Chemical $A$ is used for water softening to remove temporary hardness. $A$ reacts with $Na_2CO_3$ to generate caustic soda. When $CO_2$ is bubbled through $A$,it turns cloudy. What is the chemical formula of $A$?

The carbonates of alkaline earth metals decompose on heating to give:
$I$. $CO_2$
$II$. Metal oxide
$III$. $H_2 O$
$IV$. $CO$

Match the compounds in List-$I$ with their chemical formulas in List-$II$ and select the correct answer using the codes given below:
List-$I$ (Compounds) | List-$II$ (Formulas)
$(A)$ Plaster of Paris | $(i) \, CaSO_4 \cdot 2H_2O$
$(B)$ Epsomite | $(ii) \, CaSO_4 \cdot \frac{1}{2} H_2O$
$(C)$ Kieserite | $(iii) \, MgSO_4 \cdot 7H_2O$
$(D)$ Gypsum | $(iv) \, MgSO_4 \cdot H_2O$

Which of the following statements is incorrect?

Which of the following is an amphoteric hydroxide?

Discuss the general characteristics and gradation in properties of alkaline earth metals.