Nomenclature of organic compounds Questions in English

(B) Isoamylene is a common name for $2-$methyl$-2-$butene.
Its structure is $CH_3-C(CH_3)=CH-CH_3$.
According to $IUPAC$ nomenclature rules,the longest carbon chain containing the double bond is selected,which has $5$ carbons (pentene).
The double bond is at the $2$nd position,and a methyl group is at the $2$nd position.
Therefore,the correct $IUPAC$ name is $2-$methyl$-2-$butene.

(B) $1$. Identify the principal functional group: The $-OH$ group has the highest priority,so the parent chain is a cyclobutene derivative named as cyclobut$-2-$en$-1-$ol.
$2$. Numbering the ring: The carbon attached to the $-OH$ group is assigned position $1$. The numbering should proceed towards the double bond to give it the lowest possible locant.
$3$. Assigning locants: If we number clockwise starting from the $-OH$ carbon,the double bond starts at position $2$ and the methyl group is at position $4$. If we number counter-clockwise,the double bond starts at position $3$ and the methyl group is at position $2$. Following the lowest locant rule for the double bond,we choose the clockwise numbering.
$4$. Final Name: The substituent is a methyl group at position $4$. Thus,the correct $IUPAC$ name is $4-$methylcyclobut$-2-$en$-1-$ol.

(C) The structure $C_6H_5CH=CHCOOH$ consists of a phenyl group attached to a three-carbon chain containing a carboxylic acid group and a double bond.
The longest carbon chain containing the carboxylic acid group has $3$ carbon atoms,making it a derivative of propanoic acid.
The double bond starts at the $2^{nd}$ carbon atom,so it is named prop$-2-$enoic acid.
$A$ phenyl group $(-C_6H_5)$ is attached to the $3^{rd}$ carbon atom.
Combining these,the $IUPAC$ name is $3-$phenylprop$-2-$enoic acid.
Its common name is cinnamic acid.

(D) The given compound is $CH_3-COO-CH_2-COOH$.
The principal functional group is the carboxylic acid $(-COOH)$,which gets the $C-1$ position.
The parent chain is ethanoic acid ($C-1$ is the carboxyl carbon,$C-2$ is the methylene carbon).
The substituent at the $C-2$ position is the $CH_3-COO-$ group,which is named as ethanoyloxy.
Combining these,the $IUPAC$ name is $2-$ethanoyloxyethanoic acid.

(A) The principal functional group is the aldehyde group $(-CHO)$,so the parent chain is benzaldehyde.
Numbering starts from the carbon attached to the $-CHO$ group as $C-1$.
Proceeding to give the lowest possible locants to the substituents,the methoxy group $(-OCH_3)$ is at position $2$ and the nitro group $(-NO_2)$ is at position $4$.
Following alphabetical order for substituents,the name is $2-$methoxy$-4-$nitrobenzaldehyde.

(A) $1$. The structure is $CH_3(CH_2)_4-CH=CH-CH_2-CH=CH-(CH_2)_7COOH$.
$2$. The longest carbon chain contains $18$ carbon atoms,so the parent alkane is octadecane.
$3$. There are two double bonds at positions $9$ and $12$ (numbering from the $COOH$ group as $C-1$).
$4$. The configuration at both double bonds is $cis$ because the hydrogen atoms are on the same side of the double bond.
$5$. Therefore,the $IUPAC$ name is $cis, cis-9, 12-$ octadecadienoic acid.

(B) The principal functional group is $-COOH$ (suffix: $-oic \ acid$).
The other groups are $-OH$ (hydroxy),$-Cl$ (chloro),$-CH_3$ (methyl),and $=O$ (oxo).
Numbering starts from the $-COOH$ carbon.
The parent chain has $7$ carbons with a double bond at $C4$ ($4$-heptene).
Alphabetical order of prefixes: chloro,hydroxy,methyl,oxo.

(C) The given compound is $CH_3OOC-CH(CH_2OH)-COOCH_3$.
This is an ester derivative of propanedioic acid.
The parent chain is a $3-$carbon chain with two ester groups $(-COOCH_3)$ at positions $1$ and $3$.
There is a hydroxymethyl group $(-CH_2OH)$ attached at the $2^{nd}$ position.
Thus,the $IUPAC$ name is Dimethyl $2-$hydroxymethylpropanedioate.

(D) $1.$ Identify the longest carbon chain containing the maximum number of $-CHO$ groups. The longest chain contains $6$ carbon atoms,including two $-CHO$ groups at the ends.
$2.$ Number the chain starting from the end that gives the substituent the lowest locant. Numbering from the right gives the substituent at position $3$.
$3.$ The substituent $-CH_2-CHO$ is named as a "formylmethyl" group.
$4.$ Combining these,the $IUPAC$ name is $3-$(formylmethyl)hexane$-1,6-$dial.

(C) $1$. Identify the principal functional group: The ester group $(-COOC_2H_5)$ has higher priority than the acid chloride group $(-COCl)$.
$2$. The parent chain is the benzoate ester,and the $-COCl$ group is treated as a substituent named 'chlorocarbonyl'.
$3$. Numbering the benzene ring: The carbon attached to the ester group is position $1$. The $-COCl$ group is at position $2$.
$4$. Therefore,the $IUPAC$ name is ethyl $2-$(chlorocarbonyl) benzoate.

(B) The given compound is $CH_3-O-CO-CH_2-COOH$.
The principal functional group is the carboxylic acid $(-COOH)$.
The parent chain consists of two carbon atoms,which is ethanoic acid.
The substituent at the $2^{nd}$ position is the methoxycarbonyl group $(-COOCH_3)$.
Therefore,the $IUPAC$ name is $2-$ methoxycarbonyl ethanoic acid.

(A) $1$. Identify the longest carbon chain containing the double bond. The chain has $5$ carbon atoms,so the parent alkane is pentane,and with the double bond at position $1$,it is pent-$1$-ene.
$2$. Number the chain starting from the end closer to the double bond. The double bond starts at $C-1$.
$3$. Identify the substituents: $A$ cyclohexyl group is attached at $C-1$,and a methyl group is attached at $C-3$.
$4$. Combining these,the $IUPAC$ name is $1$-cyclohexyl-$3$-methylpent-$1$-ene.

(A) $1.$ Select the longest carbon chain containing the double bond. The longest chain has $9$ carbons,so the parent alkane is nonane,and the alkene is nonene.
$2.$ Number the chain starting from the left to give the double bond the lowest possible locant,which is $C3$.
$3.$ Identify the substituents: an ethyl group at $C5$ and methyl groups at $C3$ and $C6$.
$4.$ Arrange substituents alphabetically: $5-$ethyl comes before $3, 6-$dimethyl.
$5.$ Combining these,the correct $IUPAC$ name is $5-$ethyl$-3, 6-$dimethylnon$-3-$ene.

(C) monovalent group is formed by removing one hydrogen atom from an alkane or arene,while a divalent group is formed by removing two hydrogen atoms from the same carbon atom.
$1$. Benzoyl group $(C_6H_5CO-)$ is monovalent.
$2$. Benzyl group $(C_6H_5CH_2-)$ is monovalent.
$3$. Benzal group $(C_6H_5CH=)$ is divalent,as it is derived by removing two hydrogen atoms from the methyl group of toluene $(C_6H_5CH_3)$.
$4$. $p-$Tolyl group $(CH_3-C_6H_4-)$ is monovalent.

(D) In option $(d)$,the structure $CH_2=CH-CH(C_2H_5)-CHO$ is correctly named as $2-$ ethylbut $-3-$ enal.
$(a)$ $CH_3-COOCH_3$ is methyl ethanoate.
$(b)$ $NH_2-CONH_2$ is urea or diaminomethanone.
$(c)$ $CH_3-CH(C_2H_5)-CH_2-CH(CH_3)_2$ is $2,4-$ dimethylhexane.

(B) $1$. The principal functional group is the carboxylic acid $(-COOH)$ attached to the cyclopropane ring. The carbon atom of the ring attached to the $-COOH$ group is assigned position $1$.
$2$. The substituents are an ethenyl group $(-CH=CH_2)$ and an ethynyl group $(-C\equiv CH)$.
$3$. Numbering the ring to give the lowest locants to the substituents: if we number clockwise or counter-clockwise,the substituents are at positions $2$ and $3$.
$4$. According to $IUPAC$ rules,substituents are listed in alphabetical order: 'ethenyl' comes before 'ethynyl'.
$5$. Therefore,the ethenyl group is at position $2$ and the ethynyl group is at position $3$.
$6$. The correct name is $2-$ethenyl$-3-$ethynylcyclopropane carboxylic acid.

(A) $1.$ The principal functional group is the amide $(-CONHBr)$.
$2.$ The longest carbon chain containing the amide group has $4$ carbons,so the parent name is butanamide.
$3.$ Numbering starts from the amide carbon: $C1$ is the amide carbon,$C2$ has a keto group $(=O)$,and $C3$ has a methyl group $(-CH_3)$.
$4.$ The bromine atom is attached to the nitrogen,denoted as $N-bromo$.
$5.$ Therefore,the $IUPAC$ name is $N-Bromo-2-oxo-3-methylbutanamide$.

(C) $1$. Identify the longest carbon chain containing the principal functional group $(-OH)$ and the double bond. The chain has $7$ carbons,so the parent alkane is heptane.
$2$. 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 $3$.
$3$. The double bond starts at carbon $4$ (between $C4$ and $C5$),so it is a hept$-4-$en$-3-$ol derivative.
$4$. There is a methyl group at position $5$.
$5$. Combining these,the name is $5-$methylhept$-4-$en$-3-$ol.

(D) The given structure is $CH_3CH_2-CH(COOCH_2CH_3)-COOH$.
$1$. Identify the principal functional group: The carboxylic acid group $(-COOH)$ has higher priority than the ester group $(-COOR)$. Thus,the parent chain is a butanoic acid derivative.
$2$. Numbering the chain: The carbon of the $-COOH$ group is assigned position $1$. The carbon attached to the ester group is at position $2$.
$3$. Substituent identification: At position $2$,there is an ethoxycarbonyl group $(-COOCH_2CH_3)$.
$4$. Combining the parts: The parent chain is a $4$-carbon chain (butanoic acid). At position $2$,we have an ethoxycarbonyl substituent. Therefore,the name is $2-$ethoxycarbonylbutanoic acid.

(C) In the $IUPAC$ nomenclature of organic compounds,the ester functional group $(-COOR)$ is named as an 'oate' suffix when it is the principal functional group. However,when it is treated as a substituent or when the carbon of the ester group is not included in the parent chain,it is named using the prefix 'alkoxycarbonyl' or 'carbalkoxy'.

(B) According to the $IUPAC$ priority rules for functional groups,the decreasing order of priority is:
$1. -COOH$ (Carboxylic acid)
$2. -SO_3H$ (Sulphonic acid)
$3. -CONH_2$ (Amide)
$4. -CHO$ (Aldehyde)
Therefore,the correct order is $-COOH > -SO_3H > -CONH_2 > -CHO$.
Thus,option $B$ is correct.

(A) The given radical is $-CH_2-CH(OH)-CH_3$.
To name this radical,we identify the longest carbon chain attached to the main group.
The carbon atom attached to the main chain is assigned position $1$.
Thus,the chain is a propyl group ($3$ carbons).
At position $2$,there is a hydroxyl $(-OH)$ group.
Therefore,the correct $IUPAC$ name for this radical is $2-$hydroxypropyl.

(D) The ethyl group is $-CH_2-CH_2-$.
When a carboxy group $(-COOH)$ is attached to the second carbon atom of the ethyl chain,it is named as $2$-carboxyethyl.
The structure is $-CH_2-CH_2-COOH$.

(A) The given structure is $CH_2=CH-CH(OH)-CH_3$.
$1$. Identify the longest carbon chain containing the principal functional group $(-OH)$ and the double bond. The chain has $4$ carbon atoms,so the parent alkane is butane.
$2$. Number the chain from the end that gives the lowest possible locant to the principal functional group $(-OH)$.
$3$. Numbering from right to left: $C_1$ is $CH_3$,$C_2$ is $CH(OH)$,$C_3$ is $CH$,$C_4$ is $CH_2$. The $-OH$ group is at position $2$ and the double bond is at position $3$.
$4$. The name is constructed as: (alkene part) + (alcohol part) = But-$3$-en-$2$-ol.

(B) $1$. Identify the principal functional group: The compound is a cyclic alkene. The double bond gets priority in numbering.
$2$. Number the ring: Start numbering from the double bond carbons such that the substituents get the lowest possible locants. Assign $C-1$ and $C-2$ to the double bond carbons.
$3$. If we assign $C-1$ to the carbon with the ethyl group and $C-2$ to the carbon with the two methyl groups,the locants are $1-$ethyl and $2, 2-$dimethyl.
$4$. If we assign $C-1$ to the carbon with the two methyl groups and $C-2$ to the carbon with the ethyl group,the locants are $1, 1-$dimethyl and $2-$ethyl.
$5$. According to the $IUPAC$ rule of lowest locant set,$(1, 1, 2)$ is preferred over $(1, 2, 2)$.
$6$. Therefore,the correct numbering gives the name $2-$Ethyl-$1, 1-$dimethylcyclohex-$2-$ene (or $2-$Ethyl-$1, 1-$dimethyl-$2-$cyclohexene).

(C) The given compound is a cyclic ether containing a three-membered ring with one oxygen atom,known as an epoxide.
According to $IUPAC$ nomenclature rules for cyclic ethers,the prefix 'epoxy' is used followed by the name of the corresponding alkane.
The oxygen atom is bonded to the $1^{st}$ and $2^{nd}$ carbon atoms of the three-carbon chain.
Therefore,the correct $IUPAC$ name is $1, 2-$Epoxypropane.

(C) The structure consists of a benzene ring substituted with an amino group $(-NH_2)$ and a methoxy group $(-OCH_3)$ at the para $(1,4)$ positions.
According to $IUPAC$ nomenclature rules,the parent compound is aniline (benzeneamine) because the amino group takes priority over the ether group.
The carbon atom attached to the $-NH_2$ group is assigned position $1$.
Consequently,the methoxy group $(-OCH_3)$ at the para position is assigned position $4$.
Therefore,the correct $IUPAC$ name is $4$-methoxyaniline.

(D) The structure of neopentane is $CH_3-C(CH_3)_2-CH_3$.
To determine the $IUPAC$ name:
$1$. Identify the longest carbon chain,which contains $3$ carbon atoms (propane).
$2$. Identify the substituents attached to the chain. There are two methyl groups attached to the second carbon atom.
$3$. Combining these,the $IUPAC$ name is $2, 2-$dimethylpropane.
Hence,the correct option is $D$.

(C) $1$. Identify the parent chain: The structure is a cyclopropane ring.
$2$. Numbering: Number the ring starting from the substituent that comes first alphabetically. Here,$bromo$ $(Br)$ comes before $chloro$ $(Cl)$. So,assign $C-1$ to the carbon with $Br$ and $C-2$ to the carbon with $Cl$.
$3$. Stereochemistry: The $Br$ and $Cl$ atoms are on opposite sides of the ring plane,which indicates a $trans$ configuration.
$4$. Combining the parts: The name is $trans-1-bromo-2-chlorocyclopropane$.

(B) The allyl group is $CH_2=CH-CH_2-$.
The neopentyl group is $(CH_3)_3C-CH_2-$.
When these two groups are joined,the structure becomes $CH_2=CH-CH_2-CH_2-C(CH_3)_3$.
The longest carbon chain containing the double bond has $6$ carbons.
Numbering starts from the double bond: $CH_2(1)=CH(2)-CH_2(3)-CH_2(4)-C(CH_3)_2(5)-CH_3(6)$.
There are two methyl groups at the $5$th position.
Thus,the $IUPAC$ name is $5,5-$dimethylhex$-1-$ene.

(D) $1$. Identify the principal functional group: The ester group $(-COOCH_3)$ has higher priority than the hydroxyl group $(-OH)$. Therefore,the parent compound is an ester of benzoic acid,which is named as a benzoate.
$2$. Numbering the ring: The carbon atom of the benzene ring attached to the ester group is assigned position $1$. The hydroxyl group is at the meta position relative to the ester group,which corresponds to position $3$.
$3$. Naming the substituents: The substituent on the oxygen of the ester is a methyl group,and the hydroxyl group is at position $3$.
$4$. Combine the parts: The name is methyl $3-$hydroxybenzoate.

(C) To determine the correct structure of $6-$amino$-4-$hydroxycyclohex$-2-$ene$-1-$sulphonic acid,we follow the $IUPAC$ nomenclature rules:
$1$. The principal functional group is the sulphonic acid group $(-SO_3H)$,which gets the lowest possible number,$1$.
$2$. The ring is a cyclohexene ring. The double bond starts at position $2$ (between $C_2$ and $C_3$).
$3$. The amino group $(-NH_2)$ is at position $6$.
$4$. The hydroxy group $(-OH)$ is at position $4$.
$5$. Looking at the options,structure $C$ correctly places the $-SO_3H$ at $C_1$,the double bond between $C_2$ and $C_3$,the $-NH_2$ at $C_6$,and the $-OH$ at $C_4$.

(D) According to $IUPAC$ nomenclature rules for unsaturated hydrocarbons containing both double and triple bonds:
$1$. The principal chain is selected such that it contains both the double and triple bonds,if possible.
$2$. Numbering is done such that the set of locants for the multiple bonds is as low as possible.
$3$. If there is a tie in the locant set (e.g.,$1, 5$ vs $1, 5$),the double bond is given preference over the triple bond for the lower number.
Analyzing the options:
- Option $A$: $CH_2=CH-CH_2-CH_2-C\equiv CH$. Numbering from left gives locants $1$ (ene) and $5$ (yne). This is correct.
- Option $B$: $CH\equiv C-CH_2-CH=CH-CH_3$. Numbering from right gives locants $1$ (yne) and $5$ (ene). This is correct.
- Option $C$: $CH_2=CH-CH_2-CH=CH-C\equiv CH$. Numbering from left gives locants $1, 4$ (enes) and $6$ (yne). This is correct.
- Option $D$: $CH_2=CH-CH_2-CH=CH-C\equiv CH$. The numbering shown in the image is $1, 2, 3, 4, 5, 6, 7$. The double bonds are at $1$ and $4$,and the triple bond is at $6$. However,the structure shown in the image for $D$ labels the triple bond at $6$ but the numbering sequence is inconsistent with the chain length or connectivity compared to standard $IUPAC$ rules for this specific structure. Specifically,the numbering in $D$ is $1, 2, 3, 4, 5, 6, 7$ where the double bond is at $4$ and $5$ in the image,which is incorrect as the double bond should be at $4$ and $5$ but the numbering $4-5$ is written as $4$ and $5$ on the same bond,which is invalid.

(B) $1$. Identify the principal functional group or the parent chain. Here,the cyclic ring (cyclohexadiene) is the parent chain.
$2$. Number the ring starting from the carbon attached to the ethenyl group as $1$,or such that the double bonds get the lowest possible locants.
$3$. If we start numbering from the carbon attached to the ethenyl group as $1$,the double bonds are at positions $2$ and $4$. This gives the name $1-$ethenylcyclohexa$-2,4-$diene.
$4$. However,according to $IUPAC$ rules for numbering,we should give the lowest locants to the double bonds. If we number the ring such that the double bonds are at $1$ and $3$,the ethenyl group will be at position $5$. This gives the name $5-$ethenylcyclohexa$-1,3-$diene.
$5$. Comparing the locant sets: $(1, 2, 4)$ vs $(1, 3, 5)$. The set $(1, 3, 5)$ is preferred as it provides lower locants for the double bonds.
$6$. Therefore,the correct $IUPAC$ name is $5-$ethenylcyclohexa$-1,3-$diene.

(C) $1$. Identify the parent chain: The parent chain is a cyclohexane ring.
$2$. Identify substituents: There is an ethyl group $(-CH_2CH_3)$ and two methyl groups $(-CH_3)$ attached to the ring.
$3$. Numbering the ring: According to $IUPAC$ rules,we number the ring to give the lowest possible locants to the substituents. If we start numbering from the carbon with the two methyl groups as $1$,the substituents are at positions $1, 1,$ and $3$. If we start from the carbon with the ethyl group as $1$,the substituents are at $1, 3,$ and $3$.
$4$. Alphabetical order: Ethyl comes before methyl. Comparing the sets of locants $(1, 1, 3)$ vs $(1, 3, 3)$,the set $(1, 1, 3)$ is lower. However,we must also consider alphabetical priority when the locant sets are different. Assigning $1$ to the carbon with the ethyl group gives the name $1-$ethyl$-3,3-$dimethylcyclohexane. Assigning $1$ to the carbon with the two methyl groups gives $3-$ethyl$-1,1-$dimethylcyclohexane. Comparing the locants,$1, 1, 3$ is preferred over $1, 3, 3$. Therefore,the correct name is $3-$ethyl$-1,1-$dimethylcyclohexane.

(B) The given structure is a cyclohexane ring attached to a carbonyl chloride group $(-COCl)$.
According to $IUPAC$ nomenclature rules,when a functional group like $-COCl$ is attached directly to an alicyclic ring,the carbon atom of the functional group is not included in the parent ring name.
Instead,the suffix $carbonyl \ chloride$ is used for the $-COCl$ group attached to the ring.
Therefore,the correct $IUPAC$ name is $Cyclohexanecarbonyl \ chloride$.

(A) $1$. Identify the longest carbon chain containing the principal functional group (carboxylic acid). The chain has $7$ carbons,so the parent alkane is heptane.
$2$. Number the chain starting from the carboxylic acid carbon as $C-1$.
$3$. The double bonds are at positions $2$ and $5$. The suffix for the acid is $-oic$ acid,and for two double bonds,it is $-dienoic$ acid.
$4$. There are methyl groups at positions $2$ and $6$.
$5$. Combining these,the name is $2, 6-$ dimethylhepta$-2, 5-$dienoic acid.

(C) According to $IUPAC$ nomenclature rules for cyclic compounds containing multiple functional groups:
$1$. The principal functional group is given the lowest possible locant.
$2$. Between $-OH$ (alcohol) and $-SH$ (thiol),the $-OH$ group has higher priority.
$3$. Therefore,the carbon atom attached to the $-OH$ group should be numbered $1$.
$4$. The numbering should then proceed in a direction that gives the lowest possible locants to the other substituents and the double bond.
$5$. In structure $C$,the $-OH$ group is at position $1$,the double bond starts at position $2$,and the $-SH$ group is at position $4$. This follows the lowest locant rule for the double bond and substituents $(1, 2, 4)$.
$6$. Thus,structure $C$ represents the correct numbering.

(A) To determine the structure of $3,4-$dimethylpent$-1-$en$-3-$ol,we follow these steps:
$1$. The parent chain is 'pent',which means it has $5$ carbon atoms.
$2$. The suffix '$-1-$en' indicates a double bond at the $1^{st}$ position.
$3$. The suffix '$-3-$ol' indicates a hydroxyl group $(-OH)$ at the $3^{rd}$ position.
$4$. The prefix '$3,4-$dimethyl' indicates two methyl groups $(-CH_3)$ attached at the $3^{rd}$ and $4^{th}$ positions.
$5$. Combining these,the structure is $CH_2=CH-C(OH)(CH_3)-CH(CH_3)-CH_3$.
$6$. Looking at the options,the structure in image $814-a898$ correctly represents this molecule: a $5-$carbon chain with a double bond at $C1$,an $-OH$ group at $C3$,and methyl groups at $C3$ and $C4$.

(D) According to $IUPAC$ rules,when three or more identical carbon-containing functional groups are directly attached to an unbranched carbon chain,the carbon atoms of these groups are not included in the parent chain.
For three $-CHO$ groups attached to a propane backbone,the suffix "tricarbaldehyde" is used.
The parent chain is propane ($3$ carbons).
Therefore,the correct $IUPAC$ name is Propane$-1,2,3-$tricarbaldehyde.

(C) The given structure is $CH_3-CH(CH_2-CH_3)-CH_2-Br$.
Expanding the ethyl group,we get $CH_3-CH_2-CH(CH_3)-CH_2-Br$.
The longest carbon chain containing the bromine atom has $4$ carbon atoms,so the parent alkane is butane.
Numbering the chain from the end closer to the bromine atom,we get $Br$ at $C1$ and a methyl group at $C2$.
According to $IUPAC$ rules,substituents are listed in alphabetical order (bromo before methyl).
Therefore,the $IUPAC$ name is $1$-bromo-$2$-methylbutane.

(B) $1$. In cyclic alkenes,the double bond is given priority in numbering,starting from the carbons of the double bond such that substituents get the lowest possible locants.
$2$. Assign position $1$ to the carbon attached to the chlorine atom and position $2$ to the other carbon of the double bond.
$3$. Following this,the bromine atom is at position $3$.
$4$. Thus,the correct $IUPAC$ name is $3-$bromo$-1-$chlorocyclohexene.

(B) $1$. In the given cyclic compound,the double bond is present between $C1$ and $C2$. According to $IUPAC$ rules,the double bond should be given priority and numbered such that it gets the lowest possible locants ($1$ and $2$).
$2$. We start numbering from the carbon atom of the double bond that allows the substituent to have the lowest possible number.
$3$. If we number the double bond carbons as $1$ and $2$,the methyl group is at position $1$ and the bromine atom is at position $6$.
$4$. Thus,the correct numbering gives the $6-$bromo and $1-$methyl substituents.
$5$. Combining these,the name is $6-$Bromo$-1-$methylcyclohexene.

(B) $1$. Identify the principal functional group: The $-OH$ group has higher priority than the double bond,so it gets the lowest possible locant,$1$.
$2$. Number the ring: Start numbering from the carbon attached to the $-OH$ group as $1$. To give the double bond the lowest locant,proceed towards the double bond.
$3$. Numbering path: If we number clockwise,the double bond starts at $C-2$. If we number counter-clockwise,the double bond starts at $C-4$. Thus,clockwise is correct.
$4$. Assign locants: The $-OH$ is at $C-1$,the double bond starts at $C-2$,and the methyl group is at $C-5$.
$5$. Construct the name: The parent chain is cyclopentene. Combining these,we get $5-$methylcyclopent$-2-$en$-1-$ol.

(C) To determine the structure of $3-$ethyl$-2-$hydroxy$-4-$methylhex$-3-$en$-5-$ynoic acid,we follow these steps:
$1$. The parent chain is a hexenoic acid,meaning it has $6$ carbon atoms with a carboxylic acid group at $C-1$.
$2$. The suffix $-3-$en$-5-$ynoic acid indicates a double bond at position $3$ and a triple bond at position $5$.
$3$. Substituents are an ethyl group at position $3$,a hydroxy group at position $2$,and a methyl group at position $4$.
$4$. Constructing the chain: $C1(COOH)-C2(OH)-C3(Et)=C4(Me)-C5\#C6$.
$5$. Comparing this with the given options,the structure corresponds to the one shown in the solution image.

(A) The given compound is a cyclic anhydride derived from a dicarboxylic acid.
$1$. The parent chain is a four-carbon chain containing a double bond,which is $but-2-ene$.
$2$. The anhydride functional group is formed from the $1,4-$dicarboxylic acid positions.
$3$. Numbering starts from one of the carbonyl carbons. Following alphabetical order for substituents,the ethyl group at position $2$ and the methyl group at position $3$ gives the name $2-$Ethyl$-3-$methylbut$-2-$ene$-1,4-$dioic anhydride.

(A) Succinic acid has the structural formula $HOOC-CH_2-CH_2-COOH$.
The longest carbon chain containing both carboxyl groups consists of $4$ carbon atoms.
Therefore,the $IUPAC$ name is $Butane-1,4-dioic$ $acid$.

(C) The structure of the compound is $CH_2=CH-CH(CH_3)_2$.
To name this compound according to $IUPAC$ rules:
$1$. Select the longest carbon chain containing the double bond. The longest chain has $4$ carbon atoms,so the parent alkane is butane.
$2$. Number the chain from the end that gives the lowest locant to the double bond. Starting from the left,the double bond starts at carbon $1$.
$3$. Identify the substituent. There is a methyl group at position $3$.
$4$. Combining these,the name is $3-$methylbut$-1-$ene.
Hence,the correct option is $(C)$.

(B) $1$. Identify the principal functional group: The carboxylic acid group $(-COOH)$ has higher priority than the ester group $(-O-CO-CH_3)$. Thus,the parent chain is a cyclopentene carboxylic acid.
$2$. Numbering the ring: Start numbering from the carbon attached to the $-COOH$ group as $C-1$. To give the double bond the lowest possible locant,proceed towards the double bond. Thus,the double bond starts at $C-2$.
$3$. Identify substituents: The $-O-CO-CH_3$ group is an ethanoyloxy group (or acetoxy group) located at the $C-4$ position.
$4$. Combine the parts: The name is $4-$ethanoyloxycyclopent$-2-$ene$-1-$carboxylic acid,which is commonly written as $4-$ethanoyloxycyclopent$-2-$ene carboxylic acid.

(A) Let us analyze each option based on $IUPAC$ nomenclature rules:
$A$. For $1,5$-dimethylcyclopentene,the double bond gets priority. Numbering starts from the double bond such that substituents get the lowest possible locants. The correct name is $1,2$-dimethylcyclopentene.
$B$. For $3,4$-dimethylpent-$1$-en-$3$-ol,the principal functional group is alcohol $(-OH)$,which gets the lowest locant. The chain is numbered starting from the end closer to the $-OH$ group. The name is correct.
$C$. For $6$-bromo-$3,3$-dimethylcyclohexene,the double bond is between $C1$ and $C2$. Numbering starts from the double bond towards the substituent. The name is correct.
$D$. For $5$-hydroxycyclopent-$2$-en-$1$-ol,the principal functional group is $-OH$. The double bond is between $C1$ and $C2$ (or $C2$ and $C3$ depending on numbering). The correct $IUPAC$ name is cyclopent-$2$-ene-$1,4$-diol.
Comparing the options,the name in option $A$ is incorrect as it should be $1,2$-dimethylcyclopentene.