I was trying to find the meaning of "shruggish indifference" but I couldn't find a right meaning of shruggish . The sentence was " He had listend to it with shruggish indifference". Would you tell me the meaning of shruggish in this context? Thank you.

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Answer

SHRUGGISH is not a real word.   It just means related to or like a shrug.  And a shrug is the gesture of indifference.

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He did not care at all.

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The verb "to shrug" means to raise your shoulders in a way that shows that you don't care.

"Shruggish" is making an adjective out of that verb, 
although I don't think this is an actual word.

The sentence means "he listened in a way that showed he did not care."