Nomenclature of organic compounds Questions in English

(N/A) The structures of the requested alkyl groups are as follows:
$(i)$ Isobutyl group: $(CH_3)_2CH-CH_2-$
$(ii)$ Isopropyl group: $(CH_3)_2CH-$
$(iii)$ Isopentyl group: $(CH_3)_2CH-CH_2-CH_2-$

(N/A) The given structure is $(CH_3)_3CCH(CH_3)CH_2CH_3$.
To find the $IUPAC$ name,we identify the longest carbon chain,which contains $6$ carbons (hexane).
Numbering the chain from the end that gives the substituents the lowest possible locants,we get substituents at positions $2, 2,$ and $3$.
Thus,the $IUPAC$ name is $3, 4, 4$-trimethylhexane. (Note: The provided image in the prompt corresponds to a different structure,$3$-ethyl-$2, 2$-dimethylpentane).

(A) The structure is $(CH_3)_3C-CH(C_2H_5)_2$.
First,identify the longest carbon chain,which contains $6$ carbons (hexane).
Numbering from the left gives substituents at positions $2, 2, 3$.
The correct $IUPAC$ name is $3-$ethyl$-2,2-$dimethylpentane.
The name $3-$methyl$-4,4-$dimethylpentane is incorrect because it does not identify the longest carbon chain correctly and violates the rules for selecting the parent chain and numbering.

(N/A) In $IUPAC$ nomenclature,when naming substituted alkanes,substituents must be listed in alphabetical order.
In the name $2,2-$dimethyl$-3-$ethylpentane,the methyl group is listed before the ethyl group,which violates the alphabetical priority rule.
According to $IUPAC$ rules,'ethyl' must precede 'methyl' because '$e$' comes before '$m$' in the alphabet.
Therefore,the correct $IUPAC$ name is $3-$ethyl$-2,2-$dimethylpentane.

(B) The correct name is $1, 3-$dimethylbutyl.
The numbering of the substituent group starts from the carbon atom that is directly attached to the parent chain,which is assigned the number $1$.
Therefore,the methyl group at the first carbon and the methyl group at the third carbon result in the name $1, 3-$dimethylbutyl.

(N/A) The decreasing order of priority is: $-CN > >C=O > -OH > -NH_2 > >C=C < > -C \equiv C$
$(b)$ The decreasing order of priority is: $-COOH > -COOR > -COCl > -CONH_2 > -CN > -CHO > >C=O$
$(c)$ The decreasing order of priority is: $-SO_3H > -CN > -COR > >C=C < > -C \equiv C$

(N/A)

Formula	Functional Group,Prefix,and Suffix
$(a)$ $CH_3CH_2CH_2COOH$	Name: Carboxylic acid; Prefix: $Carboxy$; Suffix: $oic \ acid$
$(b)$ $CH_3CH_2CH_2COO^{-}Na^{+}$	Name: Carboxylate salt; Prefix: $-$; Suffix: $oate$
$(c)$ $CH_3CH_2COOCH_3$	Name: Ester; Prefix: $Alkoxycarbonyl$; Suffix: $oate$

(N/A)

$IUPAC$ Name	Functional Group (Name)
$(i)$ Methanesulphonic acid	$-SO_3H$ (Sulphonic acid)
$(ii)$ $1$-Nitropropane	$-NO_2$ (Nitro)
$(iii)$ Pentanamide	$-CONH_2$ (Amide)
$(iv)$ $2$-Aminopentane	$-NH_2$ (Amine)

(A) The prefixes and suffixes for the given functional groups are as follows:
| Group | Prefix | Suffix |
| :--- | :--- | :--- |
| $(i)$ $-COCl$ | Chlorocarbonyl | $-oyl \ chloride$ |
| $(ii)$ $-CONH_2$ | Carbamoyl | $-amide$ |
| $(iii)$ $-COOR$ | Alkoxycarbonyl | $-oate$ |
| $(iv)$ $-CHO$ | Formyl or Oxo | $-al$ |
| $(v)$ $-COOH$ | Carboxy | $-oic \ acid$ |
| $(vi)$ $-COX$ | Halocarbonyl | $-oyl \ halide$ |
| $(vii)$ $-CO-$ | Oxo | $-one$ |
| $(viii)$ $-C \equiv N$ | Cyano | $-nitrile$ |
| $(ix)$ $-COO^-$ | $-$ | $-oate$ |

(N/A)

Compound	Structural Formula
$(i)$ Ethanoic acid	$CH_3-COOH$
$(ii)$ Ethanal	$CH_3-CHO$
$(iii)$ Ethanol	$CH_3-CH_2-OH$
$(iv)$ Ethene	$CH_2=CH_2$

(N/A)

Compound	$IUPAC$ Name	Common Name
$(i)$ $HO-CH_2-CH_2-CH_2-OH$	Propane$-1,3-$diol	Trimethylene glycol
$(ii)$ $HO-CH_2-CH(OH)-CH_2-OH$	Propane$-1,2,3-$triol	Glycerol
$(iii)$ $OHC-CHO$	Ethane$-1,2-$dial	Glyoxal
$(iv)$ $CH_3COOCH_3$	Methyl ethanoate	Methyl acetate
$(v)$ $CH_3COOCH_2CH_3$	Ethyl ethanoate	Ethyl acetate
$(vi)$ $CHCl_2-CCl_3$	$1,1,1,2,2-$Pentachloroethane	Pentachloroethane

(N/A) The structures are drawn based on the $IUPAC$ nomenclature rules:
$(i)$ The parent chain is decane ($10$ carbons). At position $3$,there is an ethyl group. At position $4$,there is a $1, 1-$dimethylpropyl group. At positions $4$ and $7$,there are methyl groups.
$(ii)$ The parent chain is undecane ($11$ carbons). At position $5$,there is a $1-$methylbutyl group. At position $7$,there is a $2-$methylbutyl group.

(N/A) $CH_3-CH_2-CH(CH_3)-CH(CH_3)-CH_2-CH_3$
$(b)$ $CH_3-CH_2-CH_2-CH_2-C(CH_3)(CH_2CH_3)-CH(CH_2CH_3)-CH_2-CH_2-CH_3$
$(c)$ $A$ cyclopentane ring with a methyl group attached.
$(d)$ $A$ cyclohexane ring with ethyl groups at positions $1, 3,$ and $5$.
$(e)$ $CH_2=CH-CH=CH_2$
$(f)$ $HC\equiv C-C\equiv CH$
$(g)$ $CH_2=CH-CH=CH-C\equiv CH$

(N/A) $(i)$ The parent chain has $5$ carbon atoms with a double bond at position $2$ and a carboxylic acid group at position $1$. Thus,the name is $pent-2-enoic$ acid.
$(ii)$ The longest chain containing the double bond has $6$ carbon atoms. Numbering from the left,we have a methyl group at $C-2$,an isopropyl group at $C-3$,and two methyl groups at $C-4$. Thus,the name is $3-isopropyl-2,4,4-trimethylpent-1-ene$.

(N/A) $(i)$ True: Anisole is methoxybenzene,$C_6H_5OCH_3$.
$(ii)$ True: $CH_3COCH_3$ is commonly known as acetone ($IUPAC$: propanone).
$(iii)$ True: Benzene has the molecular formula $C_6H_6$.
$(iv)$ False: $C_2H_6$ is ethane,not methane $(CH_4)$.
$(v)$ True: Pentane is $C_5H_{12}$ and propane is $C_3H_8$.

(N/A) $(1)$ Framework model
$(2)$ Ball and stick model
$(3)$ Cyclo
$(4)$ Icosane and Triacontane

(N/A) $(1)$ $5$-oxohexanoic acid
$(2)$ $CH_2=CHCH_2CH(OH)CH_3$
$(3)$ Cyclohex$-2-$en$-1-$ol,$-OH$
$(4)$ $-CHO$,$-OH$

(N/A) $(1)$ Methyl ethanoate and methyl propanoate.
$(2)$ Three (ortho,meta,and para).
$(3)$ Methoxybenzene and Anisole.
$(4)$ The structure is provided in the image.

(A) According to the $IUPAC$ rules for nomenclature,the principal functional group must be included in the longest carbon chain.
Here,the carboxyl group $(-COOH)$ is the principal functional group and the hydroxyl group $(-OH)$ is a substituent. The longest chain must contain the principal functional group $(-COOH)$.
Among the given options,the chain containing the $-COOH$ group and the $-OH$ group as part of the main structure or as a substituent must be selected such that the principal functional group gets the lowest possible locant.
The selection in option $(a)$ is correct because it identifies the longest chain that includes the principal functional group $(-COOH)$ and allows for the correct naming of the substituents.

(A) For compound $(a)$: The longest carbon chain containing the ketone functional group $(>C=O)$ is numbered such that the ketone group gets the lowest possible locant. The chain has $7$ carbons,a ketone at position $2$,an ethyl group at position $3$,a methyl group at position $4$,and a double bond at position $5$. The $IUPAC$ name is $3$-ethyl-$4$-methylhept-$5$-en-$2$-one.
For compound $(b)$: The ring is numbered starting from the double bond such that the double bond carbons get positions $1$ and $2$,and the substituent $-NO_2$ gets the lowest possible locant. The $-NO_2$ group is at position $3$. The $IUPAC$ name is $3$-nitrocyclohex-$1$-ene.

(N/A) $CH_3CH_2CH_2COCl$: The functional group is acid chloride $(-COCl)$. Its name is acid chloride,the suffix is $-oyl \ chloride$,and the prefix is $chlorocarbonyl-$.
$(b)$ $CH_3CH_2CH_2CONH_2$: The functional group is amide $(-CONH_2)$. Its name is amide,the suffix is $-amide$,and the prefix is $carbamoyl-$.
$(c)$ $CH_3CH_2CH_2CHO$: The functional group is aldehyde $(-CHO)$. Its name is aldehyde,the suffix is $-al$,and the prefix is $formyl-$.

(N/A) $(i)$ $CH_3CH_2CH_2CH_2COCl$: The functional group is $-COCl$ (Acyl chloride). The $IUPAC$ name is $pentanoyl$ $chloride$.
$(ii)$ $CH_3CH_2CN$: The functional group is $-CN$ (Nitrile). The $IUPAC$ name is $propanenitrile$.
$(iii)$ $CH_3CH_2CHO$: The functional group is $-CHO$ (Aldehyde). The $IUPAC$ name is $propanal$.
$(iv)$ $CH_3CH_2CH_2OH$: The functional group is $-OH$ (Alcohol). The $IUPAC$ name is $propan-1-ol$.

(N/A) $(i)$ Ethyne: $HC \equiv CH$
$(ii)$ Ethanenitrile: $CH_3-C \equiv N$
$(iii)$ Ethanoyl chloride: $CH_3-COCl$
$(iv)$ Ethyl ethanoate: $CH_3-COOCH_2CH_3$

(N/A) $(i)$ Butanone: The structure is $CH_3-CO-CH_2-CH_3$.
$(ii)$ Ethanamide: The structure is $CH_3-CONH_2$.

The $IUPAC$ and common names are as follows:
$(i)$ $HCOOH$: $IUPAC$ name is $Methanoic \ acid$,Common name is $Formic \ acid$.
$(ii)$ $CH_2Cl_2$: $IUPAC$ name is $Dichloromethane$,Common name is $Methylene \ chloride$.
$(iii)$ $CHCl_3$: $IUPAC$ name is $Trichloromethane$,Common name is $Chloroform$.
$(iv)$ $ClCH_2COOH$: $IUPAC$ name is $2-Chloroethanoic \ acid$,Common name is $Chloroacetic \ acid$.
$(v)$ $(COOH)_2$: $IUPAC$ name is $Ethanedioic \ acid$,Common name is $Oxalic \ acid$.

(A) The $IUPAC$ nomenclature rules are applied to each structure:
$(i)$ The longest chain has $5$ carbons with a double bond at $C-2$ and a bromine at $C-4$. Name: $4$-Bromopent-$2$-ene.
(ii) The longest chain has $5$ carbons with a double bond at $C-2$,a methyl group at $C-3$,and a bromine at $C-4$. Name: $4$-Bromo-$3$-methylpent-$2$-ene.
(iii) The longest chain has $4$ carbons with a double bond at $C-2$,a methyl group at $C-2$,and a bromine at $C-1$. Name: $1$-Bromo-$2$-methylbut-$2$-ene.
(iv) The longest chain has $5$ carbons with a double bond at $C-2$,a methyl group at $C-2$,and a bromine at $C-1$. Name: $1$-Bromo-$2$-methylpent-$2$-ene.
Therefore,the correct matching is: $(i-a, ii-b, iii-c, iv-d)$.

(A-P, B-Q, C-S, D-R) The $IUPAC$ names are determined by identifying the longest carbon chain containing the double bond and assigning the lowest possible locants to substituents and the double bond.
$(A)$ $CH_3-CH=CH-CH_2Br$: Longest chain is $4$ carbons,double bond at $C-2$,bromo at $C-1$. Name: $1$-Bromobut-$2$-ene $(p)$.
$(B)$ $CH_2=C(CH_3)-CH_2Br$: Longest chain is $3$ carbons,double bond at $C-1$,methyl at $C-2$,bromo at $C-3$. Name: $3$-Bromo-$2$-methylpropene $(q)$.
$(C)$ $CH_3-C(CH_3)=CH-CH_2Br$: Longest chain is $5$ carbons,double bond at $C-2$,methyl at $C-2$,bromo at $C-1$ (Wait,re-evaluating: $CH_3-C(CH_3)=CH-CH_2Br$ is $1$-bromo-$2$-methylbut-$2$-ene). Let's re-check the options.
Correct mapping:
$(A) \rightarrow (p)$ $1$-Bromobut-$2$-ene
$(B) \rightarrow (q)$ $3$-Bromo-$2$-methylpropene
$(C) \rightarrow (s)$ $1$-Bromo-$2$-methylbut-$2$-ene
$(D) \rightarrow (r)$ $4$-Bromopent-$2$-ene
Final matching: $(A-p, B-q, C-s, D-r)$.

(A) The $IUPAC$ names for the given dicarboxylic acids are as follows:
$A$. Phthalic acid is Benzene$-1,2-$dicarboxylic acid $(A-2)$.
$B$. Oxalic acid is Ethane$-1,2-$dioic acid $(B-5)$.
$C$. Succinic acid is Butane$-1,4-$dioic acid $(C-4)$.
$D$. Adipic acid is Hexane$-1,6-$dioic acid $(D-1)$.
$E$. Glutaric acid is Pentane$-1,5-$dioic acid $(E-3)$.
Therefore,the correct matching is: $A-2, B-5, C-4, D-1, E-3$.

(A-2, B-4, C-1, D-3) The matching is as follows:
$A$. The structure is a cyclohexane ring with an $-\text{OH}$ group at position $1$ and a $-\text{Br}$ group at position $3$. Thus,it is $3$-bromocyclohexanol $(A-2)$.
$B$. The longest chain containing the $-\text{OH}$ group has $4$ carbons. Numbering starts from the carbon attached to $-\text{OH}$. It is $2$-bromo-$3$-methylbut-$2$-en-$1$-ol $(B-4)$.
$C$. The longest chain has $6$ carbons. The substituents are at positions $2$ and $5$. It is $2, 5$-dimethylhexane-$1, 3$-diol $(C-1)$.
$D$. The longest chain has $6$ carbons with a double bond at position $1$ and an $-\text{OH}$ group at position $3$. It is $\text{hex-}1\text{-en-}3\text{-ol}$ $(D-3)$.
Therefore,the correct match is $A-2, B-4, C-1, D-3$.

(A) The ethyl group is derived from ethane $(C_2H_6)$ by removing one hydrogen atom. The formula is $CH_3CH_2-$ or $C_2H_5-$.

(A) $1$. Identify the principal functional group: The compound contains a carboxylic acid $(-COOH)$ group and an aldehyde $(-CHO)$ group. According to $IUPAC$ priority rules,the carboxylic acid group has higher priority than the aldehyde group. Therefore,the parent chain must include the carbon of the $-COOH$ group,and the suffix will be $-oic \ acid$.
$2$. Number the carbon chain: Start numbering from the carboxylic acid carbon as $C-1$. The longest chain containing the principal functional group and the double bond is a $6-$carbon chain.
$3$. Identify substituents: The aldehyde group at $C-6$ is treated as a substituent and named as $oxo-$. There is a methyl group at $C-2$ and another methyl group at $C-5$.
$4$. Assemble the name: The substituents are $2,5-$dimethyl and $6-oxo$. The double bond is at $C-3$. Combining these,the name is $2,5-$dimethyl$-6-$oxo$-hex-3-$enoic acid.

(A) $1$. Identify the principal functional group: The carboxylic acid group $(-COOH)$ is the principal functional group,so the parent chain is a cyclopentanecarboxylic acid.
$2$. Numbering the ring: The carbon atom attached to the $-COOH$ group is assigned position $1$. We number the ring to give the substituents the lowest possible locants. Moving clockwise,the methyl group is at position $2$ and the bromo group is at position $4$.
$3$. Naming: Substituents are listed alphabetically: Bromo before Methyl. Thus,the name is $4-$Bromo$-2-$methylcyclopentanecarboxylic acid.

(D) $1$. Identify the principal functional group: The aldehyde group $(-CHO)$ has the highest priority,so the parent chain is benzaldehyde.
$2$. Number the ring: Start numbering from the carbon attached to the $-CHO$ group as $C-1$. Proceed in the direction that gives the lowest locants to the substituents.
$3$. Assign positions: The $-NO_2$ group is at $C-2$,the $-CH_2OH$ (hydroxymethyl) group is at $C-4$,and the $-NH_2$ (amino) group is at $C-5$.
$4$. Assemble the name: Arrange the substituents alphabetically (amino,hydroxymethyl,nitro). The name is $5-$amino$-4-$hydroxymethyl$-2-$nitrobenzaldehyde.

(D) To determine the $IUPAC$ name,we identify the principal functional group,which is the ketone group $(-one)$.
We number the ring starting from the ketone carbon as $C-1$.
We then number the ring to give the lowest possible locants to the double bond and the hydroxyl group.
Starting from the ketone carbon $(C-1)$,we proceed towards the double bond to give it the lowest locant ($C-3$ to $C-4$ double bond).
Thus,the hydroxyl group is at position $5$.
The correct $IUPAC$ name is $5-$hydroxycyclohex$-3-$en$-1-$one.

(B) To determine the $IUPAC$ name,we follow these rules:
$1$. The principal functional group is the double bond,so the ring is numbered starting from the double bond.
$2$. We number the ring to give the lowest possible locants to the substituents ($-OCH_3$ and $-NO_2$).
$3$. Starting from the double bond,if we number clockwise,the substituents are at positions $3$ and $5$. If we number counter-clockwise,they are at positions $4$ and $6$. The set $(3, 5)$ is lower than $(4, 6)$.
$4$. Thus,the double bond is between $C1$ and $C2$,the $-NO_2$ group is at $C3$,and the $-OCH_3$ group is at $C5$.
$5$. Alphabetically,'methoxy' comes before 'nitro'.
$6$. The correct $IUPAC$ name is $5-$Methoxy$-3-$nitrocyclohexene.

(A) To determine the $IUPAC$ name,we follow the alphabetical order for substituents on the benzene ring.
$1$. The substituents are chloro $(-Cl)$,methyl $(-CH_3)$,and nitro $(-NO_2)$.
$2$. Alphabetically,'chloro' comes before 'methyl',which comes before 'nitro'.
$3$. We number the ring to give the lowest possible locants to the substituents: $1-$chloro,$2-$methyl,and $4-$nitro.
$4$. Thus,the correct $IUPAC$ name is $1-$Chloro$-2-$methyl$-4-$nitrobenzene.

(D) $1$. Identify the longest carbon chain containing the principal functional group $(-OH)$. The chain has $6$ carbons,so the parent alkane is hexane.
$2$. Number the chain starting from the end closer to the principal functional group $(-OH)$. Thus,the $-OH$ group is at position $2$.
$3$. Identify the substituents: an amino group $(-NH_2)$ at position $4$ and an ethyl group $(-CH_2CH_3)$ at position $3$.
$4$. Arrange the substituents alphabetically: amino comes before ethyl.
$5$. Combining these,the $IUPAC$ name is $4-$amino$-3-$ethylhexan$-2-$ol.

(C) $1$. Identify the longest carbon chain containing both the double and triple bonds. The chain has $6$ carbons,so the parent name is hexen-yne.
$2$. Numbering starts from the end that gives the lower locant to the multiple bonds. Numbering from the right gives the double bond at position $2$ and the triple bond at position $4$. Thus,it is hex$-2$-en$-4$-yne.
$3$. At position $2$,there is a bromo group. So,$2$-bromohex$-2$-en$-4$-yne.
$4$. Determine the configuration $(E/Z)$ at the double bond. Assign priorities using Cahn-Ingold-Prelog rules:
- At $C-2$: $-Br$ (high priority) and $-CH_3$ (low priority).
- At $C-3$: $-C\equiv C-CH_3$ (high priority) and $-H$ (low priority).
- Since the high priority groups ($-Br$ and $-C\equiv C-CH_3$) are on opposite sides,the configuration is $E$.
$5$. The correct name is $(2E)-2$-bromohex$-2$-en$-4$-yne.

(C) To determine the structure of $2,6-$Dimethyldec$-4-$ene,follow these steps:
$1$. The parent chain is $decene$,which contains $10$ carbon atoms.
$2$. The double bond is located at the $4^{th}$ position (between $C4$ and $C5$).
$3$. There are methyl groups at the $2^{nd}$ and $6^{th}$ positions.
$4$. Analyzing the options,we look for a $10$-carbon chain where the double bond starts at $C4$ and methyl substituents are at $C2$ and $C6$.
$5$. Structure $C$ represents a $10$-carbon chain with a double bond at the $4^{th}$ position and methyl groups at the $2^{nd}$ and $6^{th}$ positions,which matches the $IUPAC$ name $2,6-$Dimethyldec$-4-$ene.

(D) $1$. Identify the longest carbon chain containing the principal functional group ($-OH$ group). The chain has $6$ carbons,so the parent alkane is hexane.
$2$. Number the chain from the end that gives the lowest locant to the principal functional group $(-OH)$. Numbering from right to left gives the $-OH$ group at position $3$.
$3$. Identify the substituents: $Br$ at position $1$,$CH_3$ at position $4$,and $Cl$ at position $5$.
$4$. Arrange the substituents in alphabetical order: $1-$bromo,$5-$chloro,$4-$methyl.
$5$. Combining these,the correct $IUPAC$ name is $1-$bromo$-5-$chloro$-4-$methylhexan$-3-$ol.

(C) $1$. Identify the principal functional group: The aldehyde group $(-CHO)$ has the highest priority and is assigned position $1$.
$2$. Select the longest carbon chain containing the principal functional group and the double bond: The chain has $7$ carbons,making it a heptenal derivative.
$3$. Number the chain: Starting from the aldehyde carbon as $C-1$,the ketone group is at $C-3$,the double bond starts at $C-4$,the methyl group is at $C-4$,and the nitro group is at $C-6$.
$4$. Assemble the name: $4-$methyl$-6-$nitro$-3-$oxohept$-4-$enal.

(B) According to the $IUPAC$ priority rules for functional groups,the order of decreasing priority is: $ -COOH > -SO_3H > -COOR > -COCl > -CONH_2 > -CN > -CHO > C=O > -OH > -NH_2 > -OR > -R $.
Comparing the given options with the standard $IUPAC$ priority table:
Option $B$ is $-SO_3H > -COCl > -CONH_2 > -CN$,which follows the correct decreasing order of priority among the groups listed.

(A) In $\gamma-$methylcyclohexanecarbaldehyde,the parent ring is cyclohexane with a carbaldehyde $(-CHO)$ group attached at position $1$.
The carbon atom directly attached to the $-CHO$ group is the $\alpha-$carbon.
The next carbon is the $\beta-$carbon,and the carbon after that is the $\gamma-$carbon.
Therefore,the methyl group is attached at the $3-$position relative to the $-CHO$ group on the cyclohexane ring.
This corresponds to the structure where the methyl group is at the meta position relative to the $-CHO$ group.

(C) The given compound is $CH_3-CO-CH(CH_3)-CH_2-CH_2-Cl$.
To name this compound according to $IUPAC$ rules,we first identify the longest carbon chain containing the principal functional group,which is the ketone group.
The numbering starts from the end that gives the ketone group the lowest possible locant.
Numbering from the left gives the ketone at position $2$.
The chain has $5$ carbons,so the parent alkane is pentane,and the ketone is pentan$-2-$one.
There is a methyl group at position $3$ and a chloro group at position $5$.
Combining these,the correct $IUPAC$ name is $5-$chloro$-3-$methylpentan$-2-$one or $5-$chloro$-3-$methyl$-2-$pentanone.

(D) The principal functional group is the ketone group,so the carbon atom of the carbonyl group is assigned position $1$.
To determine the numbering,we follow the rule of lowest locants for substituents and multiple bonds.
Starting from the carbonyl carbon as $C_1$,if we number clockwise,the double bond starts at $C_2$ and the hydroxyl group is at $C_5$.
If we number counter-clockwise,the double bond starts at $C_5$ and the hydroxyl group is at $C_3$.
Comparing the locant sets $(2, 5)$ and $(3, 5)$,the set $(2, 5)$ is preferred because it provides a lower number at the first point of difference.
Therefore,the correct $IUPAC$ name is $5$-hydroxycyclohex-$2$-en-$1$-one.

(A) $1$. Identify the longest carbon chain. The longest chain in the given structure contains $7$ carbon atoms,so the parent alkane is heptane.
$2$. Number the chain from the end that gives the substituents the lowest possible locants. Numbering from right to left gives the methyl groups positions at $2$ and $4$.
$3$. Therefore,the $IUPAC$ name is $2,4$-dimethylheptane.

(A) The $IUPAC$ name $3-$methylpent$-2-$ene indicates a pentene chain (five carbon atoms) with a double bond at the $2^{nd}$ position and a methyl group at the $3^{rd}$ position.
The structure is written as:
$CH_3-CH=C(CH_3)-CH_2-CH_3$
Breaking it down:
$1.$ The parent chain is pentene ($5$ carbons).
$2.$ The double bond starts at carbon $2$.
$3.$ $A$ methyl group $(-CH_3)$ is attached to carbon $3$.
Comparing this to the given options,the structure corresponds to the skeletal representation where the double bond is between $C_2$ and $C_3$,and a methyl group is attached to $C_3$.

(A) To determine the $IUPAC$ name of the given compound $CH_3CH_2CH_2CH_2-C(=CH_2)-CH_2CH_2CH_3$:
$1$. Identify the longest carbon chain containing the double bond. The longest chain has $6$ carbon atoms,making it a hexene derivative.
$2$. Number the chain starting from the end that gives the double bond the lowest possible locant. Here,the double bond is at position $1$.
$3$. At position $2$,there is a propyl group $(-CH_2CH_2CH_3)$.
$4$. Combining these,the name is $2$-propylhex$-1$-ene.

(B) To find the number of $C-C$ sigma bonds,we analyze the structure of the given compound (a naphthalene derivative with a ketone and an alkyne chain).
By counting the $C-C$ single bonds in the naphthalene ring and the side chain,we identify the total number of $C-C$ sigma bonds.
As shown in the labeled structure,there are $17$ $C-C$ sigma bonds in total.
Therefore,the correct option is $(b)$.

(B) To identify $2,3$-dimethylhexane,we perform $IUPAC$ nomenclature on the given structures:
$(i)$ The longest chain has $6$ carbons. Numbering from the right gives substituents at positions $3$ and $4$. Thus,it is $3,4$-dimethylhexane.
$(ii)$ The longest chain has $6$ carbons. Numbering from the right gives substituents at positions $2$ and $3$. Thus,it is $2,3$-dimethylhexane.
$(iii)$ The longest chain has $6$ carbons. Numbering from the left gives substituents at positions $3$ and $4$. Thus,it is $3,4$-dimethylhexane.
$(iv)$ The longest chain has $6$ carbons. Numbering from the left gives substituents at positions $2$ and $4$. Thus,it is $2,4$-dimethylhexane.
Therefore,the correct structure for $2,3$-dimethylhexane is $(ii)$.