The set that contains atomic numbers of only transition elements, is:

For any element to be called a transition element, it must belong to the d-block of the periodic table. In precise terms, a transition element is one whose atom in the ground state or in any of its common oxidation states possesses an incompletely filled $$ (n-1)d $$ subshell. Thus the elements of groups $$3$$ to $$12$$—with atomic numbers from $$21$$ to $$30$$, $$39$$ to $$48$$ and $$57$$/$$72$$ to $$80$$ (excluding the atypical fully-d10 pair Zn, Cd, Hg)—qualify as transition elements. We now examine each option one by one, checking every atomic number against this definition.

Option A: The set is $$\{37,\;42,\;50,\;64\}$$. We have $$37$$ (Rb, an alkali metal, s-block), $$42$$ (Mo, group 6 d-block, transition), $$50$$ (Sn, p-block), and $$64$$ (Gd, a lanthanide, f-block). Because three of the four members lie outside the d-block, this set does not consist solely of transition elements.

Option B: The set is $$\{21,\;25,\;42,\;72\}$$. Checking each member:

$$21 \rightarrow \text{Sc}$$ lies in group 3 and clearly has the configuration $$[Ar]\;3d^{1}4s^{2}$$ with an incompletely filled $$3d$$ subshell, so it is a transition element.

$$25 \rightarrow \text{Mn}$$ lies in group 7 with configuration $$[Ar]\;3d^{5}4s^{2}$$—again a typical d-block, hence a transition element.

$$42 \rightarrow \text{Mo}$$ lies in group 6; its configuration $$[Kr]\;4d^{5}5s^{1}$$ shows an incomplete $$4d$$ subshell, so it is a transition element.

$$72 \rightarrow \text{Hf}$$ lies just below Zr in group 4 with configuration $$[Xe]\;4f^{14}5d^{2}6s^{2}$$, possessing two electrons in $$5d$$. Therefore, it is also a transition element.

Since every atomic number in this option corresponds to a d-block element meeting the definition, Option B indeed contains only transition elements.

Option C: $$\{9,\;17,\;34,\;38\}$$ includes F, Cl, Se, and Sr—respectively p-block, p-block, p-block, and s-block—hence fails the criterion.

Option D: $$\{21,\;32,\;53,\;64\}$$ has Sc (transition), but Ge, I, and Gd are p-block or f-block, so the set is mixed and therefore unsuitable.

On comparing all four sets, only the second set meets the requirement completely.

Hence, the correct answer is Option 2.