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The IUPAC name of the compound
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A ) 2-amino-3-hydroxypropanoic acid
B ) 1-hydroxy-2-amino propan-3-oic acid
C ) 1-amino-2-hydroxy propanoic acid
D ) 3-hydroxy-2-amino propanoic acid

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Answer
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Hint: Determine the number of carbon atoms in the parent carbon chain. Identify different substituents and the principal functional group. Number the chain from the end containing the carboxylic functional group. Use alphabetical order of the substituents.

Complete step by step answer:
The longest continuous chain contains 3 carbon atoms. Hence, the parent carbon atom is propane.

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Three different functional groups are present. These are carboxylic group, amino group and hydroxyl group.

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Carboxylic group gets preference over amino and hydroxyl groups. Hence, the suffix in the IUPAC name is propanoic acid. In the name of the corresponding alkane, propane, the suffix ‘ane’ is replaced with the suffix ‘oic acid’ to obtain the name propanoic acid.
The numbering of the chain is started from the end containing carboxylic group. The carbon atom of the carboxylic acid gets number 1, the carbon atom of amino group gets number 2 and the carbon atom of hydroxyl group gets number 3.

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Two substituents amino and hydroxyl are named in the alphabetical order as prefixes amino and hydroxyl.
The IUPAC name of the given compound is 2-amino-3-hydroxypropanoic acid.

Hence, the option A ) is the correct answer.

Note: The name 1-hydroxy-2-amino propan-3-oic acid is incorrect as the numbering of the chain is not started from the end containing hydroxyl group.
The name 1-amino-2-hydroxy propanoic acid is incorrect as the numbering of the chain is not started from the carbon containing amino group.
The name 3-hydroxy-2-amino propanoic acid is incorrect as the alphabetical order of substituents is not followed.