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A metal M readily forms its sulphate $MSO_{4}$ which is water soluble. It forms its oxide $MO$ which becomes inert on heating. It forms an insoluble hydroxide $M(OH)_{2}$ which is soluble in $NaOH$ solution. Then M is:
A. $Mg$
B. $Ba$
C. $Ca$
D. $Be$

Answer
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Hint: Here one has to test each option if it is satisfying the conditions in the question keeping in mind the basic characteristics of the oxides and hydroxides of the elements such as hydroxide of magnesium is insoluble in water.

Complete step by step answer:
We have to eliminate the options in the above question so we have to analyse the options.
First of all Be forms highly soluble beryllium sulfate however $Mg$ also makes reasonably soluble sulphate while $Ca$ and $Ba$ cannot do so. Therefore we can see the rest of the properties for the $Mg$ and $Be$ only. Be forms water insoluble beryllium hydroxide $(Be(OH)_2)$ and $Mg$ also do the same. On heating, beryllium oxide becomes inert to heating due to an increase in the degree of polymerization. Beryllium hydroxide dissolves in sodium hydroxide solution to form sodium beryllate $(Na_2BeO_2)$ while $Mg$ cannot do so.
$Be(OH)_2+2NaOH\longrightarrow Na2BeO_2+H_2O$

Hence we can say the correct option is $D$.


Note: Properties of hydroxides of the given elements purely depends on their capability of making ions in water that ultimately is the result of their bonding strength with the Hydroxide ion so one can get an idea of solubility without knowing any fact of it simply by thinking about the attraction forces commanded by the elements in the options similar thing can be applied to the formation of oxides as given in the question.
The hydroxides include the natural alkalies of the research center and modern cycles. The hydroxides of the alkali metals, lithium, sodium, potassium, rubidium, and cesium, are the strongest bases and the most stable and most dissolvable of the hydroxides.