The correct order of polarizing power is
$
  (a){\text{ }}B{e^{ + 2}} > M{g^{ + 2}} > C{a^{ + 2}} > {K^ + } \\
  (b){\text{ }}B{e^{ + 2}} > C{a^{ + 2}} > M{g^{ + 2}} > {K^ + } \\
  (c){\text{ M}}{{\text{g}}^{ + 2}} > C{a^{ + 2}} > B{e^{ + 2}} > {K^ + } \\
  (d){\text{ M}}{{\text{g}}^{ + 2}} > B{e^{ + 2}} > C{a^{ + 2}} > {K^ + } \\
 $

Hint – In this question use the Fajan’s rule, to figure out the correct order of polarization. Since all the options are dealing with cations only thus first figure out the correct order of the size of cations. The polarizing power will eventually be the reverse of this series formed.

Complete answer:
According to Fajans’ rule polarizing power will be increased by:
$\left( 1 \right)$ High charge and small size of the cation.
$\left( 2 \right)$ High charge and large size of the anion.
Now in the given elements all are cations so the decreasing order of polarizing power is increasing order of the size (atomic radius) of the elements and decreasing order of the charge.
Now as we know k belongs to the first group in a periodic table and Be, Mg and Ca belong to the second group.
Now as we know that when we move from left to right in the period the size of the atom decreases and when we move from top to bottom in the group the size of the atom increases.
So the increasing order of the size of the elements are
$Be < Mg < Ca < k$
And the decreasing order of the charge (as charge is +1 for 1st group and +2 for 2nd group).
$Be = Mg = Ca > K$
So the decreasing order of the polarizing power according to above information is
$B{e^{ + 2}} > M{g^{ + 2}} > C{a^{ + 2}} > {K^ + }$
So this is the required answer.
Hence option (A) is the correct answer.

Note – Polarization has different definitions with respect to cation and anion. The ability of cation to distort an anion is called as the polarization power of cation whereas the tendency of the anion to become polarized by the cation is known as its polarizability moreover, polarizing power can be defined as the ability of the cation to attract electron cloud towards itself. Since the smaller size of cation leads to greater density of charge thus it will eventually be able to attract larger electron clouds towards itself.