• Correct sentence: It is no use arguing with him; he never changes his mind.
Explanation:
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Rule: After it is no use (or it's of no use), we do not use a preposition or infinitive. 
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The structure is: It is no use + verb-ing. 
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Here, arguing is the present participle (verb + ing) following the rule. 
More examples:
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It's no use crying over spilled milk. 
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It's no use locking the door now. 
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It's no use trying again. 
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It's no use arguing with a drunk. 
Note: All other options are incorrect because they violate this structure.
