During the borax bead test with CuSO$$_4$$, a blue green colour of the bead was observed in oxidising flame due to the formation of

In the borax bead test, borax (Na$$_2$$B$$_4$$O$$_7$$ · 10H$$_2$$O) is heated and decomposes as follows:

$$\text{Na}_2\text{B}_4\text{O}_7 \xrightarrow{\Delta} 2\text{NaBO}_2 + \text{B}_2\text{O}_3$$

When CuSO$$_4$$ is used, in the oxidising flame, copper remains as Cu$$^{2+}$$ (in the form of CuO).

The boric anhydride (B$$_2$$O$$_3$$) reacts with the metal oxide:

$$\text{B}_2\text{O}_3 + \text{CuO} \to \text{Cu(BO}_2\text{)}_2$$

Copper metaborate, Cu(BO$$_2$$)$$_2$$, gives the characteristic blue-green colour to the bead in the oxidising flame.

The answer is Option C: Cu(BO$$_2$$)$$_2$$.