The order of increasing ionic radius of the following is:

The given options are:
a) K Li Mg2 Al3
b) K Mg2 Li Al3
c) Li K Mg2 Al3
d) Al3 Mg2 Li K

To determine the order of increasing ionic radius, we need to consider the charge on the ions and the position of the elements in the periodic table.

Charge on the ions:
- The charge on potassium (K) is +1.
- The charge on lithium (Li) is +1.
- The charge on magnesium (Mg2+) is +2.
- The charge on aluminum (Al3+) is +3.

Position in the periodic table:
- Potassium (K) is in Group 1 (alkali metals).
- Lithium (Li) is in Group 1 (alkali metals).
- Magnesium (Mg) is in Group 2 (alkaline earth metals).
- Aluminum (Al) is in Group 13 (boron group).

Explanation:
Ionic radius generally increases as we move down a group and decreases as we move across a period from left to right.

In option a) K Li Mg2 Al3, potassium (K) and lithium (Li) are both alkali metals in Group 1. As we move down Group 1, the ionic radius increases. Therefore, the ionic radius of K is larger than Li. However, magnesium (Mg2+) and aluminum (Al3+) have higher charges, which result in a smaller ionic radius compared to potassium and lithium. Therefore, the order of increasing ionic radius for option a) is K < li="" />< mg2+="" />< />

In option b) K Mg2 Li Al3, magnesium (Mg2+) has a higher charge than potassium (K), resulting in a smaller ionic radius for Mg2+ compared to K. Therefore, the order of increasing ionic radius for option b) is K < mg2+="" />< li="" />< />

In option c) Li K Mg2 Al3, the same reasoning as option a) applies. Potassium (K) has a larger ionic radius compared to lithium (Li), and magnesium (Mg2+) and aluminum (Al3+) have smaller ionic radii due to their higher charges. Therefore, the order of increasing ionic radius for option c) is Li < k="" />< mg2+="" />< />

In option d) Al3 Mg2 Li K, aluminum (Al3+) has the highest charge among the given elements, resulting in the smallest ionic radius. Magnesium (Mg2+) has a smaller ionic radius compared to lithium (Li) and potassium (K). Therefore, the order of increasing ionic radius for option d) is Al3+ < mg2+="" />< li="" />< />

Therefore, the correct answer is option d) Al3 Mg2 Li K, as it represents the correct order of increasing ionic radius.