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$\text{NaOH}$ is a strong base because:
(A) it gives $\text{O}{{\text{H}}^{-}}$ ion
(B) it can be oxidised
(C) it ionises completely
(D) both A and C

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Hint: Sodium hydroxide or caustic soda or $\text{NaOH}$ is a base. It is strong alkali having $\text{pH}$ value 12 and for concentrated solutions, the value is 13–14. Sodium metal belongs to alkali metal, so its hydroxide is basic. Strength means the extent of dissociation. Check the products of its dissociation.

Complete step by step answer:
One formula unit of sodium hydroxide or $\text{NaOH}$ contains one sodium cation and one hydroxide anion. Or, we can say that its one mole contains one mole of sodium cations and one mole of hydroxide anions. On dissociation it, gives $\text{NaOH}\to \text{N}{{\text{a}}^{+}}+\text{O}{{\text{H}}^{-}}$.
$\text{NaOH}$ is basic. Let us discuss that. There are three different concepts of acid and bases. One, Arrhenius, other is Bronsted-Lowry and Lewis theory. Let us discuss
S. No. Name of theoryDefinition of these theories and reason for its acidity and basicity
1.ARRHENIUS CONCEPTBases are species that contains hydroxyl $\left( \text{O}{{\text{H}}^{-}} \right)$ ions or produce $\text{O}{{\text{H}}^{-}}$ ions on ionization. $\text{NaOH}$ on its dissociation produces $\text{O}{{\text{H}}^{-}}$ ions . So, it is a base.
2.BRONSTED-LOWRY CONCEPTBases are species that have the ability to accept hydrogen ions $\left( {{\text{H}}^{+}} \right)$ . $\text{NaOH}$ reacts with strong acid $\text{HCl}$ to produce salt $\text{NaCl}$ and water. This is an example of a neutralisation reaction. So,$\text{NaOH}$ionises to form $\text{O}{{\text{H}}^{-}}$ ions which in turn will accept the ${{\text{H}}^{+}}$ ions coming from $\text{HCl}$, forming out water $\left( {{\text{H}}_{2}}\text{O} \right)$.


The correct answer to this question is option (D), both A and C.

Additional information:
Application of sodium hydroxide:
(1) Sodium hydroxide is extensively used in the paper industry.
(2) It is used in the Bayer process of aluminium production.

Note: The answer to this question can be interpreted practically. Caustic soda solution is basic, so can be identified through the litmus test. Red litmus will convert to a blue colour when it comes in contact with the base solution. So, $\text{NaOH}$ is a base.