The correct usage of the apostrophe is given in option (d): "The new motorcycle engine is mother's."
The apostrophe is used in three ways: to form possessive nouns, to indicate letter omissions, and to indicate plurals;
Do not use apostrophes to form possessive pronouns (e.g., his / her computer) or non-possessive noun plurals.
Therefore, option (d) is the correct usage of apostrophes.
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