereospecific nature of these pathways.

List-$I$ (Reagent)	List-$II$ (Product)
$A$. $KOH$ (alc)	$I$. Nitrile
$B$. $KCN$ (alc)	$II$. Ester
$C$. $AgNO_2$	$III$. Alkene
$D$. $CH_3COOAg$	$IV$. Nitroalkane

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$A$ dihalogen derivative '$X$' of a hydrocarbon with three carbon atoms reacts with alcoholic $KOH$ to give another hydrocarbon which forms a red precipitate with ammoniacal $Cu_2Cl_2$. '$X$' gives an aldehyde upon reaction with aqueous $KOH$. What is the compound '$X$'?

Match List-$I$ with List-$II$.
$1$-Bromopropane is reacted with reagents in List-$I$ to give products in List-$II$.

List-$I$ (Reagent) List-$II$ (Product)

$A$. $KOH$ (alc) $I$. Nitrile

$B$. $KCN$ (alc) $II$. Ester

$C$. $AgNO_2$ $III$. Alkene

$D$. $CH_3COOAg$ $IV$. Nitroalkane

What is retention and inversion of configuration? Explain with suitable examples.

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