A basic oxide will be formed by the element:
(A) K
(B) S
(C) P
(D) Kr

Hint: It is empirical to know that the basic oxides are formed by metals i.e. metallic oxides are basic in nature.
The metal element from all of the given choices will be forming a basic oxide.

Complete step by step answer:
Let us study in brief about the oxides;
Oxides-
These are the compounds with one or more oxygen atoms chemically bonded with another element. They are mostly binary in nature and are called oxides as they have a combination of oxygen with another element.
Facts-
-The oxide combining with water to give an acid is known as acidic oxide.
-The oxide that results in a base in water is known as basic oxide.
-It is possible that an oxide can neither be acidic nor basic thus, neutral in nature.
Now,
Acidic oxides-
These are the oxides of non-metals. They are also known as acid anhydrides which on reaction with water produce an acid. Similarly, when they combine with bases, they produce salts.
Basic oxides-
These are the oxides of metals. They are also known as base anhydrides and generally originated from group 1 and group 2 elements of the modern periodic table.
If they are soluble in water, they produce hydroxides. Also, they react with acids to produce salts.
Thus, from above explanation and facts we can say that potassium is the only element (metal) from all the given option which can form basic oxide i.e. ${{K}_{2}}O$ .

Therefore, option (A) is correct.

Note: Do note that $K{{O}_{2}}$ is a superoxide formed when potassium reacts with oxygen as,
${{K}_{\left( s \right)}}+{{O}_{2\left( g \right)}}\to K{{O}_{2\left( s \right)}}$
Sometimes $K{{O}_{2}}$ can also be referred to as ${{K}_{2}}O$ which is also potassium oxide. Both are correct so, do not get confused here.