arrange in increasing solubility in water : Mg(OH)2 , Sr(OH)2, Ba(OH)2,​ Ca(OH)2 

Solubility of metallic hydroxides increases down the group in the alkaline earth metal. So the increasing order is
Mg(OH)2 < Ca(OH)2 < Sr(OH)2 < Ba(OH)2.
Higher the hydration energy compared to lattice energy, ​higher will be the solubility
 

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yes, do it
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