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The word "idle" can be used in multiple ways:
As an adjective: meaning not active or in use. Example: He stood idle on the road..
As a verb: meaning to run slowly while disconnected (often used for engines). Example: Let the engine idle for a minute..
However, "idle" is often confused with "idol", which means an object of worship.
Let's analyze the sentences:
I - Correct. "Idly" is the adverb form of "idle," meaning without activity or purpose.
II - Correct. "Idle" as a verb meaning to run without load.
III - Incorrect. It should be "idol" (object of worship), not "idle."
Hence, option (a) is the answer.