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(C) Molecules having an integer value for the degree of unsaturation $(DU)$ can exist in a free state as stable compounds.$DU = \frac{\sum n(v-2)}{2}

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$C_6H_{12}O$

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(C) Molecules having an integer value for the degree of unsaturation $(DU)$ can exist in a free state as stable compounds.$DU = \frac{\sum n(v-2)}{2} + 1$, where $n$ is the number of atoms and $v$ is the valency of the atom.For $C_7H_9O$: $DU = \frac{7(4-2) + 9(1-2) + 1(2-2)}{2} + 1 = \frac{14-9+0}{2} + 1 = 3.5$.For $C_8H_{12}O$: $DU = \frac{8(4-2) + 12(1-2) + 1(2-2)}{2} + 1 = \frac{16-12+0}{2} + 1 = 3.0$.For $C_6H_{12}O$: $DU = \frac{6(4-2) + 12(1-2) + 1(2-2)}{2} + 1 = \frac{12-12+0}{2} + 1 = 1.0$.For $C_{10}H_{17}O$: $DU = \frac{10(4-2) + 17(1-2) + 1(2-2)}{2} + 1 = \frac{20-17+0}{2} + 1 = 2.5$.Since $C_8H_{12}O$ and $C_6H_{12}O$ have integer values, $C_6H_{12}O$ is a stable compound.

Amongst the following, the one which can exist in free state as a stable compound is

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