Which compound possesses maximum as well as least solubility in water?

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You can't predict solubility reasoning, you have to remember solubility rules in your case this one:

  1. Most hydroxide salts are only slightly soluble. Hydroxide salts of Group I elements are soluble. Hydroxide salts of Group II elements (Ca, Sr, and Ba) are slightly soluble. Hydroxide salts of transition metals and Al3+Al3+ are insoluble. Thus, Fe(OH)3, Al(OH)3, Co(OH)2Fe(OH)3, Al(OH)3, Co(OH)2 are not soluble. 

So in this case Ca(OH)2Ca(OH)2 even if slightly soluble theoretically should be the right answer.

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